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Mathematics Through Aboriginal Storytelling

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Math Catcher | Mathematics through Aboriginal Storytelling

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For today's learners: We present the Math Catcher Outreach Program in the classroom to encourage elementary and high school students to recognize how math is used in everyday life and how it forms the basis for many of our daily decisions and life-long choices.

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Pop question - no Googling: How many of Japan's Nobel laureates were awarded medals for their work in physics?

The answer: 10, or nearly half of the total. You could deduce from this that Japan is good at physics. Furthermore, you could deduce that Japan is good at math, which is, arguably, the bedrock of physics. And math is something Japan does very well.

If you wanted to create an arbitrary division of nations, you could start with division - long division and short division, and multiplication. And fractions, algebra and geometry: some of the stuff that = math. At the top of the pile would be a cluster of East Asian nations, such as Singapore, South Korea and Japan - countries that repeatedly score high in international rankings. Meanwhile, at the bottom of the class lie Israel, Hungary and, notably, the United States. As much as math itself is a puzzle, so too is the reason behind why Japan, along with other Asian countries, continually outperforms countries in the West in math.

Since 2000 the OECD club of developed nations has been tracking and testing 15-year-olds in dozens of countries in math, reading and science every three years in what are known as the PISA (Programme for International Student Assessment) tests. Japan has never dropped out of the top 10 in math. In the last round of tests, administered in 2012, Japan was placed second in mathematic performance and first in both reading and science amongst the OECD countries.

This summer, American journalist Elizabeth Green wrote an essay for The New York Times Magazine titled "Why do Americans stink at math?" It could just as easily have been headlined "What can Japan teach America about teaching math?" since much of the article was given over to the experiences of a Japanese math teacher, Akihiko Takahashi, who trained and taught in Tokyo before moving to Chicago in the 1990s, ostensibly to continue teaching math. His other motive was to continue his research into the pioneering work of a group of math educators in America he had first encountered as a novice teacher in Japan.

Green's essay was a primer for her book "Building a Better Teacher," published in August. In the book, Green outlines how after transitioning to America, Takahashi was alarmed to observe that students on the whole were being subjected to a stifling form of math that most readers will probably be familiar with: "I, We, You," a ritualistic series of steps in which the teacher dictates a problem to the students, the class works together on similar problems, and finally the students work through more of the same problems. Japan, Green says, had traded "I, We, You" for "You, Y'all, We," in which the process is altered: Students begin with solving a specific problem, then work in peer groups and finally altogether.

The other idea Green hit upon in her explanation of why math teaching in Japan may be more effective is jugyōkenkyū, in which teachers are routinely observed in order to help hone their craft. Observation lessons are standard practice in schools in Japan; however, this is not universally the case elsewhere, where teachers tend to view the classroom as their domain, off limits to prying eyes.

The focus of Green's book is American education policy and practice, and while it explains some of the differences in teaching between Japan and the U.S., superficially and otherwise, it still does not get to the root of why, on the whole, Japan excels at math. Is it the teaching methodology that differs or the attitude to learning? Or is it how much is spent - in time and money - on education, publicly and privately?

To find out, I went back to class. First, I brushed up on statistics.

Students in Japan spend nearly 235 minutes a week learning math, according to Miki Tadakazu, an education analyst with the OECD, only about 20 minutes more than the OECD average.

In PISA's 2012 questionnaire, Japanese 15-year-olds reported spending an average of just over half an hour a week in a commercial after-school learning environment - read juku - which is in line with the OECD average. In fact, the Japanese polled came in below the OECD average in time spent on all other forms of after-school work, whether it was teacher-set homework or study assisted by a home tutor, family member or computer.

And one more statistic before class finishes: Japan spends less on education than most OECD countries, allocating it less than 4 percent of its GDP. So, if quantity is not the key to Japan's math success, could it be quality?

In researching this article, I attended a mixture of private and public schools - a private elementary school and three public junior high schools - to observe math classes and interview math teachers.

While waiting in the cafeteria of Ritsumeikan Primary School in Kyoto, third-graders were busy wiping down the tables. A few students pushed their cloths towards me, more in curiosity than in an effort to clean. I asked one boy, in English, what his favorite subject was.

"Math," he replied immediately.

I wanted to laugh: Was this an omen or was he a plant? But 50 minutes later, I could see why.

All the classrooms at Ritsumeikan Primary School are open; the wall where the door should be is missing, so if one class was to erupt in noise, it would cause a disturbance in all classes. At Oike Junior High School, a public school in downtown Kyoto, it was slightly similar: All teachers kept their doors open during their lessons. The idea, I think, is to magnify disturbances, or "acting up" as it was called in my time, but at both schools the only noise came in the form of excitement - excitement for math.

At Ritsumeikan, Kunito Ito, a pleasant coach-like teacher, started his class with the customary aisatsu (greetings) and followed this with a problem he had put up on the board - that day they were tackling solving equations with multiple fractions - instructing his fifth-graders to tackle it. So far, so predictable.

But then it got interesting. The first student to finish shot a hand up. Ito walked over, glanced at the problem and circled it, to signal it was correct. The student was then up and out of his seat.

Another hand shot up. But this time the first student had taken the role of teacher, or corrector. Ito was made redundant from the get-go as students darted around the class, checking and aiding their peers.

Throughout the 50-minute class, Ito subverted the "I, You, We" ritual. Students were called on to work in groups, individually, to stand up and present their answers at their desk and to come to the board and present their answers. He particularly enjoyed it when students arrived at different answers, or different routes to the same answer. As a class, they discussed how they arrived at the same answer through disparate routes.

Looking back on my own math education, we rarely, if ever, treated math as a discursive subject; but both at Ritsumeikan Primary and Oike Junior High, the teachers had students routinely work in pairs or bigger groups and talk about the problems. It seems so obvious in hindsight: Math is also a type of language, so why wouldn't you discuss it like we do English, Japanese or social studies?

After the class, Ito told me: "If you teach what you learn, you will remember about 90 percent. If I stand at the board and just lecture, through listening to the teacher the students will retain far less - say, 40 percent - so it's far more effective to have them discussing problems and teaching each other. Also, it's important that there is very little downtime or rest time. You need to keep motivating them."

These sentiments were echoed at Oike Junior High School. Tanaka-sensei's third-grade class began with a group presentation using the electronic whiteboard. The four boys had two minutes to summarize and present the findings from the previous class, using a case example.

"It's hard for them," Tanaka said afterwards, "as they only started doing this in September of last year."

His class of around 20 students was more or less identical to Ito's: a continual mix of group problem-solving, discussions and presentations (although granted, the primary-schoolers were a little more enthusiastic).

"If it's only me up there teaching in front of the class, I'm not helping students to get high scores in PISA tests," Tanaka said. "But if you think about how to get students to think by themselves, you need to do a lot of research for this."

Jugyōkenkyū can help, especially with novice teachers. However, from my interviews with math teachers, personal research seemed more important and effective.

"In a way, jugyōkenkyū is important," conceded Shingo Fujinawa, a Kyoto University graduate and math teacher at Ibaraki Nishi High School. "It was a good opportunity to be inspired and recognize my teaching skill at that time. But I felt as if it had been a kind of ritual for a beginner teacher.

"Personally, my present teaching skill comes from my everyday experiences with my students as well as other media such as books, TV, which are much better than two observation classes in themselves."

Other teachers told me of how they tried to stay abreast of new and different ways of teaching using teaching books and DVDs, as well as attending seminars and through informal discussions with colleagues. Investing so much personal time in your occupation is not unusual in Japan, where teachers often have an outsized role in addition to that of teacher: as counselor, surrogate parent.

"Japanese teachers work very hard for their students," Tadakazu from the OECD told me via email. "They spend lots of their own time engaged in extracurricular activities. Teachers in Japan play a wider variety of roles for students than other countries' teachers, whose main task is limited within their lessons. This perspective may support the fact that the dropout rate of Japanese students are very low."

Of course, the elephant in the room is juku. In each interview, I asked teachers if they thought there was a link between Japan's high standings in PISA and the fact that so many of their students attend juku. Even at a fee-paying school such as Ritsumeikan, where annual tuition costs are over ¥1 million, more than 50 percent of students attend juku. This figure can peak at as high as 90 percent in schools across the country in the final year of junior high and senior high, as students cram for entrance tests to get into high school and university.

Generally teachers are receptive of jukus and saw the complimentary role they play, especially in getting students past those all-important tests. It's also worth remembering that a lot of teachers went to juku themselves and quite possibly taught there during university.

"Juku fills a role in preparing students for passing exams. However, school teaches you more than one answer and it allows for more creativity. Juku will show you the answer and the most efficient way to get it," Ito said.

The fact that the math teachers I observed could spend so much time teaching instead of attending to matters of discipline may also impact on student ability and scores. Add to that teachers who have an active interest in their subject and their students, and this may go some way toward a theory of why Japan does math so well.
Learning Curve covers issues related to education in Japan. Your comments and story ideas: community@japantimes.co.jp

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Teaching quality, not lesson quantity, may be key to Japan's top math marks | The Japan Times

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Pop question - no Googling: How many of Japan's Nobel laureates were awarded medals for their work in physics? The answer: 10, or nearly half of the total. You could deduce from this that Japan is good at physics. Furthermore, you could deduce that Japan is good at math, which is, arguably, the bedrock of physics.

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A blog post from the FEDCAN blog. (For teachers)

This resource guide (*contains lesson plans*), for Grades 8 & 9, intends to help teachers incorporate new approaches in Mathematics that are more reflective of the realities of First Peoples in the province of British Columbia. These resources are intended to help all students appreciate mathematics within all human cultures and activities, give all students a better undersatnding of First Peoples within historical and contemporary contexts, as well as help Aboriginal students feel more comfortable in mathematics learning situations.

From the website: "This document was created by the First Nations Education Steering Committee and the First Nations Schools Association with the support of the BC Ministry of Education and the Education Partnerships Program of Aboriginal Affairs and Northern Development Canada."

A collection of math lesson plans from OISE Centre for Urban Studies that embed social justice issues regarding First Nations. (Grade 6; Level Junior)

From the website: "With this website, we have two purposes

1. to provide some meaningful and engaging contexts to enrich the classroom experiences that students may have with respect to mathematics, and

2. to support the building of cultural awareness and understanding by highlighting social games within the First Nations' cultures." (Grade 4 and up; Level Junior/ Intermediate/ Senior)

by Running-Horse Livingston

From the website: "Wigwametry focuses on teaching geometry through the scale-model construction of a traditional Native American structure. The goal for this workshop is to prepare teachers to help students understand the mathematical, historical and social importance of the wigwam structure in Northern Woodland cultures. Participants will learn how to help students construct a scale model of the traditional home using geometric properties of circles and spheres." (For teachers)

From the website: "The main purpose of the short films, which are 3-4 minutes in length, is to relate stories about the adventures of animated characters. The scenarios take place in Aboriginal cultural and physical environments. The resolution of a particular plot always requires some mathematical knowledge. Plots in our stories are a mixture of adventures and math puzzles with the aim of catching a viewer's attention and interest (thus the title of our project). Each story closes with an open-ended question that should spark discussions and lead to further activities. The question at the end of each story is purposefully not answered in the story." (Level Junior/ Intermediate)

(Grades K-4) Subject Strands: Language Arts, Social Studies, Visual Arts, Math.

From the lesson: "Using oral legends as told by Haida elders (produced by CBC Radio), we are developing mathematics lessons for us in Kindergarten-grade 12 classrooms."

From the lesson: "We engage Aboriginal learners in math and science through the use of First Nations imagery and storytelling."

From the video: "Deborah Sparrow of Musqueam First Nation demonstrates how blanket weaving can be used to teach students about science, history, geography, and math in a cross-curricular manner."

From the video: "Dr. Nathalie Sinclair (Simon Fraser University) learning about the Ojibwe number systems with Jason Jones (Native Language Curriculum Coordinator, Rainy River District School Board)."

Aboriginal games organized by mathematical content (Grade 4 and up)

Includes descriptions of a variety of Aboriginal games that promote mathematical problem-solving and games of chance, strategy and lifestyle. (Grade 4 and up)

Learn about this Mi'kmaq game which includes both math and chance, and play it vs. the computer on this CBC website!

*Contains lesson plans.*

From the website: "With Birch Bark biting being a nearly lost art form, along with the Aboriginal cultural connections, learning about how to create Birch Bark bitings and the mathematical, scientific, social and artistic aspects behind these artworks may be very interesting and relevant to the students in your classroom. By addressing the essential questions throughout the subjects, your students will be able to have a better understanding of the Mi'kmaw culture as well as the different cultural understandings and approaches to Science, Art and Mathematics."

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DEEPENINGKNOWLEDGE :: Math :: Deepening Knowledge: Aboriginal Peoples Curriculum Database

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A blog post from the FEDCAN blog. (For teachers) This resource guide (*contains lesson plans*), for Grades 8 & 9, intends to help teachers incorporate new approaches in Mathematics that are more reflective of the realities of First Peoples in the province of British Columbia.

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Top Rated Educational Math Books for Children (134 books)

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134 books based on 107 votes: Math Curse by Jon Scieszka, How Much Is a Million? by David M. Schwartz, Sir Cumference and the First Round Table: A Math A…

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How you can be good at math, and other surprising facts about learning | Jo Boaler | TEDxStanford

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What do we make of a boy like Thomas?

Thomas (his middle name) is a fifth-grader at the highly competitive P.S. 334, the Anderson School on West 84th. Slim as they get, Thomas recently had his long sandy-blond hair cut short to look like the new James Bond (he took a photo of Daniel Craig to the barber). Unlike Bond, he prefers a uniform of cargo pants and a T-shirt emblazoned with a photo of one of his heroes: Frank Zappa. Thomas hangs out with five friends from the Anderson School. They are "the smart kids." Thomas's one of them, and he likes belonging.

Since Thomas could walk, he has heard constantly that he's smart. Not just from his parents but from any adult who has come in contact with this precocious child. When he applied to Anderson for kindergarten, his intelligence was statistically confirmed. The school is reserved for the top one percent of all applicants, and an IQ test is required. Thomas didn't just score in the top one percent. He scored in the top one percent of the top one percent.

But as Thomas has progressed through school, this self-awareness that he's smart hasn't always translated into fearless confidence when attacking his schoolwork. In fact, Thomas's father noticed just the opposite. "Thomas didn't want to try things he wouldn't be successful at," his father says. "Some things came very quickly to him, but when they didn't, he gave up almost immediately, concluding, 'I'm not good at this.' " With no more than a glance, Thomas was dividing the world into two-things he was naturally good at and things he wasn't.

For instance, in the early grades, Thomas wasn't very good at spelling, so he simply demurred from spelling out loud. When Thomas took his first look at fractions, he balked. The biggest hurdle came in third grade. He was supposed to learn cursive penmanship, but he wouldn't even try for weeks. By then, his teacher was demanding homework be completed in cursive. Rather than play catch-up on his penmanship, Thomas refused outright. Thomas's father tried to reason with him. "Look, just because you're smart doesn't mean you don't have to put out some effort." (Eventually, he mastered cursive, but not without a lot of cajoling from his father.)

Why does this child, who is measurably at the very top of the charts, lack confidence about his ability to tackle routine school challenges?

Thomas is not alone. For a few decades, it's been noted that a large percentage of all gifted students (those who score in the top 10 percent on aptitude tests) severely underestimate their own abilities. Those afflicted with this lack of perceived competence adopt lower standards for success and expect less of themselves. They underrate the importance of effort, and they overrate how much help they need from a parent.

When parents praise their children's intelligence, they believe they are providing the solution to this problem. According to a survey conducted by Columbia University, 85 percent of American parents think it's important to tell their kids that they're smart. In and around the New York area, according to my own (admittedly nonscientific) poll, the number is more like 100 percent. Everyone does it, habitually. The constant praise is meant to be an angel on the shoulder, ensuring that children do not sell their talents short.

But a growing body of research-and a new study from the trenches of the New York public-school system-strongly suggests it might be the other way around. Giving kids the label of "smart" does not prevent them from underperforming. It might actually be causing it.

For the past ten years, psychologist Carol Dweck and her team at Columbia (she's now at Stanford) studied the effect of praise on students in a dozen New York schools. Her seminal work-a series of experiments on 400 fifth-graders-paints the picture most clearly.

Dweck sent four female research assistants into New York fifth-grade classrooms. The researchers would take a single child out of the classroom for a nonverbal IQ test consisting of a series of puzzles-puzzles easy enough that all the children would do fairly well. Once the child finished the test, the researchers told each student his score, then gave him a single line of praise. Randomly divided into groups, some were praised for their intelligence. They were told, "You must be smart at this." Other students were praised for their effort: "You must have worked really hard."

Why just a single line of praise? "We wanted to see how sensitive children were," Dweck explained. "We had a hunch that one line might be enough to see an effect."

Then the students were given a choice of test for the second round. One choice was a test that would be more difficult than the first, but the researchers told the kids that they'd learn a lot from attempting the puzzles. The other choice, Dweck's team explained, was an easy test, just like the first. Of those praised for their effort, 90 percent chose the harder set of puzzles. Of those praised for their intelligence, a majority chose the easy test. The "smart" kids took the cop-out.

Why did this happen? "When we praise children for their intelligence," Dweck wrote in her study summary, "we tell them that this is the name of the game: Look smart, don't risk making mistakes." And that's what the fifth-graders had done: They'd chosen to look smart and avoid the risk of being embarrassed.

In a subsequent round, none of the fifth-graders had a choice. The test was difficult, designed for kids two years ahead of their grade level. Predictably, everyone failed. But again, the two groups of children, divided at random at the study's start, responded differently. Those praised for their effort on the first test assumed they simply hadn't focused hard enough on this test. "They got very involved, willing to try every solution to the puzzles," Dweck recalled. "Many of them remarked, unprovoked, 'This is my favorite test.' " Not so for those praised for their smarts. They assumed their failure was evidence that they weren't really smart at all. "Just watching them, you could see the strain. They were sweating and miserable."

Having artificially induced a round of failure, Dweck's researchers then gave all the fifth-graders a final round of tests that were engineered to be as easy as the first round. Those who had been praised for their effort significantly improved on their first score-by about 30 percent. Those who'd been told they were smart did worse than they had at the very beginning-by about 20 percent.

Dweck had suspected that praise could backfire, but even she was surprised by the magnitude of the effect. "Emphasizing effort gives a child a variable that they can control," she explains. "They come to see themselves as in control of their success. Emphasizing natural intelligence takes it out of the child's control, and it provides no good recipe for responding to a failure."

In follow-up interviews, Dweck discovered that those who think that innate intelligence is the key to success begin to discount the importance of effort. I am smart, the kids' reasoning goes; I don't need to put out effort. Expending effort becomes stigmatized-it's public proof that you can't cut it on your natural gifts.

Repeating her experiments, Dweck found this effect of praise on performance held true for students of every socioeconomic class. It hit both boys and girls-the very brightest girls especially (they collapsed the most following failure). Even preschoolers weren't immune to the inverse power of praise.

Jill Abraham is a mother of three in Scarsdale, and her view is typical of those in my straw poll. I told her about Dweck's research on praise, and she flatly wasn't interested in brief tests without long-term follow-up. Abraham is one of the 85 percent who think praising her children's intelligence is important. Her kids are thriving, so she's proved that praise works in the real world. "I don't care what the experts say," Jill says defiantly. "I'm living it."

Even those who've accepted the new research on praise have trouble putting it into practice. Sue Needleman is both a mother of two and an elementary-school teacher with eleven years' experience. Last year, she was a fourth-grade teacher at Ridge Ranch Elementary in Paramus, New Jersey. She has never heard of Carol Dweck, but the gist of Dweck's research has trickled down to her school, and Needleman has learned to say, "I like how you keep trying." She tries to keep her praise specific, rather than general, so that a child knows exactly what she did to earn the praise (and thus can get more). She will occasionally tell a child, "You're good at math," but she'll never tell a child he's bad at math.

But that's at school, as a teacher. At home, old habits die hard. Her 8-year-old daughter and her 5-year-old son are indeed smart, and sometimes she hears herself saying, "You're great. You did it. You're smart." When I press her on this, Needleman says that what comes out of academia often feels artificial. "When I read the mock dialogues, my first thought is, Oh, please. How corny. "

No such qualms exist for teachers at the Life Sciences Secondary School in East Harlem, because they've seen Dweck's theories applied to their junior-high students. Last week, Dweck and her protégée, Lisa Blackwell, published a report in the academic journal Child Development about the effect of a semester-long intervention conducted to improve students' math scores.

Life Sciences is a health-science magnet school with high aspirations but 700 students whose main attributes are being predominantly minority and low achieving. Blackwell split her kids into two groups for an eight-session workshop. The control group was taught study skills, and the others got study skills and a special module on how intelligence is not innate. These students took turns reading aloud an essay on how the brain grows new neurons when challenged. They saw slides of the brain and acted out skits. "Even as I was teaching these ideas," Blackwell noted, "I would hear the students joking, calling one another 'dummy' or 'stupid.' " After the module was concluded, Blackwell tracked her students' grades to see if it had any effect.

It didn't take long. The teachers-who hadn't known which students had been assigned to which workshop-could pick out the students who had been taught that intelligence can be developed. They improved their study habits and grades. In a single semester, Blackwell reversed the students' longtime trend of decreasing math grades.

The only difference between the control group and the test group were two lessons, a total of 50 minutes spent teaching not math but a single idea: that the brain is a muscle. Giving it a harder workout makes you smarter. That alone improved their math scores.

"These are very persuasive findings," says Columbia's Dr. Geraldine Downey, a specialist in children's sensitivity to rejection. "They show how you can take a specific theory and develop a curriculum that works." Downey's comment is typical of what other scholars in the field are saying. Dr. Mahzarin Banaji, a Harvard social psychologist who is an expert in stereotyping, told me, "Carol Dweck is a flat-out genius. I hope the work is taken seriously. It scares people when they see these results."

Since the 1969 publication of The Psychology of Self-Esteem, in which Nathaniel Branden opined that self-esteem was the single most important facet of a person, the belief that one must do whatever he can to achieve positive self-esteem has become a movement with broad societal effects. Anything potentially damaging to kids' self-esteem was axed. Competitions were frowned upon. Soccer coaches stopped counting goals and handed out trophies to everyone. Teachers threw out their red pencils. Criticism was replaced with ubiquitous, even undeserved, praise.

Dweck and Blackwell's work is part of a larger academic challenge to one of the self-esteem movement's key tenets: that praise, self-esteem, and performance rise and fall together. From 1970 to 2000, there were over 15,000 scholarly articles written on self-esteem and its relationship to everything-from sex to career advancement. But results were often contradictory or inconclusive. So in 2003 the Association for Psychological Science asked Dr. Roy Baumeister, then a leading proponent of self-esteem, to review this literature. His team concluded that self-esteem was polluted with flawed science. Only 200 of those 15,000 studies met their rigorous standards.

I am smart, the kids' reasoning goes; I don't need to put out effort. Expending effort becomes stigmatized-it's public proof that you can't cut it on your natural gifts.

After reviewing those 200 studies, Baumeister concluded that having high self-esteem didn't improve grades or career achievement. It didn't even reduce alcohol usage. And it especially did not lower violence of any sort. (Highly aggressive, violent people happen to think very highly of themselves, debunking the theory that people are aggressive to make up for low self-esteem.) At the time, Baumeister was quoted as saying that his findings were "the biggest disappointment of my career."

Now he's on Dweck's side of the argument, and his work is going in a similar direction: He will soon publish an article showing that for college students on the verge of failing in class, esteem-building praise causes their grades to sink further. Baumeister has come to believe the continued appeal of self-esteem is largely tied to parents' pride in their children's achievements: It's so strong that "when they praise their kids, it's not that far from praising themselves."

By and large, the literature on praise shows that it can be effective-a positive, motivating force. In one study, University of Notre Dame researchers tested praise's efficacy on a losing college hockey team. The experiment worked: The team got into the playoffs. But all praise is not equal-and, as Dweck demonstrated, the effects of praise can vary significantly depending on the praise given. To be effective, researchers have found, praise needs to be specific. (The hockey players were specifically complimented on the number of times they checked an opponent.)

Sincerity of praise is also crucial. Just as we can sniff out the true meaning of a backhanded compliment or a disingenuous apology, children, too, scrutinize praise for hidden agendas. Only young children-under the age of 7-take praise at face value: Older children are just as suspicious of it as adults.

Psychologist Wulf-Uwe Meyer, a pioneer in the field, conducted a series of studies where children watched other students receive praise. According to Meyer's findings, by the age of 12, children believe that earning praise from a teacher is not a sign you did well-it's actually a sign you lack ability and the teacher thinks you need extra encouragement. And teens, Meyer found, discounted praise to such an extent that they believed it's a teacher's criticism-not praise at all-that really conveys a positive belief in a student's aptitude.

In the opinion of cognitive scientist Daniel T. Willingham, a teacher who praises a child may be unwittingly sending the message that the student reached the limit of his innate ability, while a teacher who criticizes a pupil conveys the message that he can improve his performance even further.

New York University professor of psychiatry Judith Brook explains that the issue for parents is one of credibility. "Praise is important, but not vacuous praise," she says. "It has to be based on a real thing-some skill or talent they have." Once children hear praise they interpret as meritless, they discount not just the insincere praise, but sincere praise as well.

Scholars from Reed College and Stanford reviewed over 150 praise studies. Their meta-analysis determined that praised students become risk-averse and lack perceived autonomy. The scholars found consistent correlations between a liberal use of praise and students' "shorter task persistence, more eye-checking with the teacher, and inflected speech such that answers have the intonation of questions."

Dweck's research on overpraised kids strongly suggests that image maintenance becomes their primary concern-they are more competitive and more interested in tearing others down. A raft of very alarming studies illustrate this.

In one, students are given two puzzle tests. Between the first and the second, they are offered a choice between learning a new puzzle strategy for the second test or finding out how they did compared with other students on the first test: They have only enough time to do one or the other. Students praised for intelligence choose to find out their class rank, rather than use the time to prepare.

In another, students get a do-it-yourself report card and are told these forms will be mailed to students at another school-they'll never meet these students and don't know their names. Of the kids praised for their intelligence, 40 percent lie, inflating their scores. Of the kids praised for effort, few lie.

When students transition into junior high, some who'd done well in elementary school inevitably struggle in the larger and more demanding environment. Those who equated their earlier success with their innate ability surmise they've been dumb all along. Their grades never recover because the likely key to their recovery-increasing effort-they view as just further proof of their failure. In interviews many confess they would "seriously consider cheating."

Students turn to cheating because they haven't developed a strategy for handling failure. The problem is compounded when a parent ignores a child's failures and insists he'll do better next time. Michigan scholar Jennifer Crocker studies this exact scenario and explains that the child may come to believe failure is something so terrible, the family can't acknowledge its existence. A child deprived of the opportunity to discuss mistakes can't learn from them.

My son, Luke, is in kindergarten. He seems supersensitive to the potential judgment of his peers. Luke justifies it by saying, "I'm shy," but he's not really shy. He has no fear of strange cities or talking to strangers, and at his school, he has sung in front of large audiences. Rather, I'd say he's proud and self-conscious. His school has simple uniforms (navy T-shirt, navy pants), and he loves that his choice of clothes can't be ridiculed, "because then they'd be teasing themselves too."

After reading Carol Dweck's research, I began to alter how I praised him, but not completely. I suppose my hesitation was that the mind-set Dweck wants students to have-a firm belief that the way to bounce back from failure is to work harder-sounds awfully clichéd: Try, try again.

But it turns out that the ability to repeatedly respond to failure by exerting more effort-instead of simply giving up-is a trait well studied in psychology. People with this trait, persistence, rebound well and can sustain their motivation through long periods of delayed gratification. Delving into this research, I learned that persistence turns out to be more than a conscious act of will; it's also an unconscious response, governed by a circuit in the brain. Dr. Robert Cloninger at Washington University in St. Louis located the circuit in a part of the brain called the orbital and medial prefrontal cortex. It monitors the reward center of the brain, and like a switch, it intervenes when there's a lack of immediate reward. When it switches on, it's telling the rest of the brain, "Don't stop trying. There's dopa [the brain's chemical reward for success] on the horizon." While putting people through MRI scans, Cloninger could see this switch lighting up regularly in some. In others, barely at all.

What makes some people wired to have an active circuit?

Cloninger has trained rats and mice in mazes to have persistence by carefully not rewarding them when they get to the finish. "The key is intermittent reinforcement," says Cloninger. The brain has to learn that frustrating spells can be worked through. "A person who grows up getting too frequent rewards will not have persistence, because they'll quit when the rewards disappear."

That sold me. I'd thought "praise junkie" was just an expression-but suddenly, it seemed as if I could be setting up my son's brain for an actual chemical need for constant reward.

What would it mean, to give up praising our children so often? Well, if I am one example, there are stages of withdrawal, each of them subtle. In the first stage, I fell off the wagon around other parents when they were busy praising their kids. I didn't want Luke to feel left out. I felt like a former alcoholic who continues to drink socially. I became a Social Praiser.

Then I tried to use the specific-type praise that Dweck recommends. I praised Luke, but I attempted to praise his "process." This was easier said than done. What are the processes that go on in a 5-year-old's mind? In my impression, 80 percent of his brain processes lengthy scenarios for his action figures.

But every night he has math homework and is supposed to read a phonics book aloud. Each takes about five minutes if he concentrates, but he's easily distracted. So I praised him for concentrating without asking to take a break. If he listened to instructions carefully, I praised him for that. After soccer games, I praised him for looking to pass, rather than just saying, "You played great." And if he worked hard to get to the ball, I praised the effort he applied.

Just as the research promised, this focused praise helped him see strategies he could apply the next day. It was remarkable how noticeably effective this new form of praise was.

Truth be told, while my son was getting along fine under the new praise regime, it was I who was suffering. It turns out that I was the real praise junkie in the family. Praising him for just a particular skill or task felt like I left other parts of him ignored and unappreciated. I recognized that praising him with the universal "You're great-I'm proud of you" was a way I expressed unconditional love.

Offering praise has become a sort of panacea for the anxieties of modern parenting. Out of our children's lives from breakfast to dinner, we turn it up a notch when we get home. In those few hours together, we want them to hear the things we can't say during the day- We are in your corner, we are here for you, we believe in you.

In a similar way, we put our children in high-pressure environments, seeking out the best schools we can find, then we use the constant praise to soften the intensity of those environments. We expect so much of them, but we hide our expectations behind constant glowing praise. The duplicity became glaring to me.

Eventually, in my final stage of praise withdrawal, I realized that not telling my son he was smart meant I was leaving it up to him to make his own conclusion about his intelligence. Jumping in with praise is like jumping in too soon with the answer to a homework problem-it robs him of the chance to make the deduction himself.

But what if he makes the wrong conclusion?

Can I really leave this up to him, at his age?

I'm still an anxious parent. This morning, I tested him on the way to school: "What happens to your brain, again, when it gets to think about something hard?"

"It gets bigger, like a muscle," he responded, having aced this one before.

Additional reporting by Ashley Merryman

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The Power (and Peril) of Praising Your Kids -- New York Magazine - Nymag

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What do we make of a boy like Thomas? Thomas (his middle name) is a fifth-grader at the highly competitive P.S. 334, the Anderson School on West 84th. Slim as they get, Thomas recently had his long sandy-blond hair cut short to look like the new James Bond (he took a photo of Daniel Craig to the barber).

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Conquering Math Anxiety - The Power of Yay Math: Robert Ahdoot at TEDxAJU

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The magic of Fibonacci numbers

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The magic of Fibonacci numbers | Arthur Benjamin

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Beauty and Power of Math, by William Tavernetti

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The Beauty and Power of Mathematics | William Tavernetti | TEDxUCDavis

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Math Magic Tricks

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Math Magic Tricks | Crafts for Kids | PBS KIDS for Parents

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Bring a little magic to mathematics with these three magic tricks!

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Access and Equity in Mathematics Education

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Access and Equity in Mathematics Education

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Ways to incorporate social justice issues into your math teaching.

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Ways to incorporate social justice issues into your math teaching.

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Curated by educational leader Jonathan Osler, RadicalMath empowers STEM educators to address issues of social and racial justice in math classrooms. RM is a hub for curriculum, resources, and professional development opportunities.

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Why do Japanese Children Lead the world in Numeracy and Literacy?

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Why do Japanese Children Lead the world in Numeracy and Literacy?

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Japan's state education system is often criticised for quashing original thought among pupils in favour of rote learning, and for placing an emphasis on theory rather than practical skills, especially when it comes to English. But it is this traditional approach that has helped Japanese pupils easily outperform their counterparts in England and Northern Ireland.

Formal, intense instruction in maths and the Japanese language begins at the age of six and continues through to 15, the earliest age at which pupils can leave school. Those who elect to go on to senior high school - the rough equivalent of an English sixth form college and a traditional route to higher education - through to age 18 must study an eclectic range of subjects, including maths, Japanese literature and English.

Japanese senior high school teachers, and their pupils, are often incredulous when they learn that 16- to 18-year-olds in England can drop maths and literature and study just three A-level subjects of their choice. Japan's approach - rote learning accompanied by regular reviewing and testing - has proved hugely successful in establishing basic academic skills among pupils. The country's literacy rate is frequently put at 99%.

According to guidelines introduced by the education ministry, Japanese children should have learned how to read 1,006 kanji - Chinese characters used in the modern Japanese writing system - by the time they leave primary school, and a further 1,130 characters by the time they end their compulsory education at the age of 15.

Those who continue to senior high school are expected to be able to write all 2,000-plus characters - considered the minimum requirement to function in Japanese society.

Japanese children are thought to develop a working knowledge of basic mathematical patterns early on, thanks to the use in primary school classrooms of the soroban, a type of abacus based on the Chinese suanpan. Most young children in Japan own a soroban, and it is not unusual for older shopkeepers, schooled in the art of the abacus before the spread of electronic calculators, to use one to tot up bills.

Japan's approach to academic basics has its drawbacks, however. Even well-educated adults display poor communication skills in English, despite having studied the language as an exam subject for six years at junior and senior high school. At the same time, though, many pupils leave school with a good working knowledge of English grammar and decent comprehension skills.

The stress on memorising information and passing exams, which begins in primary school and continues through to senior high, has been blamed for stifling critical, independent thought and placing too much pressure to succeed on children as young as five.

Japan, like South Korea - which performed well in OECD numeracy tests among 16- to 14-year-olds - is home to a huge number of cram schools, called juku. There, children of all ages spend their evenings receiving extra tuition in the hope of edging ahead of their peers in the race for a place at a prestigious university.

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Why do Japanese children lead the world in numeracy and literacy?

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Japan's state education system is often criticised for quashing original thought among pupils in favour of rote learning, and for placing an emphasis on theory rather than practical skills, especially when it comes to English. But it is this traditional approach that has helped Japanese pupils easily outperform their counterparts in England and Northern Ireland.

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A different approach to teacher leaning.

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This essay is part of the larger radio documentary Teaching Teachers, which you can listen to in its entirety on this website or on our podcast feed (iTunes).
***

In the early 1990s an American researcher named Catherine Lewis was working on a book about education in Japan. The book had nothing to do with how kids learned math, but sitting for hours in Japanese classrooms she realized she was learning all kinds of interesting things about math that she'd never thought about before.

She noticed, for example, that there are many ways to figure out the area of a parallelogram. When she was in school, this had been taught to her as a formula. She'd never been asked to think about what the formula meant or where it came from. She was just expected to memorize it.

In Japanese classrooms, however, teachers took a different approach. After learning how to find the area of a rectangle, students would be given a parallelogram. Their task was to take what they knew about rectangles to try to figure out the area of this new shape.

"And here were Japanese 11-year olds coming up with multiple ways to derive the formula for area of a parallelogram just based on their knowledge of area of a rectangle, and just based on cutting up or redrawing with concrete materials," says Lewis. "It opened up a whole new world of mathematics to me, that I'd never seen in my own education."

She asked the Japanese teachers - how did you learn to teach this way?

These teaching strategies came from the United States, they told her.

"And I was dumbfounded," she says. "Because I had never seen these in U.S classrooms."

But these teaching strategies had come from the United States. American researchers and mathematicians had been advocating since the 1980s for what is known as a " problem- solving " approach to teaching math. But this problem-solving approach hadn't made it into American classrooms.

This was really curious. Education ideas developed in the U.S. weren't being used by American teachers, but they were being used in Japan.

"So I asked teachers, how did you - personally - learn to teach this way? And they all said, 'Lesson study.'"

Lesson study is a form of professional development Japanese teachers use to help them improve and to incorporate new ideas and methods into their teaching.

It turns out math lessons in Japan used to look a lot like lessons in the U.S. - lots of memorizing formulas, not much hands-on learning or exploring mathematical ideas and concepts. But when researchers develop new ideas about teaching and learning, Japanese teachers have an effective way to learn those new ideas, and practice them.

American teachers don't.

Japanese Lesson Study

The name for lesson study in Japanese is jugyokenkyu. "Jugyo" means teaching and learning. "Kenkyu" means study or research. So, the study or research of teaching and learning.

Here's how lesson study works.

A group of teachers comes together and identifies a teaching problem they want to solve. Maybe their students are struggling with adding fractions.

Next, the teachers do some research on why students struggle with adding fractions. They read the latest education literature and look at lessons other teachers have tried. Typically they have an "outside adviser." This person is usually an expert or researcher who does not work at the school but who's invited to advise the group and help them with things like identifying articles and studies to read.

After they've done the research, the teachers design a lesson plan together. The lesson plan is like their hypothesis: If we teach this lesson in this way, we think students will understand fractions better.

Then, one of the teachers teaches the lesson to students, and the other teachers in the group observe. Often other teachers in the school will come watch, and sometimes educators from other schools too. It's called a public research lesson.

During the public research lesson, the observers don't focus on the teacher; they focus on the students. How are the students reacting to the lesson? What are they understanding or misunderstanding? The purpose is to improve the lesson, not to critique the teacher.

In the United States, we tend to think that improving education is about improving teachers - recruiting better ones, firing bad ones.

But the Japanese think about improving teaching. It's a very different idea, says James Hiebert, an education researcher at the University of Delaware who has written about lesson study.

"Everything we do in the U.S. is focused on the effectiveness of the individual," Hiebert says. "Is this teacher effective? Not, are the methods they're using effective, and could they use other methods?"

Hiebert says to improve education in the United States, we need to shift from thinking about how to improve teachers to thinking about how to improve teaching. Lesson study is one way to do that, he says.

Some American teachers are doing it, but it's harder to do in America than in Japan.

No one to turn to for help

Jasmine Bankhead needed to figure out a way to improve teaching at her school.

It was 2013. She was the new principal of the O'Keeffe School of Excellence, an elementary school on Chicago's South Side that had been struggling for years. Finally, the school district had taken dramatic action by firing the principal, the staff and all the teachers.

That's when Bankhead was hired. Her job was to turn a failing school into a successful one, with all the same kids, but an entirely new teaching staff that she got to choose.

"Everything we do in the U.S. is focused on the effectiveness of the individual. 'Is this teacher effective?' Not, 'Are the methods they're using effective, and could they use other methods?'"
-James Hiebert

Bankhead had a very clear idea about what kind of teaching she wanted to see at her school. She calls it "inquiry-based" teaching. It's an approach, supported by research, that begins by posing questions to students rather than presenting them with facts or knowledge. It's the opposite of the way she was taught.

"My teachers stood in the front and talked," she says. "And that was it."

To help the teachers at O'Keeffe learn how to do inquiry-based teaching, she gave them training. Lots of training. She set up workshops and sent them to professional development days.

But, it wasn't working. She and her administrative team would visit classrooms, hoping to see all this great inquiry-based teaching. What they saw instead were a lot of teachers standing at the front of the room, talking. The teachers were learning about inquiry-based teaching at the workshops, but they didn't know how to actually do it when they got back to their classrooms. So they fell back on what they remembered about how their teachers taught, says Bankhead.

This is a common complaint about the traditional approach to teacher professional development in the United States. Teachers go to workshops and professional development days where they might get great new ideas about teaching. But when they get back to their classrooms and try to put those ideas into practice, all kinds of questions come up. And the expert who led the workshop isn't there to help. Often, there's no one to turn to for help.

Teachers in the United States have been expected to go into their classrooms, shut their doors, and figure things out on their own.

Bankhead and her administrative team realized the typical American approach wasn't going to work if they wanted to dramatically change teaching at their school. One of the O'Keeffe assistant principals had recently learned about lesson study in a class taught by a Japanese professor. They decided to get in touch with the professor, see if he could help them.

Bringing Lesson Study to Chicago

Akihiko Takahashi is a professor of math education at DePaul University. Before that, he was an elementary school teacher in Japan. He first came to the United States in the early 1990s looking for all the great approaches to teaching math that he and his colleagues in Japan had learned about from American researchers. When he couldn't find these approaches being used in classrooms, he soon realized why: There was no lesson study in the United States.

"If there's no lesson study," he says, "how can teachers learn how to improve instruction?"

Takahashi now helps run an organization called Lesson Study Alliance that helps American teachers, mostly in Chicago, learn lesson study. He started it with a former American teacher, Tom McDougal, who was frustrated with the lack of good professional development in U.S. schools. Since 2010, McDougal and Takahashi have worked with more than 20 schools in the Chicago area. One of them is O'Keeffe.

Lesson Study at O'Keeffe

I visited O'Keeffe in January 2015 to talk with teachers about their experience with lesson study and to see a public research lesson.

One of the first things to understand about lesson study is that it's a long process, kind of the opposite of the one-day workshop American teachers are used to. Teachers come together to identify a problem they want to solve. Then they spend months doing research and planning a lesson.

"I'd rather struggle together than struggle by myself."
-teacher Angela Flores

I spent most of my time at O'Keeffe with a group of three teachers who had been working together as part of a lesson study group since the previous summer. Angela Flores and Melissa Warner teach third grade. Wanna Allen teaches fourth grade math and science.

When they first came together to identify the teaching problem they wanted to solve, they had several things on their mind. One, they knew the overall goal for the school was for teachers to work on inquiry-based teaching. Two, they were thinking about the Common Core. That's a set of new education standards that lay out what kids should know and be able to do in each grade. Teachers at O'Keeffe - and across the country - are still figuring out how to teach the standards. Lesson study, they thought, would be a good way to do that.

"I'd rather struggle together than struggle by myself," says Flores. She liked the idea of lesson study right away.

Flores, Warner and Allen decided to plan a math lesson that would focus on the third grade Common Core math standards for geometry. They noticed that kids often struggled with understanding how to find the area of a shape. Memorizing the formula "length times width" wasn't a problem for many of them, but they didn't seem to understand what the formula meant. If they were asked to find the area of an odd shape - a parallelogram or a few rectangles put together - kids often had no idea where to begin.

It took months of planning and consultation with McDougal and Takahashi to come up with a lesson plan.

"It's a lot of meeting after school," says Warner.

That gets a laugh from her colleagues. They don't get paid for this extra time. Their principal, Bankhead, does arrange for subs to come in occasionally to free them up for planning. But for the most part, doing lesson study requires teachers to be willing to work at night and on weekends.

"The pay is in the results," says Allen. "You're getting better as a teacher."

That's the hope anyway.

The Public Research Lesson

After nearly six months of planning, Allen, Warner and Flores are ready for their public research lesson. Warner has volunteered to teach it.

"I'm excited," says Warner on the day of the lesson. "I feel like we've put a lot of work into it. We really want feedback. And I think we're ready!"

The lesson takes place on a Friday afternoon. Third-graders have gotten special permission from their parents to stay after school. They get a quick snack of pizza and then file back into their classroom, where a crowd applauds for them as they enter and sit down at their desks.

The crowd includes teachers from O'Keeffe plus some visitors from another Chicago school where administrators are thinking about starting lesson study. McDougal and Takahashi are here too. The observers are all holding clipboards and iPads, ready to take notes.

"Mathematicians," Ms. Warner says to her students, "please open your math journals and find our new learning from yesterday."

All this week in class, kids have been learning how to calculate the area of a rectangle. They've learned the standard algorithm, length times width. They've also learned a method called "tiling." That means dividing the rectangle into units and counting up the units.

The goal of this lesson is to find the area of a different kind of shape. It's a fat L-shaped figure. It looks like this:

Warner gives each student a copy of the shape. "I want you to start thinking about some ways you could find the area," she says.

The kids begin working, quietly, on their own. Ms. Warner walks around the room, leaning over each kid, taking notes on what they're doing. Occasionally she asks a kid to explain his or her thinking. But she doesn't tell them what to do. She just listens and observes.

This is a technique she learned from doing lesson study. It's a technique Japanese teachers commonly use. There's actually a name for it in Japanese.

"Kikan-Shido," says Takahashi. "Kikan means between desks. Shido means teaching."

Teaching between the desks. In Japanese, there are a bunch of words and phrases that describe specific things teachers do to help children learn. This vocabulary about teaching comes from years of doing lesson study. We don't have this kind of vocabulary in the United States.

Warner gives her kids several minutes to work on figuring out the area of the L on their own. Then she calls them to the rug at the front of the room where they're going to talk about how they did the problem. One of the goals of this lesson is to help kids learn how to "construct viable arguments and critique the reasoning of others." This is something that comes from the Common Core.

"Jimetta, could you explain to us what you started to draw in your shape here?" The kids are on the rug, crowded around Ms. Warner, eager to share their methods for finding the area of the L.

Jimetta starts to explain, some other kids chime in, and pretty quickly, there's confusion. Some students calculated the perimeter of the L instead of the area. This is something Ms. Warner was expecting. As part of the lesson study process, teachers think ahead of time about how kids are likely to respond to the lesson. What are the common misconceptions? What are kids likely to do wrong? Warner and her colleagues came up with a list of 18 different incorrect methods for finding the area of the L. Her goal here on the rug is to go through some of those incorrect methods, see if other students can find the flaws, and eventually steer everyone in the direction of methods that work.

"Dre'Shawn, bring up what you were just talking to Kenneth about," Ms. Warner says. She knows that Dre'Shawn and Kenneth have not confused area and perimeter; it says so right there in the notes she was taking as kids were working on their own.

"Kenneth and I said that you don't supposed to count all the sides, you only supposed to count the vertical and the horizontal," says Dre'Shawn.

He's up on his knees, excited to share what he knows.

"Yeah! Exactly!" say some of the kids. But others look confused. There's a lot of back and forth about the difference between area and perimeter. It gets a bit loud and rowdy, and Dre'Shawn is getting antsy because he wants to show the class how he found the area of the L. Finally, Ms. Warner calls on him.

"I put one line on the side, 'cause I wanted to make both of the problems into a separate," says Dre'Shawn.

He's having a hard time explaining his method, but he did it right. He divided the L into two rectangles and calculated the area of each one.

Ms. Warner shows the class what Dre'Shawn wrote on his paper. There are lots of "oohs" and "ahs" from the kids. This seems to be a breakthrough moment. To see if students really get it, Ms. Warner asks them to turn to the person next to them and talk about Dre'Shawn's method. The class erupts into conversation, and it's clear pretty quickly that lots of kids are still confused.

"I don't really get that," says one girl, looking grumpy.

Ms. Warner calls the class back to focus on her. She tries to steer the conversation in a productive direction, but it's hard. A bunch of kids are still stuck on perimeter. Others have split the shape in two but don't realize you have to add the area of the two rectangles together. And some insist you need to multiply the area of the two rectangles. Warner looks a bit stressed, the visitors at the back of the room are scribbling away on their clipboards, and when it's all over and the kids have gone home, Warner declares: "That was so hard. That was the hardest lesson I've ever taught."

Warner is kind of down on herself. She thinks most of the kids didn't get it. But then a really interesting thing happens.

One of the O'Keeffe teachers who had nothing to do with the planning for this lesson comes to the front of the room and leads a post-lesson discussion. This is where the visitors in the room share what they observed. Their job was to watch the kids. How were the students reacting to the lesson? What were they understanding or misunderstanding?

They've gathered all kinds of information that one teacher leading a lesson could never gather on her own. This information helps Warner see that more of the kids may have gotten it than she realized.

"I was listening to (Tracy) when he was talking on the rug," says Angela Flores, referring to one of the boys in the class. "He had really good ideas but he wasn't able to articulate them."

This prompts a discussion about how the lesson might be structured differently next time. Maybe it's not a good idea to bring kids to the rug to talk. Maybe that was too confusing and chaotic. The post-lesson discussion focuses on whether the lesson worked, not whether the teacher did a good job. When the discussion is done, Warner looks relieved.

Warner says lesson study has helped her think about teaching in a new way.

"It was about me before," she says. "It was like, these are the things I'm going to teach you, and this is my end result."

She was more focused on whether kids could demonstrate what they'd learned on an assignment or a test. She was less aware of how kids were actually learning.

Lesson study helps you "get into new habits as a thinker, and as an instructor," Warner says. "And I see such a difference in my kids because of it. I feel like in the past, if my kids got an unfamiliar problem, they would just shut down, not know what to do. Now everyone's creating a solution, and then we're ready to talk about it."

Lesson study is a welcome change from the old way of doing professional development, Warner says. It's no longer "you going back to your classroom and stumbling around with an idea."

Now, she says, there's someone to give you feedback and say, try it this way.

"It's turned my practice around."

Results

Teachers at O'Keeffe haven't been doing lesson study long enough to know what kind of impact it's having on student learning. Other schools in Chicago that have been doing lesson study have seen test score growth, but there's no way to know for sure whether that's because of lesson study.

"I'm seeing much better teaching, and there's an attitude in the building that we're all in this together. That's what we needed here."
-principal Jasmine Bankhead

There is some evidence that lesson study improves teaching. A recent review of research on professional development in the United States looked at 643 studies on approaches to improving math teaching. Only two of the approaches were found to have positive effects on students' math proficiency. One of them was lesson study.

Jasmine Bankhead, the principal at O'Keeffe, believes lesson study is having a big impact at her school.

"I'm seeing much better teaching, and there's an attitude in the building that we're all in this together," she says. "That's what we needed here. I know that as I plan and budget that I have to make room for this type of collaboration in my school, so that my teachers can continue to grow."

Catherine Lewis, the American researcher in Japan who got so interested in lesson study back in the 1990s, has been helping teachers in the United States learn lesson study for 15 years. She recently asked one of the teachers she'd been working with, what's the biggest change with lesson study?

She says the teacher told her, "The talk around the water cooler has really changed. We used to hide it when we had a failure. And everybody has failures in teaching. But we used to hide them. And now, we're perfectly comfortable saying, 'You know, I don't have a good way of teaching division with remainders. What do you do? Can I come see it in your classroom?'"

It's hard to know how many teachers in the United States are doing lesson study. There's no official count. Lewis estimates thousands of teachers are doing it.

There's even a whole state that's trying it: Florida, which got a federal grant in 2010 to encourage its schools to adopt lesson study.

But lesson study can be challenging in American schools. There are practical challenges, like finding time for teachers to plan together and watch each other teach. Japanese teachers have this kind of time built into their work schedule.

And there are cultural challenges. The organizing principle behind Japanese lesson study is that the best ideas for improving education come from teachers. It's a bottom up kind of approach.

In the United States, education improvement tends to be top-down.

"The American approach has been to write and distribute reform documents and ask teachers to implement those recommendations," says Hiebert.

Lesson study flips the script. It's one of the reasons so many American teachers who try lesson study like it. But it's also why lesson study can be a fragile enterprise in the United States. There are plenty of stories about educators who start lesson study, then a new principal comes in with a different idea about how to do things, and lesson study falls apart.

Another challenge for lesson study in American schools is the fact that it's a long and intensive process.

"We are so addicted to quick fixes," says Hiebert. "If it doesn't fix things in two years, it's not worth it."

We have this attitude about teachers too, he says. Research shows that teachers in the United States improve the most early in their careers, but after about three to five years in the classroom, they're about as good as they're going to get. If you're not a great teacher after a few years, you might as well quit or be fired. That's the thinking in the United States anyway.

But in Japan, you're not considered an expert teacher until you've been in the classroom for at least 10 years. The Japanese take teacher learning seriously, Hiebert says. They believe teachers will improve if they work in a system that values improvement.

The United States needs that kind of system, he says.

"We have an education system that is always reforming, but not always improving."
This essay is part of the larger radio documentary Teaching Teachers, which you can listen to in its entirety on this website or on our podcast feed (iTunes).

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A different approach to teacher learning: Lesson study

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This essay is part of the larger radio documentary Teaching Teachers, which you can listen to in its entirety on this website or on our podcast feed (iTunes). *** In the early 1990s an American researcher named Catherine Lewis was working on a book about education in Japan.

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Bar Model

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Introduction to The Bar Model (Strip Diagram) - Math Problem Solving Method

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http://moldingminds.com/video-introduction-to-the-bar-model/ A bar model -- also known as a bar diagram, strip diagram, strip model, tape method, tape diagram, Singapore method, etc. -- is a way to visually organize data for math problem solving. You can use a bar model to help you visualize and solve almost every kind of arithmetic problem.

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The Singapore approach to teaching maths has become so popular that "Singapore maths" has become a familiar phrase with teachers and students in at least 14 countries, even as far as South Africa and Chile.

It has produced results too.

Studies in Britain, India and the United States have shown that the test scores of their pupils at the primary school level improve when they are taught mathematics the Singapore way.

But some overseas teachers may face issues in trying to incorporate content from Singapore maths into their own national curriculum. For instance, not all British secondary schools that incorporate Singapore maths adopt customised teaching materials.

So the National Institute of Education (NIE) is embarking on a pilot project to learn how Singapore- style teaching techniques for maths can be better incorporated into a foreign curriculum.

Last September, a team of five academics from NIE's Mathematics and Mathematics Education Academic Group was formed to design teaching materials for Australia. They will be used to teach mathematics the Singapore way to students in Grades 5 to 7 in Australian schools. That is roughly equivalent to Primary 5 to Secondary 1 levels here.

Benefits of the Singapore approach to teaching maths:
*Operates according to a "spiral" design, meaning that textbooks are sequential in nature and build on concepts and skills that students have learnt previously.

*A 2015 study found that the pictorial approach was effective when teaching South African learners who have special needs and a language barrier.

*Students are engaged in the process of learning concepts and problem-solving skills, instead of blindly memorising formulas and rules.
Issues when incorporating the Singapore method overseas:
*The fit between the national curriculum and the Singapore approach needs to be considered. In Britain, the pressure on schools to cover a large number of maths topics in the national curriculum each year creates tension with the Singapore maths approach, which emphasises building solid foundations before moving on.

*Some teachers in New Jersey in the US reported that it was difficult to make the transition to Singapore maths, as Singapore's approach is more teacher-driven, slower-paced and goes into greater depth.

*Teachers need professional development and school management teams need to be brought on board to ensure a smooth transition.

*The methods, such as the model approach, can be used only to solve certain topics and problems, and should not be seen as a one-size-fits-all solution to all maths problems.

The move is part of a project managed by the Australian Academy of Science (AAS) called the reSolve: Mathematics by Inquiry programme to help students learn mathematics in an innovative and engaging way.

After the pilot, which will involve schools in the states of Victoria and South Australia, the NIE academics will gather feedback, fine- tune the programme and make it available to teachers across Australia's more than 9,000 schools. NIE hopes to complete this in February next year.

The reSolve programme will also train 240 teachers to champion the programme in their schools, and more than 400 schools have expressed their interest.

Another round of trials will be conducted later this year, with more schools in other states.

These resources will cover three units in Australia's national curriculum, and use visual means such as objects, pictures and diagrams to teach concepts. These include the model method, which refers to the use of bar drawings that visually represent quantities.

Associate Professor Lee Ngan Hoe, who is leading the Singapore team of researchers, said overseas teachers "may not know the philosophy and principles behind some methods, so there may be a mismatch in terms of how the (teaching) methods are used".

Emeritus Professor Kaye Stacey, the director of special topics for Australia's reSolve programme, said that while Singapore was chosen as a partner because its approach is "particularly well developed", the Australian team must ascertain the degree to which the resources developed are appropriate for Australian schools and accepted by teachers.

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Customising 'Singapore maths' for use in schools abroad

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The Singapore approach to teaching maths has become so popular that "Singapore maths" has become a familiar phrase with teachers and students in at least 14 countries, even as far as South Africa and Chile. It has produced results too.

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The Singapore Math method marked a change in how math was taught in many American classrooms and homeschool settings. The program uses a three-step learning model, moving from the concrete (such as showing something using manipulatives) to the pictorial (creating a visual representation on paper) to the abstract (solving problems).

Singapore Math closely aligns with the Common Core State Standards Initiative, which may be positive or negative, depending on your views about Common Core. The sequential learning allows students to grow without unnecessary busywork, which is great for many students but may be confusing for those who drop into the curriculum later because of a move or a change in schools.

What Is Singapore Math?

It's not the content that makes Singapore Math different from other methods; it's the philosophy. Rather than rote memorization, the framework of Singapore Math is developed around the idea that learning to problem-solve and develop mathematical thinking are the key factors to being successful in math. Without a solid foundational base, students won't have anything to draw on when it comes to increasingly complicated math learning.

This doesn't mean, however, that the skills elementary students learn are simplistic. Rather, the view is that when teaching a concept or a skill, it's essential to spend as much time as needed for students to master the skill. That way, you're not moving on to the next concept with the thought that earlier skills can always be retaught if necessary. Teachers can simply revisit instead, opening up more instructional time.

The CPA Approach

History of Singapore Math

What is referred to as Singapore Math in other countries is, for Singapore, simply math. The program, developed under the supervision of the Singaporean Minister of Education, was introduced as the Primary Mathematics Series in 1982.

In 1998, Jeff and Dawn Thomas realized that the math program they brought back from Singapore and used to supplement their own child's schoolwork could be helpful to schools and homeschoolers across the nation. As the program began garnering attention, the couple incorporated under the name Singaporemath.com Inc. and marketed their books under Singapore Math, a registered trademark.

In the U.S., Singapore Math first gained popularity among homeschoolers and small private schools. Singapore is consistently a top country in Trends in International Mathematics and Science Study (TIMSS), revealing Singapore's fourth-graders and eighth-graders as the leading math performers in the world. Of note, Singapore remains the top-performing country as of the 2019 TIMSS.

Singapore Math Curriculum

With so much interest in the method, in 2007, U.S. educational publisher Houghton-Mifflin Harcourt teamed up with the leading academic publisher in Singapore to publish and distribute a math series called "Math in Focus: The Singapore Approach." This series and the Thomas' "Dimensions Math" and "Primary Mathematics" are the only curriculum packages available to United States educators and parents for teaching the Singapore math method.

The Singapore curriculum comes with a textbook, workbook, and teacher's or home instructor's guides. The textbooks present new concepts, the workbooks offer practice to solidify the concepts, and the guides provide lesson plans and instructions for using the books.

Singapore Math in Action

A typical third-grade math instruction might go something like this: "Today we're going to learn about long division." Students watch while the teacher demonstrates the steps and actions necessary to solve a long division problem.

Singapore Math instruction looks different. Instead of watching a demonstration of a new math concept and then doing similar problems to reinforce the idea, students are tasked with mastering the theory at the onset.

For instance, with the long division example, a parent or teacher might say, "I have some pennies I want to put in some jars." The instructor then places baggies of pennies and jars on the table. They then clarify, "I have 17 pennies I want to share equally in 5 jars." First, students must figure out how that might work and then share their ideas about what sharing equally means and how they approached the problem.

Singapore Math Pros and Cons

Singapore Math's unique focus on building problem-solving skills aligns with the Common Core State Standards. While some people see this as a benefit, others find it more detrimental.

Some find Singapore Math confusing for children to learn as part of a Common Core Standards framework and find that it unnecessarily complicates the teaching of mathematical principles to young children.

Singapore Math is popular with homeschoolers, private schools, and public schools alike-and for good reason. Research into the pedagogy of countries whose students excel in math, like Singapore and Japan, has found these countries' use of diagrams in teaching math can provide a valuable bridge between early and advanced learning stages and encourage intuitive problem-solving skills.

Some benefits of Singapore Math include the following:

It asks for students to build meaning to learn concepts and skills instead of rote memorization of rules and formulas.

It aligns with the Common Core State Standards Initiative.

It covers fewer topics in a year but in an in-depth way that ensures students have a foundation to move forward without needing to relearn concepts.

Textbooks and workbooks are simple to read with clear and concise graphics.

Textbooks are sequential, building on previously learned concepts and skills, which offers learning acceleration without additional work.

Despite the number of pros to Singapore Math and some research suggesting that it is superior to traditional U.S. textbooks, some schools find that the method is not easy to implement.

Some drawbacks of Singapore Math include the following:

It aligns with the Common Core State Standards (yes, this can be a pro and a con, depending on whom you ask).

It may not work well for a nomadic student population. Many students move in and out of school districts, which isn't a big problem when the math programs are similar. However, since Singapore Math is sequential and doesn't re-teach concepts or skills, using the program could potentially set these students up for failure whether they're moving into or out of a district using it.

It has less of a focus on applied mathematics than traditional U.S. math textbooks. For instance, Everyday Mathematics, a curriculum developed by the University of Chicago, which came out around the same time as Singapore Math, emphasizes data analysis using real-life, multiple-step math problems. On the other hand, Singapore Math's approach is more conceptual and ideological.

It requires extensive and ongoing teacher training, which is neither financially nor practically feasible in some school districts and not always practical for homeschooled children.

Supplies are consumable and must be re-ordered for every classroom every year, which can put a financial burden on already strained school budgets and homeschoolers alike.

Frequently Asked Questions

How do you teach Singapore Math?

Teaching Singapore Math follows a Concrete, Pictorial, Abstract (CPA) approach that helps students understand math by building on existing knowledge. In the concrete phase, you will encourage students to interact with physical objects to work out problems. In the pictorial step, you will help students mentally connect their objects and visual representation. In the abstract phase, you will guide students to use numbers and math symbols.

How is Singapore Math different?

Singapore Math differs from other math curriculums in its approach. Instead of rote memorization and drilling concepts through similar problems, Singapore Math teaches students how to mathematically think so that they can rely on the theory and build on concepts.

How can I help my child with Singapore Math?

Remember that Singapore Math utilizes a progressive learning process that includes helping kids understand the concrete, the pictorial, and the abstract. If you are your child's teacher, be sure to utilize the teacher's guides, which offer lesson plans and instructions. Whether you are homeschooling or supporting a child who attends public or private school from home, you may find online communities, like Singapore Math's Facebook group, helpful.

How do I know what level to start at in Singapore Math?

Singapore Math's grades align with U.S. schools. Even so, it may be helpful to have your child take Singapore Math's placement test.

What grades does Singapore Math cover?

Singapore Math is for students in Pre-K through 8th grade.

What comes after Singapore Math?

Since Singapore Math teaches students critical mathematical thinking skills, students can transition to nearly any math curriculum after Singapore Math.

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Is Singapore Math Right for Your Student?

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The Singapore Math method marked a change in how math was taught in many American classrooms and homeschool settings. The program uses a three-step learning model, moving from the concrete (such as showing something using manipulatives) to the pictorial (creating a visual representation on paper) to the abstract (solving problems).

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Website full of great ideas for grades K-12

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Ways to incorporate First Peoples Principles of learning

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Ways to incorporate First Peoples Principles of learning

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The Adventures of Txamsm Series

After School

Alego

An Aboriginal Alphabet

Animal World

B is for Basketball

The Bannock book

Beaver Steals Fire

Beneath Raven Moon

Big and Small with Northwest Coast Native Art

A Blanket of Butterflies

Byron through the Seasons

Canoe He Called Loo Taas

Caring for Me Series

Catching Spring

Cedar Readers Series

Cedar Readers A to Z Series

Ch'askin: A Legend of the Sechelt People

Chiwid

Christmas at Wapos Bay

Chuck in the City

The Class Hike

Counting on Hope

Counting to 100 in the Bighouse

Cloudwalker

Colour and Draw: Northwest Coast Native Formline

Colouring Journal: Northwest Coast First Nations and Native Art

A Coyote Solstice Tale

Dancing In My Bones

Dancing with the Cranes

Darkness Calls

Deadly Loyalties

Dipnetting with Dad

Discover the Animals: First Nations and Native Art Colouring and Learning Book

Dream Catcher

Dreaming in Indian

Eaglecrest Books - Set A

Eaglecrest Books - Set B

The Elders are Watching

Explore the Animals: Colouring and Learning Book

Exploring Quatsino

Exploring Ts'axis

Exploring Tsulquate

Fatty Legs

Fiddle Dancer

A First Nations Alphabet: ABC Book

A First Nations Alphabet to Read and Draw

From Lishamie

From the Mountains to the Sea Series

The Gathering Tree

The Gift is in the Making: Anishinaabeg Stories

Giving Thanks: A Native American Good Morning Message

The Giving Tree: A Retelling of a Traditional Métis Story

Goodbye Buffalo Bay

Good Morning World

Goodnight World : animals of the Native Northwest

Hide and Sneak

Him Standing

Hockey Challenge

Honouring the Salmon: An Anthology Told in the Voices of the Tsimshian

Hooshum for Everyone

How Fox Saved the People (D?ne Gok'eidì)

How Many Frogs Do You See

How Raven Stole the Sun

How the Coho Got His Hooked Nose

How the Fox Got His Crossed Legs

How the Robin Got Its Red Breast

I Am Raven

I Can't Have Bannock but the Beaver Has a Dam

I Have a Drum

I Help

I Know I am Precious and Sacred

I Like Who I am

I See Me

I was Born Precious and Sacred

Jack and the Boys Adventure Series

Jenneli's Dance

The Jingle Dancer

The Journey: North American Indigenous Games

The Journey of Dog Salmon

Just a Story

Just a Walk

Keepers of the Earth: Native Stories and Environmental Activities for Childrean

Keepers of the Night: Native Stories and Nocturnal Activities for Children

Kou-Skelowh/ Kwu squilxw - We are the People: A Trilogy of Okanagan Legends

Learn from the Animals of the Salish Sea: Coast Salish Native Art Colouring and Learning

Learn the Alphabet with Northwest Coast Native Art

Learn the Colours with Northwest Coast Native Art

Learn to Count with Northwest Coast Native Art

Learn and Play (2 Board Books)

The Legend of the Caribou Boy

lessons from Mother Earth

Lightfinder

Little Bear's Vision Quest

Little Cedar, Big Cedar

The Little Duck (Sikihpsis)

The Little Hummingbird

The Littlest Sled Dog

Little You

Mayuk the Grizzly Bear

The Moccasins

Missing Nimâmâ

Moonshot

Mouse Celebrates the Winter Solstice

Murphy and Mousetrap

My Elders Tell Me

My Family Has Fun

My Heart Fills with Happiness

My Life in a Kwagu'l Big House

My Life with the Salmon

My Name Is Seepeetza

Neekna and Chemai

No Time to Say Goodbye

Northwest Coast Native Animals

Not My Girl

Ojibway Animals

Ojibway Clans: Animal Totems and Spirits

The Old Man with the Otter Medicine

Orca Chief

Peace Pipe Dreams: The Truth about Lies about Indians

People of the Land: Legends of the Four Host Nations

Persistence and Change: A History of the Ts'msyen Nation

Powwow: Counting in Cree

The Rabbits Race

Racin' Jason

Raven and Eagle

Raven Brings the Light

Raven Series

Raven Tales Series

Ready for School

Relatives with Roots: A Story about Métis Women's Connection to the Land

Returning the Feathers: Five Gitxsan Stories

A Rhyming Coastal Alphabet

A River Lost

River of Salmon Peoples

River Run

Ruler of the Forest: Why Raccoon Wears a Mask - yuw'i'na'qws tthu hwthuthiqut: nutsim' yuhw 'a'lu 'ushus shtiil'a'lus tthu sxayukw'us

Salish Stories Series

Salmon Boy: A Legend of the Sechelt People

The Scout

Sealiya

Secret of the Dance

7 Generations: A Plains Cree Saga

Shannen and the Dream for a School

Sharing Our World: Animals of the Native Northwest Coast

Shi-shi-etko

Shin-chi's Canoe

The Special Visitor

Spirit of the White Bison

Stories of Robin Town Series

A Stranger at Home: A True Story

Strength and Struggle: Perspectives from First Nations, Inuit, and Métis Peoples in Canada

Strong Readers Guided Reading Series - Set A

Strong Readers Guided Reading Series - Set B

Strong Readers Métis Series

Sugar Falls: A Residential School Story

Taanishi Books

Taan's Moons: A Haida Moon Story

Tsimshian Language Series Teachings of our Grandfathers Series

Thirteen Moons on Turtle's Back

Three Feathers

Tilly: A Story of Hope and Resilience

Turtle Island Voices Series

Unusual Friendships: A Little Black Cat and a Little White Rat

Urban Tribes

A Walk on the Tundra

We All Count: A Book of Cree Numbers

We All Count: Book of Ojibway Art

We Visit Granny

We-gyet Wanders On: Legends of the Northwest

When I was Eight

When the Spirits Dance: A Cree Boy's Search for the Meaning for War

Where Did You Get Your Moccasins

Where I Belong

Which Way Should I Go

Yamohza and His Beaver Wife

Yetsa's Sweater

© 2023 - First Nation Education Steering Comittee (FNESC)

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The Adventures of Txamsm Series After School Alego An Aboriginal Alphabet Animal World B is for Basketball The Bannock book Beaver Steals Fire Beneath Raven Moon Big and Small with Northwest Coast Native Art A Blanket of Butterflies Byron through the Seasons Canoe He Called Loo Taas Caring for Me

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BC First Nations Land, Title and Governance Teachers Guide

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BC First Nations Land, Title and Governance Teachers Guide

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First Nations Education Steering Committee FNESC

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The BC First Nations Land, Title, and Governance Teacher Resource Guide is designed to support the understanding of traditional and contemporary forms of First Nations governance specific to First Nations in BC. It provides background information relevant to all teachers and students, and provides suggested activities and resources for grades 2 to 12.

This guide is divided into six different multi-grade thematic units as well as additional support material.

The introduction offers key information to support and guide teachers in facilitating the respectful and meaningful inclusion of Indigenous knowledge and perspectives in the classroom. While the first four units are organized by grade level, teachers will find activities in all of them that can be adapted to other grades as needed. Unit 5 and 6 can be applied to grades 4-12.

Introduction Blackline Masters, Unit 5 Backgrounders Bibliography

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BC First Nations Land, Title, and Governance Teacher Resource Guide - First Nations Education Steering Committee FNESC

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The BC First Nations Land, Title, and Governance Teacher Resource Guide is designed to support the understanding of traditional and contemporary forms of First Nations governance specific to First Nations in BC. It provides background information relevant to all teachers and students, and provides suggested activities and resources for grades 2 to 12.

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First Peoples Content for K-3

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Science First Peoples Resource Guide  Grades 5-9

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Science First Peoples Resource Guide  Grades 5-9

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The FNESC/FNSA Secondary Science First Peoples Teacher Resource Guide provides educators with resources to support the integration of the rich body of First Peoples (unappropriated) knowledge and perspectives into secondary Science classes (as well as other curricular areas).

The guide includes background information on how First Peoples' knowledge and perspectives in science can be recognized and included in science inquiry. It also offers curriculum planning suggestions, and provides examples of fully developed multi-grade thematic units that correspond with the BC Science Curriculum for grades 10 to 12.

While it focuses on grades secondary grades, this guide can also be applied to other grade levels and be used in conjunction with the FNESC/FNSA Science First Peoples 5-9 Teacher Resource Guide.

It is recognized that the wealth of First Peoples' science knowledge is held by communities. The guide can be used in conjunction with locally based resources that are developed by or in collaboration with, local communities. It is intended to be a starting place for educators.

Introduction Blackline Masters Bibliography

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Science First Peoples Teacher Resource Guide (SECONDARY) (2019) – First Nations Education Steering Committee FNESC

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The FNESC/FNSA Secondary Science First Peoples Teacher Resource Guide provides educators with resources to support the integration of the rich body of First Peoples (unappropriated) knowledge and perspectives into secondary Science classes (as well as other curricular areas).

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Embedding Assessment into Practice

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"Throughout the learning process, teachers and students intentionally gather evidence to inform teaching and learning. The teacher creates rich tasks, engages with the students in setting criteria, establishes exemplars, and leverages the power of questioning to allow for ongoing, timely, descriptive feedback to the students. This process assists students in moving forward toward their learning targets and goals. Students are encouraged to reflect and self-assess to build important meta-cognitive skills. Personalization lends itself to assessment as learning, where students participate in the setting of criteria and the design of inquiries, and self-and peer-assessment."
BC Curriculum website 2016

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BC Numeracy Network - How to embed assessment

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"Throughout the learning process, teachers and students intentionally gather evidence to inform teaching and learning. The teacher creates rich tasks, engages with the students in setting criteria, establishes exemplars, and leverages the power of questioning to allow for ongoing, timely, descriptive feedback to the students.

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Know, Do, Understand

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BC Numeracy Network - How do I know what my students know, can do, and understand?

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The Island Numeracy Network (INN) is a passionate group of K-12 educators from numerous districts and schools in the Vancouver Island region. This new assessment was developed to align numeracy assessment practices with current numeracy learning expectations of BC students.

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Assisting Students to become confident in Math

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"Numerous research studies (Silver, 1994) have shown that when students are given opportunities to pose mathematics problems, to consider a situation and think of a mathematics question to ask of it-which is the essence of real mathematics-they become more deeply engaged and perform at higher levels."

(Boaler, Mathematical Mindsets, 2015, p. 27)

This resource guides readers through 5 practices (anticipating, monitoring, selecting, sequencing, and connecting) to develop productive mathematical discussions.

(2nd Edition)

The next application of the 5 practices to create productive mathematical discussions is explored through a middle years focus.

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BC Numeracy Network - How do I assist students in becoming mathematicians?

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"Numerous research studies (Silver, 1994) have shown that when students are given opportunities to pose mathematics problems, to consider a situation and think of a mathematics question to ask of it-which is the essence of real mathematics-they become more deeply engaged and perform at higher levels." (Boaler, Mathematical Mindsets, 2015, p.

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The goal of this group is to ensure that all children have the opportunity to achieve their full potential in math.

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Western Initiative for Strengthening Education in Math WISE Math

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The purpose of this initiative is to form a coalition among concerned parents, citizens, employers, scientists, mathematicians, and educators with the purpose of rallying together to improve K-12 mathematics education in Western Canada. We are advocates for improved math teacher training and strengthened K-12 math curricula. Our goal is to ensure that all children have the opportunity to achieve their full potential in math so that they may enjoy lives free of innumeracy, may experience the beauty in math, and so that they may have a wide range of career opportunities.

Key Objectives

Some specific objectives for which we will advocate are listed below.

Teacher training

Teachers who are required to teach math must have a strong background in math beyond that which they are required to teach.

1. Every teacher who may be called upon to teach mathematics must have taken the academic stream of mathematics from high school in addition to math content courses at the university level.

2. Currently, almost all elementary and middle years teachers are required to teach mathematics in addition to many other subjects.

Recommendation. We recommend that math specialists be responsible for teaching math in elementary and middle years. These teachers would m0ve between classrooms and teach math full-time to many different classrooms of students, much like is the case with music teachers in elementary schools. K-8 math specialists should have taken a number of math courses at the university level which develop strong mathematical reasoning as well as courses that are specifically designed to delve deeply into the math contained in K-8 curricula.

3. Mathematics departments must have a strong role in the planning of degrees for all teachers who are required to teach math, both at the elementary and secondary levels.

Math curricula

We support a balanced approach between understanding and skills. Unfortunately, in the shift towards ensuring that children understand math concepts, which we support, several important elements of mathematics have been neglected, or completely eliminated, from curricula and math classrooms.

1. Professional mathematicians, and scientists from disciplines that use mathematics regularly, such as physics, engineering, business, economics or computer science, must have at least 50% representation on committees that shape and make decisions about overall content and the general methodology of mathematics teaching. Those who use and teach higher level math regularly are familiar with what students need to know to succeed in math and thus should have a strong voice in curriculum decisions.
Specific curriculum issues
2. Standard algorithms for addition, multiplication, subtraction, and division must be included in math curricula and they must be introduced to children early. They must be explicitly listed in math curricula, which is currently not the case in the WNCP math curriculum, and children should become fluent with these algorithms.

3. Students must practice math skills and arithmetic regularly to become proficient. Math curricula must support the development of understanding of math concepts AND the learning of basic skills and concepts through incremental practice. The two are NOT mutually exclusive. There must be a healthy balance between understanding and practice, to allow students to grow in both senses.

4. Calculator use in math classes should be minimized.

5. Teachers must be provided with appropriate instructional materials to assist them with covering curricula. Clear and well-written text books and teachers' guides, that are free of errors, student workbooks, and worksheets are necessary tools in successful mathematics instruction. Mathematicians should be involved in reviewing and assessing recommended math text books and math instructional material.

Articles that argue for the objectives on which we have initially chosen to focus can be found here.

In 2006, the US President appointed the National Math Advisory Panel, which consisted of mathematicians, math educators, and cognitive psychologists, to explore ways in which to improve mathematics achievement for all students and to devise a report based on the available rigorous research studies. For a summary of the recommendations regarding math teacher training and curriculum content, visit this page.

There are many other issues that negatively affect the attainment of a solid education in math (and in other subjects). If you would like to discuss some of these other issues, please leave a comment at our Other important issues page.

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WISE Math Mission Statement The purpose of this initiative is to form a coalition among concerned parents, citizens, employers, scientists, mathematicians, and educators with the purpose of rallying together to improve K-12 mathematics education in Western Canada. We are advocates for improved math teacher training and strengthened K-12 math curricula.

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K-12 Assessment System

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Provincial assessment | Building Student Success - B.C. Curriculum

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Provincial assessments are changing to align with the new curriculum. They provide a snapshot of student performance in key areas and, over time, can help to monitor key outcomes of B.C.’s education system.

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National Council of Teachers of Mathematics

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National Council of Teachers of Mathematics

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Ensuring Mathematical Success for All

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Every child can learn math and love it.

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JUMP Math is a non-profit that empowers teachers to multiply the potential in every classroom through research-informed, curriculum-aligned resources and approaches that ignite and nurture an enduring understanding and appreciation of math in every student.

A message to our valued customers and supporters;

Educators, parents and students are facing an unprecedented and challenging situation during this pandemic. We are fully committed to providing support, resources and services to help students continue along their educational paths.

While observing advice of governments and public health officials, JUMP Math remains fully operational as does our distributor, UTP, who continue to fulfill and ship orders.

Please reach out to our Outreach team with any questions or concerns you may have or email us at info@jumpmath.org. We want to thank you for your continued support and wish everyone good health in these difficult times.
Let us know: How can we support you?
Geared for administrators, master teachers, instructional leads, and coaches, our JUMP Math PD Provider Institute will provide extensive and practical professional development for JUMP Math coaching. Hosted by Senior Outreach Manager Amy Helmstetter and guest speakers Dr. John Mighton (JUMP Math founder) and Cecelia Daniels (Instructional Design leader, John Hopkins University), our Provider Institute will prepare you to coach and support JUMP Math teachers with confidence.

What's New

Struggling with how to explain math worksheets while your kids are schooling from home?

John Mighton (@JUMP_Math) offers some tips for teaching during the pandemic. pic.twitter.com/bm8hMDnpZ9

- CBC Radio: The Current (@TheCurrentCBC) April 28, 2020

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JUMP Math is a numeracy program. JUMP Math is dedicated to enhancing the potential in children by encouraging an understanding and a love of math in students and educators. JUMP Math replaces the self-fulfilling myth that some people are born with mathematical ability while others do not have the ability to succeed with assumptions that all children can be led to think mathematically.

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Elementary and Middle School Mathematics -Teaching Developmentally 

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Elementary and Middle School Mathematics -Teaching Developmentally 

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p 87-93, Diversity in our Classrooms

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Five Principles of Extraordinary Math Teaching | Dan Finkel 

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Five Principles of Extraordinary Math Teaching | Dan Finkel 

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Five Principles of Extraordinary Math Teaching | Dan Finkel | TEDxRainier

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A visual Approach to Learning Math

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Teaching Math Without Words, A Visual Approach to Learning Math

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Word walls in math help to enforce the vocabulary

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This math word wall set of +215 words is just what YOU need to enforce academic vocabulary and create an AMAZING bulletin board at the same time! Your students will refer to these math word wall cards over and over again!

Download the preview for a sample of words included.

Download the companion math vocabulary instruction resource pack HERE.

Download the matching ELA word wall set HERE.

Displaying academic vocabulary on a classroom math word wall is extremely important! Research shows that students need exposure to new vocabulary words multiple times before they reach mastery.

This bright colored polka dot set of Common Core math word wall cards is perfect for display in a 5th grade general education, special education, ELL or home school classroom. This math word wall set was created based on the 5th grade Common Core Math State Standards.
This 5th grade math word wall set includes:
► A math vocabulary banner.

►+215 math word wall cards - each card contains the academic vocabulary word, its definition or example and a visual representation.

► Common Core Standard codes on EVERY card

► 6 bulletin board headers (operations & algebraic thinking, number & operations in base ten, number & operations-fractions, measurement & data, geometry, blank)

► FREE suggested pacing guide for introducing each vocabulary word. Your whole year is planned for you!!!

► Blank EDITABLE template designs to create your own words

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Further enhance your vocabulary instruction with a 5th Grade Math Word Wall Instruction Packet. Over 20 weeks of daily practice and weekly quizzes to assess your students' understanding of the 5th Grade Math Academic Vocabulary. Click to view this new product!

Looking for a different math word wall card theme (chevron, zebra print, black & white; rainbow colors, polka dot, nautical, no backgrounds and MORE), grade level (3rd, 4th, 5th, 6th) or BUNDLE? Click HERE to see all the Common Core math vocabulary word wall sets I have available in my store.

Need an ELA word wall set to match? Look no further - available for grades 3rd, 4th, 5th, and 6th in polka dot, chevron, animal print, black & white, rainbow colors, nautical, no backgrounds and MORE. Click HERE to view all ELA sets.
Are you teaching the CRITICAL VERBS and NOUNS of the Common Core? It is extremely important to expose your students to this test taking vocabulary!!
Click HERE for a matching word wall set of the Common Core Critical Verbs.

Click HERE for a Critical Verbs Instruction Packet with 12 weeks of graphic organizers and quizzes.

Click HERE for Critical Verbs Games - a fun way to review instruction of these necessary academic vocabulary words.

Click HERE for Critical Nouns word wall cards.

Click HERE for a Critical Nouns Instruction Packet with 5 weeks of graphic organizers and quizzes.

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Created by Melissa O'Bryan

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Math Vocabulary Word Wall 5th Grade - Editable - Polka Dots

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This math word wall set of +215 words is just what YOU need to enforce academic vocabulary and create an AMAZING bulletin board at the same time! Your students will refer to these math word wall cards over and over again!Download the preview for a sample of words included.Download the companion mat...

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PreK - 5

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Vocabulary word wall cards/posters in all grade levels. 

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Vocabulary word wall cards/posters in all grade levels. 

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VDOE :: Mathematics Vocabulary Word Wall Cards

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ELLs count on language support in Math. 

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ELLs count on language support in Math. 

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Laura Varlas

At her district's newcomer center, English as a Second Language teacher Barbara Gottschalk would engage parents in a visual exercise: compare a math textbook from 20 years ago to the one in use today. The former, a familiar reproduction of the kind of math newcomers most likely experienced in their home countries, was defined by rows of computation. In the current textbook, however, words abound.

"You could tell just by looking at the two that even a student with a strong background in math will need some language support in a mainstream math class," says Gottschalk, who teaches at Susick Elementary in Troy, Michigan. A student with interrupted or limited schooling, she adds, will need even more language support.

With the Common Core State Standards and, especially, the skills identified in the Standards for Mathematical Practice, mathematics has increasingly emphasized conceptual understanding and reasoning, in addition to procedural know-how. "Language is the entirety of the mathematics classroom," says Megan Rowe, a math teacher at Borah High School in a linguistically diverse district outside Boise, Idaho. "From the language I use when I'm teaching to the language students use when they're reasoning among their peers-I don't know how you could ever teach mathematics now without focusing on language."

Double-Edged Disadvantage

Yet there's evidence across the education sector that many still assume English language learners (ELLs) don't need language support in math, and that belief can create a double-edged disadvantage for such students. ELLs placed in mainstream math courses with little to no language support are more likely to flounder under increased linguistic demands. However, when ELLs are tracked into remedial classes-and researcher Eduardo Mosqueda reports that this is a common and pernicious trend-it severely reduces the likelihood that they will eventually take advanced math courses.

"Once you start looking at math through the lens of language, you see linguistic demand everywhere," says San Diego State University professor Bill Zahner, a former high school math teacher. Without awareness and planning to support ELLs with that linguistic load, language will continue to be a gatekeeper to the advanced courses that lead to in-demand, well-paying careers in STEM fields. For Zahner and others, it's a question of equity: "How do we meet the needs of linguistically diverse students in math?"

Build a Baseline

When working with ELLs, it can be easy to mistake lags in language for gaps in math learning. "Just because they don't have the words doesn't mean they don't know how to do it," says Gottschalk. That's why middle school ESL teacher Beth Morrow's first rule of supporting ELLs in the math classroom is assess, don't assume. Establishing a baseline of where students are in terms of math knowledge and language proficiency helps teachers tailor the content and English supports ELLs receive.

Gottschalk uses a simple, language-free, calculation-based assessment to screen students' content knowledge. But even with pared-down assessments, cultural differences in math notation can make screening students challenging.

"Although there are some common rules that all mathematicians and scientists use, worldwide, they manifest themselves differently depending on the culture," says Cassie Eatmon, math chair at Herndon Middle School in Virginia. For example, long division is set up differently in the United States than in South American countries, and Arabic notation is written right to left. "Subtracting in Arabic looks wrong to us, but it's actually just flipped," explains Gottschalk.

Incorporate Semantic Supports

For newcomers, Eatmon recommends gradually increasing language demands. "Phrase questions that require them to produce a minimal amount of English at the beginning," she recommends. Choice questions (that require a yes/no, true/false, and ways for them to communicate nonverbally via a word card or hand signals) are a good place to start. As newcomers develop confidence with language skills, stretch expectations for discourse.

"Newcomers need special handling for a while," says Rita MacDonald, researcher at WIDA and the Wisconsin Center for Education Research (WCER). "However, students are newcomers for the short term; they are language learners for a long time."

For the long haul, ELLs will need different levels of support to engage in increasingly language-rich mathematics. Visual representations of concepts, word walls, defining word parts (prefix, root, suffix), sentence frames, and note-taking practice-common tools in language arts learning-can be adapted in order to make math-centered conversations more accessible to ELLs. For example, Eatmon recommends adapting the traditional think-pair-share processing strategy to think- write-pair-share so that students will have a script of their thoughts to refer to. "That reduces the burden on ELLs to think and talk [in a new language] at the same time," she explains.

Language in Use

Researchers at WCER have developed six specific moves teachers can make to strengthen all students' reasoning skills in mathematics, especially ELLs ( see Figure 1), as well as seven tactics students can apply when working with ideas in math ( see Figure 2). These strategies develop language through doing mathematics, what MacDonald calls a "language in use" approach. "It used to be a common belief that you had to learn language before you can do stuff. We don't believe that works," she says. "You really only learn language through shared experience, by doing something."

MacDonald recommends introducing and practicing the student moves one at a time and providing prompts and sentence frames to cue students as they clarify, restate, support, challenge, compare, explain, or build on an idea (see http://stem4els.wceruw.org/resources/Student-and-Teacher-moves.pdf for examples). The goal, says MacDonald, is to "get ELLs in the habit [of understanding] that there are so many things they can do when an idea is presented."

Practice with discourse-centered mathematics helps students build the precision that is the cornerstone of math fluency. "In regular conversation, we don't tend to be precise and specific with our language. In mathematics, you need to be, but you don't just jump to that disposition right away," explains MacDonald. You get there through experiences, like needing to explain precisely the constraints of an argument, of having to use a very specific label for something. Those experiences happen in classes where students are practicing math in all four language domains.

Designed for Discourse

In a language-rich, ELL-supporting math class, students learn math through listening, speaking, reading, and writing-the four domains of language. But many classes, not just math, tend to fixate on the listening domain. "Students get all kinds of practice listening," says Gottschalk. "But they can easily go through a whole day of school without ever having to utter a single word of academic English."

"If you set the goal that every single student has the opportunity to speak, every single day," says Rowe, "you start to realize how few opportunities there are-at least there were for me-for students to talk about math."

Rowe has refocused her teaching from "What's the math for today?" to "What's the language for today?" and says that allows her to structure learning that gets to a deeper level of math thinking. "My students aren't just robots that can regurgitate a process or steps," says Rowe. "To learn math, they have to be able to talk about it."

One of Rowe's favorite strategies for eliciting math discourse is the "partner round-up." This strategy can be used to talk through all sorts of mathematical operations. For example, if students are practicing adding fractions, each student receives a card with a different fraction on it. They then find a partner in the class and work together to successfully find the sum of their fractions. Once they do, they trade cards and find a new partner and repeat the process. "This could have easily been a worksheet-20 problems, practice adding fractions on your own," says Rowe. But when it's done as partner exercise, her students get to talk to 20 different peers and hear the different ways they think through and explain a problem. "You go from something that was content-based to language rich, and that makes a big difference especially for ELLs."

Gottschalk's school uses journaling extensively in math class. Language is modeled and practiced as students discuss, and then write about, a problem of the day, she says. Teachers can get creative with how they set up journal prompts. MacDonald suggests, "Here's my favorite wrong answer from the last class. Let's figure out why that was wrong."

Opportunities to develop language, through identifying relationships or making generalizations within sets of problems, are implicit in some of the materials teachers have, adds Zahner, but those opportunities are often not highlighted. Zahner is currently working with a team of 9th grade math teachers on a project funded by a $1 million grant from the National Science Foundation to design secondary mathematics classrooms focused on meeting the needs of ELLs. There's a real urgency, he argues, to provide teachers with resources and supports to unpack the curriculum so that opportunities for discourse and reasoning, not just right answers, are prioritized.

Weeding Wordy Problems

With language at the center of the modern math classroom, it's important to note that not all words are worthwhile in the service of math learning. In fact, there are a lot of nonessential words and distracting or confusing contexts littering math texts. "If you use an example that talks about a horse, it better be the animal and not the gymnastics equipment," Eatmon warns.

Zahner cites a textbook example of a word problem for calculating the slope of a roof. The problem talks about two- by six-inch sized pieces of wood that will be used as vertical supports for the roof. These pieces of wood are unfortunately written as "2×6's." The dimensions of the board are not actually relevant to the rest of the problem, says Zahner. But for a student from Mexico, this aspect of the problem was derailing. "His answers to every other problem were correct except for this one. He got stuck trying to figure out how to use '12,' which is two times six."

Rowe adds that sometimes her students struggle with names. "If there's a Mr. Brown in the problem, they'll wonder who that is and why his name is relevant to the problem." Rowe changes names to simple identifiers: man, woman, or person.

"When we see language complexity popping up, we have to ask, is this necessary to the mathematical development?," says Zahner. "If it's not, can we take it out or plan around it?"

On assessments, Rowe also provides students with a recording of all test questions-audio files saved to Dropbox or Google Drive and represented as a scannable QR code on students' test sheets. This helps because most ELLs' receptive or oral language proficiency is higher than their reading proficiency. Through school-provided devices or students' own phones, students hear Rowe read each question-sometimes word-for-word or paraphrased, with steps to get started, or breaking down the question in ways that they'll understand.

Context vs. Content

In addition to removing unnecessary language, Zahner advises teachers to think carefully about the number and types of contexts used to develop a mathematical concept. Although it may be helpful to use multiple contexts to show students that math concepts are all around them, don't make students master a multitude of scenarios just so they can access the math content. In one text, Zahner's team found 12 different problem contexts used to explain linear functions.

"If you've never driven on a toll road and a problem is asking you to calculate the per-mile toll, but you're stuck on what is a toll?, that's going to stop you from accessing the content," he says. Instead, Zahner suggests focusing on a few relevant, key contexts. One way to do that is to find out what students are interested in and build math problems with those contexts. For example, teachers he works with recently changed a problem about pumping water out of a pool to one about rates for downloading files to your phone. "When the teacher introduced this context, everyone was engaged because all kids have opinions about who's got the good network or good rates."

"Keep in the forefront of your mind, 'What do I want students to do?', and build your question around that," says Eatmon. Simplifying the language doesn't mean watering down the math. Keep expectations high that these kids can do the math you've taught them, she adds.

Equal Signs

Planning for language supports in math helps ELLs communicate their ideas and invites them into STEM, which can have a profound effect on their career and earning opportunities, says MacDonald. "It's this huge, epistemic equity issue."

"If we equitably involve ELLs in math-position them as idea-generators alongside their peers, instead of just passive listeners-their language is going to develop much more quickly because they'll be creating and negotiating meaning together," MacDonald adds.

Eatmon urges educators not to confuse a lack of language for a lack of intellect. With the right supports, it does not take long for their wheels to catch traction and take off, she says. Eatmon has seen ELLs make five to six years of growth over the course of one year. "It's not that they can't do it; it's that they've never been taught."

Figure 1

© 2017 The Board of Regents of the University of Wisconsin System. Used by permission. Stem4els.wceruw.org.

Figure 2

© 2017 The Board of Regents of the University of Wisconsin System. Used by permission. Stem4els.wceruw.org.

Laura Varlas is the managing editor of ASCD Express and a contributor to Education Update.

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Laura Varlas At her district's newcomer center, English as a Second Language teacher Barbara Gottschalk would engage parents in a visual exercise: compare a math textbook from 20 years ago to the one in use today. The former, a familiar reproduction of the kind of math newcomers most likely experienced in their home countries, was defined by rows of computation.

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TIPS for English Language Learners in Math.

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TIPS for English Language Learners in Math.

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Grades 7,8,9,10

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Why teach coding?

Simply put, coding can change and impact people's lives.

The effect technology - as a result of computer code - has on this world is incredible. What used to be thought of as impossible is now made possible. What's more amazing is that our technological accomplishments always open up new realms of possibilities. Cellphones, for instance, didn't stop at phone calls - they led to streaming music and eBooks and brain teasing games and the ability to map the night sky.

This suggests that learning technology and its underlying language - coding - is extremely powerful.

Coding In the Math Classroom

Coding isn't easy - learning it or teaching it. But I think we can all agree that this skill will become more and more important over time. President Obama said it himself, that American students should learn computer science if we want to stay on the "cutting edge" and remain competitive. Recently, I asked my students, "Do you think people will use computers more in the future, or less?" "More!" they all replied.

If all of this is true, then what am I doing as a math teacher to prepare these kids for what lies ahead?

I began the year reflecting on the importance of learning the 21st century skill of coding. In particular, I wondered how I could integrate coding into my classroom. This was a challenge. A couple of questions immediately came to mind:

How can I teach coding without forfeiting math content?

Rather than teaching code as a stand alone subject, how can coding be useful in supporting students' understanding of math concepts?

Coding as a Bridge to Mathematics

I tinkered around with a few types of coding software that allowed me to build a game, so I could see what the possibilities were. I built a simple game, and I do mean simple, but the development process took hours. My self-learning project began with one objective: make a cat on the screen dodge falling watermelons. That's it. It sounded simple enough in my head, but it wasn't long until I realized that even coding a simple game required a lot of thinking. How will I make the cat move? How will the watermelons fall? How will the computer know that I won? In general, how can I tell the computer to do what I want?

I realized that coding requires many of the same skills that we use in math, such as critical thinking and problem solving. Developing my simple cat game required me to "make sense of problems and persevere on a task," which sounds a lot like one of our eight Common Core Mathematical Practices. This led me to think about the rationale behind the eight practices. Teaching the mathematical practices are just as important as teaching the math content. We want students to learn math and solve problems, but we also want students to learn how to approach problems. We want students to make sense of problems, critique the reasoning of others, analyze errors and solutions, contextualize and decontextualize problems - the list goes on.

Coding can help students make sense of these eight mathematical practices. Of course, coding is just one suggestion, and I'm not saying that it's the best way to make the mathematical practices concrete for students. However, there is certainly an opportunity for math educators to integrate coding into their instruction. Besides reflecting the eight mathematical practices, coding may also help students improve their attitude towards problem solving. Just like completing any challenging math problem or finishing a difficult puzzle, the final product of my simple cat game left a satisfying impression. I felt proud of my accomplishments and hungered for a much more challenging project. In fact, this is what "learning" should feel like. I hope that in my math classes, students feel proud of their accomplishments and seek out new challenges.

My "Getting Better Together" Project

Are there other ways to integrate coding into the math classroom? I absolutely love utilizing technology in my instruction, and I'm constantly looking for ways to do more. I'm currently using resources from Code.org and ScratchED to get students to understand the behavior and language of coding.

Here's a little bit of context about who will be involved in this coding work: Students in my algebra support class - students who need extra support in that subject area - will be participating in coding once a week. These students take two math classes a day, and they were originally put in these classes to enrich and support their algebra work. I will be observing to see if teaching my students how to code will result in student growth. This will require some data collection to show evidence of effective instruction.

There are three projects that I want my students to finish by the end of the year. First, my students will create artwork using the Code.org platform. Second, I want students to draw connections to math concepts learned in their Algebra classes with their projects in coding. Lastly (if time allows), I want kids to create their own game using the ScratchED platform, present their final product, and share it with their peers. Through these projects, I want students to achieve these learning goals:

Reflect on the power of coding and how it can affect people's lives

Explain why learning how to code is important and relevant

Use constructive feedback to modify and analyze errors in coding

Share and critique games and code to enhance the user's experience

Persevere on a difficult task, especially if a problem seems unsolvable

Take ownership of their project and learning

Make connections and apply their coding skills to other classes

I'm looking forward to getting this project off the ground and I'm seeking guidance and feedback from the Tch community. I'm reaching out to other educators who have taught coding in their classrooms. I'm also wondering if there are any math teachers who have experience integrating coding into their classrooms to support students' understanding of mathematics. I feel that this is an ambitious project for me, a novice at teaching coding, and a project with an unforeseeable ending.

I anticipate many challenges ahead, but the whole point of Getting Better Together is to create a project that is impossible to do alone. Why should we settle for something small, when we could be dreaming big?
Josh Kwon teaches math at Mariner High School in Everett, WA. He is affiliated with the Martinez Foundation, which provides support programs to teachers of color in underserved public schools. He's devoting his time to finding innovative ways to teach math that will reach and engage diverse students. Connect with Josh on Twitter: @Jkwon0608.

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Why teach coding? Simply put, coding can change and impact people's lives. The effect technology - as a result of computer code - has on this world is incredible. What used to be thought of as impossible is now made possible. What's more amazing is that our technological accomplishments always open up new realms of possibilities.

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Hour of Code

This year, we're taking Hour of Code to new heights by offering coding opportunities that encompass both artificial intelligence (AI) and non-AI components.

Want to keep learning? Go beyond an hour

Teachers: Host an hour or read the How-To Guide

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Use computer science to explore and learn about AI!

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Why is Coding Important for 21st Century Kids

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As the world goes through an indefinite lockdown, one thing we all can relate to is boredom. This boulder of boredom falls a bit harder on parents as they take care of not only their own but their kid/s' boredom too. If you are one such parent, you're about to find a leading-edge solution to your problem. Increasingly gaining popularity, it may have crossed your mind already but if it has not, here it is - CODING! Yes, this period is a wonderful opportunity to make your kids learn to code which is an immensely appreciated ability to have in the 21st century. Now, you may wonder why is coding important, or is it worth it. It absolutely is! Read on to find out all that you need to know about coding for kids and get rid of all your confusion as you learn about the benefits of learning to code.

Why Is Coding Important?

First things first: what is coding and why is everybody talking about it?

Coding has intricately blended with our everyday lives - sending texts and emojis, sharing memes and jokes on smartphones, watching videos, booking movie tickets, traveling, ordering food on a Sunday afternoon while sitting in your comfy pajamas, watching Netflix; almost everything is now possible with a few taps and swipes all by coding. Moreover, looking at the direction in which technology is advancing and how it's transforming everything around us, it can be safely said that almost every job right now requires some form of computer literacy. And the possibility that jobs coming up in the near future might even require at least basic level coding, explains the importance of coding for kids. Let's have a deeper look at the benefits of learning to code.

Technology is a useful servant but a dangerous master.
- Christian Lous Lange

Today's generation is growing up in the era of ubiquitous technology, including computers and the internet. Kids these days know how to unlock cell phones, play games, and watch videos before they can even speak properly. As they grow, their proficiency in using technology further increases. But most of them don't know what goes on at the back-end that allows them all of this with such ease. Being unaware of how a certain thing happens tends to make you its slave with use and you gradually become so dependent on it that you lose your ability to think and to function without it. If kids learn to code, they can save themselves from this trap.

This was one of the many benefits of learning to code. Another major benefit is the chance to make a secure career. According to an analysis of 26 million job postings by job market analytics firm Burning Glass, about half of the jobs paying $57,000 or more per year are in occupations that commonly require applicants to have at least some computer coding knowledge. In fact, on average, jobs requiring coding skills pay $22,000 more per year than jobs that don't. They also rank among the top ten highest paying job s. Besides, coding for kids becomes rewarding when it makes them a desirable pick for recruiters, as it adds versatility to their skill set.

Till now, we've been looking at the benefits of learning to code from the perspective of the world. Does this mean there isn't much for your kids' personal growth?

Of course not! The benefits of learning to code are plenty. You teach kids to code and it brings along a boost to their creativity and cognitive skills, improves memory, adds to their brainpower, and fuels present-mindedness. Children who learn to code achieve problem-solving skills and relate to the world around them better. How? Coding essentially involves taking bigger problems and breaking them down into smaller and simpler problems. Once they get used to it, children approach problems in every other domain of their life in a similar fashion. It thus helps them deal with those seemingly daunting problems more easily and efficiently.

Moreover, learning to code can be an exciting opportunity for a family to bond and have fun together. When kids learn to code at home, parents can accompany them in this productive and fun-filled activity, and get to know them better. Another benefit of learning to code is that it is a confidence booster. Learning a new skill, something which is looked up to fosters greater confidence in children. Apart from these, coding helps with math skills and improves overall academic performance too. To further authenticate why coding is important, let's hear it from one of the biggest players of computer technology today -

Learning to write programs stretches your minds, and helps you think better, creates a way of thinking about things that I think is helpful in all domains.
- Bill Gates

How to Teach Kids to Code?

Now you know why coding is important. The next question that arises is how does one teach kids to code? The world of coding is huge but if you enter through the right door, you won't get lost. Scratch coding for kids is an ideal start for them. Scratch is a programming language especially designed for kids ages 8-16 but can be used by anyone who wishes to learn to code. There are multiple scratch-based online coding courses for kids that offer easy and understandable learning for beginners. But it is important to look for a course that takes your kids through step by step guidance on coding, just like the process of coding itself. Good online coding courses don't only teach kids to code, but let them realize all the above-mentioned benefits also. However, the best thing about online coding courses for kids is that they let your tiny tots learn to code at home. And you can make the most of it in this quarantine period. Now, here's a course that ticks all the boxes for a perfect course on coding for beginners.

Learn to Code at Home

Here ends your search for the right online coding course for kids. Introduction to Programming is STEMpedia's newly launched programming course with Scratch coding for kids at its core. It has been designed keeping in mind the current time, to make your kid's time at home worthwhile. You can teach kids to code from the comfort of your home with this engaging course where they'll enjoy learning by doing, attend live tutoring sessions, keep a check on their progress with fun quizzes and assignments, all of which will provide them a better understanding of the concepts. Besides, the course also makes kids realize their responsibility towards the pandemic crisis through a COVID-19 themed challenge at the end. The course works on PictoBlox, an easy and fun programming language based on Scratch. All in all, Introduction to Programming proves to be one of the best online coding courses for kids.

In a Nutshell

Coding is in a true sense, the building block of the technology of today and the future. Learning how to code is fast becoming a must for the generation of today. Not only is it going to help them become better innovators and develop skills necessary in the world of STEM, but it will also enhance personal development. And what could be a better time than now to teach kids to code when there's no academic pressure and they can easily learn to code at home? Don't let your kids lose the enthusiasm to learn amidst the chaos of the pandemic when they can safely learn to code at home and give them a skill for a lifetime.

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Learn to Code: Why is Coding Important for Kids - STEMpedia

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As the world goes through an indefinite lockdown, one thing we all can relate to is boredom. This boulder of boredom falls a bit harder on parents as they take care of not only their own but their kid/s' boredom too. If you are one such parent, you're about to find a leading-edge solution to your problem.

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ADHD As A Difference In Cognition, Not A Disorder: Stephen Tonti 

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ADHD As A Difference In Cognition, Not A Disorder: Stephen Tonti 

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ADHD As A Difference In Cognition, Not A Disorder: Stephen Tonti at TEDxCMU

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Living with ADHD in the age of information and social media | Theo Siggelakis 

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Living with ADHD in the age of information and social media | Theo Siggelakis 

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Living with ADHD in the age of information and social media | Theo Siggelakis | TEDxQuinnipiacU

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About the Author

About the Author

The Understood Team is made up of passionate writers, editors, and community moderators. Many of them learn and think differently, or have kids who do.

Reviewed by

Reviewed by

Daniel Ansari, PhD is a professor in developmental cognitive neuroscience at Western University, Canada.

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The Understood Team is made up of passionate writers, editors, and community moderators. Many of them learn and think differently, or have kids who do. Daniel Ansari, PhD is a professor in developmental cognitive neuroscience at Western University, Canada.

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Poster - supporting students with dyscalculia

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Poster - supporting students with dyscalculia

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What Is It?

noun [dys-cal-cu-li-a] - impaired ability to learn grade-appropriate mathematics

Most of us know that dyslexia is a learning disorder that affects reading and writing skills, but its math-challenged alter ego, dyscalculia, is light years away from being a household word.

Dyscalculia is also known as a mathematics disability or disorder. Experts say about three to 11 percent of the general population experiences it - about the same as the rate of dyslexia. And two-thirds of those with dyscalculia also have dyslexia. What's more, dyscalculia has also been found to co-occur with attention deficit disorders.

There is much less research on dyscalculia than dyslexia, despite the high incidence, says Daniel Ansari, who studies the disorder as the Canada Research Chair in developmental cognitive neuroscience at the University of Western Ontario. One reason? There may be less demand for dyscalculia solutions because it has somehow become socially acceptable to be 'useless' at math, says Vancouver dyscalculia tutor, Susan Hall. It is, for example, considered nowhere near as devastating as being unable to read, she says.

In his ongoing research, however, Dr. Ansari says he hopes to pinpoint early predictors of dyscalculia, with an eye to early diagnosis and remediation. Burgeoning research in the field, using brain scans, has located the disorder in the brain's parietal cortex. This is where experts believe structural and functional abnormalities create a disconnect between interpreting numeric symbols and the quantities they represent - much like a child with dyslexia will have trouble accessing the sound of a letter of the alphabet.

Dr. Ansari says all parents need to understand that instilling basic math concepts should be as much a part of daily life as the bedtime book. Everything from setting the table to counting out bus fare can boost a child's math comfort level. In the meantime, children suffering serious math difficulties often find treatment within dyslexia treatment circles.

A Case Study

Cassidy Engleby, 11, had severe problems with math since Grade 1, when the concept of addition eluded her.

The Coquitlam, BC girl, "...did not get the concept of numbers. They made no sense to her," says Cassidy's mom, Judy Larocque. "Cassidy spent a lot of Grade 1 with headaches and stomachaches due to the stress and frustration she felt in the classroom."

In addition to a math disorder, Cassidy also struggles with dyslexia and attention deficit disorder, but working with Susan Hall on both the dyslexia and dyscalculia fronts has worked wonders. Hall's private program is called the Davis method, named for creator Ron Davis, himself a dyslexic and the founder of an international dyslexia association. The system relies on tactile props such as clay balls to help children visualize concepts such as adding.

For Cassidy, the method has given her the boost she needed to progress in school. "Cassidy made the honour roll on her last report card," says Larocque. "I would not hesitate to say yes, it worked. Cassidy is sporting a B in math, when in the past it was difficult to stay at a C."

Is Your Child Dyscalculic?

The following symptoms often appear in primary school, according to aboutdyscalculia.org

1. Delay In Counting

Five- to sevenyear-old dyscalculic children show less understanding of basic counting principles than their peers (for example, they may think that it doesn't matter what order objects are counted in).

2. Delay In Using Counting Strategies For Addition

Dyscalculic children tend to kee pusing inefficient strategies for calculating addition facts much longer than their peers.

3. Difficulties In Memorizing Arithmetic Facts

Dyscalculic children have great difficulty in memorizing simple addition, subtraction and multiplication facts (e.g. 5 + 4 = 9), and this difficulty persists up to at least the age of thirteen.

Symptoms Still Being Researched:

1. Lack of 'Number Sense'

Dyscalculic children may have a fundamental difficulty in understanding quantity. They are slower at even very simple quantity tasks such as comparing two numbers (which is bigger, seven or nine?), and saying how many there are in groups of one to three objects.

2. Less Automatic Processing of Written Numbers

For most of us, reading the symbol '7' immediately causes our sense of quantity to be accessed. In dyscalculics this access appears to be slower and takes more effort. Thus, dyscalculic children may have difficulty in linking written or spoken numbers to the idea of quantity.

Resources:

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What Is It? noun [dys-cal-cu-li-a] - impaired ability to learn grade-appropriate mathematics Most of us know that dyslexia is a learning disorder that affects reading and writing skills, but its math-challenged alter ego, dyscalculia, is light years away from being a household word. Dyscalculia is also known as a mathematics disability or disorder.

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Misunderstood Minds . Math Difficulties | PBS

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In the late 1980s, the National Council of Teachers of Mathematics revised content and methods standards for the teaching of mathematics. At the same time, standards-based tests with rigorous math sections were included as part of the graduation requirements in many schools.

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How we can meet their needs.

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Today, as usual, Mrs. Johnson began her 3rd-grade math class by reading aloud a thinking puzzle: Charlie, the dog, was tied to a 2-meter rope. His favorite ball was lying in the grass at least 10 yards away from him. He managed to grasp the ball easily. How did he manage to do this?
Nathan's hand flew into the air just microseconds after his teacher finished posing the question. While his classmates were pondering the problem, Nathan had already formulated the answer. Surprising even Mrs. Johnson, Nathan immediately found the lateral thinking puzzle required little effort and absolutely no math. While other students were converting meters to yards, moving decimal points, and drawing pictures, Nathan realized that the other end of the rope was not attached to anything; the dog merely had a 2-meter rope tied to his collar, but was not tethered at all.

Whether Nathan had heard the "riddle" before or whether he surmised that mathematics couldn't solve the scenario remains a mystery. Nevertheless, most teachers have had similar experiences with children who are talented in mathematics and strong in logical reasoning. Unfortunately, many programs for gifted children are inadequate and poorly designed (Heid, 1983), leaving classroom teachers to struggle to meet the needs of gifted children effectively. What resources are available for these students? What assessment tools are appropriate? Do these children need acceleration or enrichment? How can we meet their needs when there are so many other demands on teachers' time? This article will address these and other questions in an attempt to shed some light on the difficult issues of challenging and nurturing children who demonstrate talent in the field of mathematics.

Characteristics of the Gifted Math Student

Whether math problems require computation skills, problem-solving strategies, inferential thinking skills, or deductive reasoning, mathematically talented students are often able to discern answers with unusual speed and accuracy. Mathematically gifted students are able to see relationships among topics, concepts, and ideas without the intervention of formal instruction specifically geared to that particular content (Heid, 1983). Due to their intuitive understanding of mathematical function and processes, they may skip over steps and be unable to explain how they arrived at the correct answer to a problem (Greenes, 1981).

For example, Mariah, an energetic, 6th-grade prealgebra student, often seems disinterested during her hourlong math class, as she doodles and appears to be preoccupied. While the teacher demonstrates the steps required for calculating the correct answer to 4b + 11= 2b + 23, Mariah leafs through her history folder. After all, she can solve these linear algebraic equations in just one step. Like many gifted students, she barely listens to the teacher's directions, does not write page numbers in her assignment book, and does not make eye contact with the teacher. Mariah views practicing step-by-step processes as a waste of time when solutions can be found by just looking at the problem.

Students who are talented in mathematics often demonstrate an uneven pattern of mathematical understanding and development, since some are much stronger in concept development than they are in computation (Rotigel, 2000; Sheffield, 1994). Gifted math students often want to know more about the "hows" and "whys" of mathematical ideas than the computational "how-to" processes (Sheffield). Since these children often prefer to learn all they can about a particular mathematical idea before leaving it for new concepts, a more expansive approach to mathematics based upon student interest may avoid the frustration that occurs when the regular classroom schedule demands that it is time to move on to another topic. A more linear approach to mathematics is often a better match for gifted children instead of the spiral curricula often found in textbook series and followed by classroom teachers. For example, when the topic of decimals is introduced, children with mathematical talent can be allowed to delve much further into the topic, learning practical applications for decimals and the connections between decimals and other mathematical topics.

Many of these students' gifted characteristics emerge during the preschool years. Bailey, a mathematically precocious 5-year-old, understands that numbers have patterns and relationships to real life. While watching a series of movie previews at the local theater, she can skillfully decide which new releases will occur before or after she turns 6 simply by noting their release dates in the upcoming year. Parents of preschoolers may report that their child demonstrates an unusual interest in mathematical concepts and particularly enjoys games involving numbers. At an early age, some gifted students note relationships between products and prices in the grocery store, the passage of time, changes in weather temperatures, and measurements of distances. Parents of these "number sense gurus" are fascinated by their children's precociousness, but are often unaware of the significance or relevance of these early mathematical discoveries.

By the time these emergent mathematical geniuses arrive for their first formal math lessons in kindergarten, they may have already established their own unique theories of number sense, sequences and patterns, problem solving, and computational strategies. Too frequently, the teachers following the curriculum merely touch on many math concepts, failing to recognize and nurture young mathematicians (Pletan, Robinson, Berninger, & Abbott, 1995). Formal instruction in elementary school classrooms often lacks challenge for the gifted learner since courses in regular classrooms sometimes have a relatively narrow range of topics, minimal investigation of concepts, repeated drill and practice, and yearly repetition. The basic mathematical concepts that are presented in kindergarten and 1st grade can be a particular problem for children who have already mastered number recognition, one-to-one correspondence, and counting. Recent studies indicate that few instructional adaptations are made to accommodate these young learners' needs (Archambault, Westberg, Brown, Hallmark, Emmons, & Zhang, 1993). Students gifted in mathematical thinking and problem solving need greater depth and breadth of topics and openended opportunities for solving more complex problems (Sheffield, 1994).

Challenges for School Districts

Misunderstandings regarding the nature of giftedness and talent abound, and busy teachers and administrators are sometimes at a loss to know how to nurture and challenge children whose abilities belie their age-based grade-level placement. However, according to the Principles and Standards for School Mathematics (National Council of Teachers of Mathematics, 2000, p. 13), these students must be supported so that they too have an opportunity to reach their mathematical potential. All too often, the regular curriculum is insufficient in depth, breadth, and pace to meet the needs of the gifted child (Wolfle, 1986). In addition, the recent emphasis on state standardized testing programs has increased the use of basic skills instruction and drill in an attempt to assure that all students will be successful on these tests (Moon, Brighton, & Callahan, 2002). A great deal of research supports the conclusion that gifted students need to use advanced materials and curricula if they are to reach their potential (Reis, Westberg, Kulikowich, & Purcell, 1998; VanTassel-Baska, 1995, 1998a).

Most educational settings do not adequately address and meet the needs of gifted students, and most teachers make only a few minor modifications to the curriculum when attempting to teach them (Archambault et al., 1993). Planning for 12 years of mathematics instruction for all students has sent many administrators and district curriculum specialists scrambling for the latest research on best practices, and the notion of meeting the needs of mathematically advanced students adds complexity to the task. The dilemma of choosing between acceleration to an advanced math class placement and providing planned enrichment activities within the regular classroom setting plagues math coordinators, curriculum specialists, superintendents, and parents.

The Critical Role of Assessment

According to the Principles and Standards for School Mathematics (NCTM, 2000, p. 23), assessment and instruction should be integrated so that assessment provides information for the teacher to use to make instructional decisions. Children who demonstrate high achievement in mathematics should be carefully evaluated to determine the extent of their talent and provide a profile of their strengths and weaknesses (Lupkowski-Shoplik, Sayler, & Assouline, 1994). Grade-level achievement test results can be somewhat helpful, for if a student scores extremely well, it may indicate that mathematics is an area of strength for him or her.

If a child scores at or above the 95th percentile on a grade-level achievement test, it is possible that the test did not have enough items of appropriate difficulty for the child, thus the score may not indicate his or her true level of understanding. In this case, it may be necessary to administer an above-level test that will contain more items of higher difficulty. Julian Stanley pioneered this concept in 1971 when he began the talent searches (Stanley & Benbow, 1986), and 30 years worth of research have shown that out-of-level testing is a valuable tool for determining the level of programmatic modification that is needed for a gifted student.

Although a variety of standardized tests may be used for out-of-level testing, research has demonstrated the effectiveness of the EXPLORE test to identify talented elementary school students (Colangelo, Assouline, & Lu, 1994; Rotigel, 2000; Rotigel & Lupkowski- Shoplik, 1999). The EXPLORE (American College Testing Program, 1997) was developed for 8th-grade students and therefore contains a sufficient number of higher level items to allow students to demonstrate their proficiency more fully. According to ACT, the EXPLORE is directly related to student educational progress and includes a large number of complex problem-solving items and fewer measures of narrow skills. Many of the regional talent searches around the country offer EXPLORE testing in mathematics, as well as other subject areas.

No evaluation should be based simply on standardized testing, however. Teacher observations, classroom-based assessment, daily performance, and social and emotional needs must be included in the evaluation. It is important that data be gathered and analyzed by a multidisciplinary team of educators who are able to make and carry out educational recommendations for the student.

Program Evaluation and Curricular Collaboration

From the administrative perspective, a needs assessment could be conducted with all math teachers to determine each teacher's individual perceptions, teaching methods, and curricular successes or problems. An investigation of repeated topics, overlapping concepts, and ineffective activities could identify weaknesses in the math program. In order to meet students' needs, many concepts and topics in the curriculum could be compacted (Reis et al., 1998). For example, ratios and proportions could be coupled with simple fractional portions of sets. Some measurement or temperature concepts could be integrated into other curricular areas like science, thus allowing for more enrichment lessons in visual logic, inferential thinking, and deductive reasoning. According to VanTassel-Baska (1998b), efficient use of time is an important consideration in the development of talent.

Challenges for Teachers

Differentiation of Instruction

Once a sufficient foundation of information is gathered, an individualized plan can be established for each mathematically gifted student. It then becomes the responsibility of classroom teachers to implement the program. The plan may include enrichment experiences; differentiation of instruction, including pretesting and compacting the curriculum; flexible cluster grouping by topic or mathematics achievement; grade skipping in math; mentoring; and increased use of technology. The decision regarding which level of intervention is necessary should be based upon the evaluation. Highly gifted students may require more intense modification such as grade skipping in mathematics. Rather than choosing one method over the other, research indicates that a combination of these approaches makes for a stronger program for divergent math thinkers (Stanley & Benbow, 1986). Daily ongoing assessment, teacher observations, achievement tests, and above-level testing can all be helpful in determining the type of program that will best meet the needs of each gifted child.

Defined by Tomlinson (1995), differentiated instruction is "the consistent use of a variety of instructional approaches to modify content, process, and/or products in response to the learning readiness and interest of academically diverse students." Teachers must add components to each lesson and modify the content for the high-ability students, as well as for those who need remediation. For example, a lesson on calculating the area of polygons might include just the basic formula for most students, but should provide various real-world applications of calculating area for gifted learners. The increased complexity of the problems should require higher order thinking skills and provide opportunities for open-ended responses. Effective differentiation of instruction is very different from the unfortunate practice of simply assigning 20 problems to the gifted child while the remainder of the class is given only 10. "More of the same piled higher" is inappropriate and may lead children to conceal their abilities in order to avoid the extra, unnecessary work.

The task of differentiating each lesson requires accessing additional resources, planning for small-group interaction, and perhaps even modifying lessons during delivery (Tomlinson, 1995). In most instructional settings, the mathematical understanding and performance of the students is diverse, so classroom teachers plan their instruction with a myriad of learners and learning styles as the focus. Using a pretesting component in the math program allows for the identification of attained skills, strategies, and achieved concepts prior to the beginning of a new unit. For the gifted population, this helps eliminate the repetition from year to year in the mathematics curriculum. Pretesting and compacting the curriculum allows for a diagnostic approach for planning the teacher's instruction and allows educators to have a more accurate account of the skills and concepts students have mastered and those they have yet to be introduced to or need to strengthen. This process provides the foundation for effective differentiation of instruction, as each student should receive instruction based upon his or her identified instructional level (Howley, 2002). As noted by Winebrenner (2003), gifted students whose programs have been compacted can spend time working on their differentiated activities while their classmates are preparing for state assessments.

Enrichment and Grouping

It is certainly possible to meet the needs of some gifted students simply by enriching and modifying the existing mathematics curriculum. Enrichment is designed to expose students to a variety of topics related to those of the regular education program and to allow for further investigation of them.

In cases where math students are grouped according to their understanding of mathematical concepts and ideas, teachers can cover concepts at an appropriate pace for the group. Pretesting and compacting of the curriculum are helpful here, as they allow the group of mathematically talented students to be appropriately challenged. In addition, a classroom of homogeneously grouped gifted students would enable a teacher to apply the Enrichment Triad Model (Renzulli, 1977). For example, once students have mastered basic algebraic concepts, additional learning opportunities would be provided in the area of divergent thinking, individual projects, and group activities that would connect those algebraic concepts with real-world events and scenarios.

Acceleration and Technology

Since many mathematically talented students have already mastered the basic skills, the enrichment activities and advanced projects their teachers have planned may not provide sufficient challenge. Indeed, for many talented youngsters, some degree of acceleration is needed based on their demonstrated achievement and ability. Simply working in the highest math class at their grade level may not meet gifted learners' needs, regardless of how well the teacher has differentiated the lessons. Gifted students may have already acquired the content and concepts presented in these classes, so acceleration to a math class at a higher grade level may be the most viable option. However, Lewis (2002) cautioned that acceleration should not be done unless it also meets the student's affective needs, which is sometimes difficult to determine.

Although accelerating a student to a higher grade-level class can present logistical problems for teachers and administrators, it is important to match not only the mathematical content with the learner's needs, but also to provide an appropriate pace of instruction for his or her rate of acquisition. Acceleration may be the only way to accomplish this. Classroom experience and research demonstrate that, even though they may be younger, children who are exceptionally talented in mathematics will learn material much more quickly and with fewer repetitions than the regular curriculum allows (Sowell, 1993). Thus, the repetitions of a spiral curriculum become redundant and mundane to a gifted math student. On the other hand, gifted students in accelerated classes have opportunities to work with advanced concepts, in-depth topic investigations, and problems with real-world applicability.

Many advances in technology can assist the classroom teacher in meeting the learning needs of gifted math students by providing opportunities to explore complex problems and mathematical ideas (NCTM, 2000, p. 14). Readily accessible classroom computers, supervised access to the Internet, and appropriate software programs offer opportunities for gifted students to advance at their own rate.

A Conclusion That's Outside the Box

Teachers sometimes experience frustration when gifted children can arrive at correct answers through nontraditional methodologies or when some of their questions are far beyond the scope of the lesson at hand. Since gifted students can often interpret, predict, and analyze mathematical situations and problems better and faster than their teachers, a significantly different instructional approach may be necessary. Successful teachers of gifted learners adapt their teaching strategies to accommodate the students' unusual thinking strategies and methodologies. Unfortunately, inexperienced or untrained teachers sometimes make provisions for the gifted by assigning them enrichment worksheets, independent projects, or reports on famous mathematicians. Quantity, in this case, does not always equal quality (Greenes & Mode, 1999; Wolfle, 1986).

Being sensitive and aware of the unique characteristics of gifted students enables teachers to set more realistic expectations in the classroom. Teachers need to be confident in their own mathematical knowledge and teaching abilities in order to accept the divergent thinking abilities of their gifted students. In Mariah's case, traditional expectations of step-by-step problem solving with paperand- pencil assignments may not be appropriate. When gifted students are able to arrive at the correct answer by following an unmarked thinking path, teachers should acknowledge this creative, divergent problem-solving strategy and not reprimand the student through missed points or a lowered grade because of not following more traditional techniques. Teachers should adapt the content where appropriate, condense the concepts where applicable, alter the pace of content acquisition, and allow for open-ended, multiple solutions to problems.

Meeting the needs of each learner is the goal of every teacher, and each grade level has its own unique challenges. Whether it is the preschooler, Bailey, who can often make math connections without formal instruction; Nathan, the 3rd grader with the quirky thinking style; or Mariah, the prealgebra student who "sees" the answer without doing the work, each student thinks "outside the box." Accessing all available resources, using a variety of assessment tools, and choosing appropriate placements for each student are all aspects of meeting the individual needs of each learner. Being aware and sensitive to the unique characteristics of gifted learners will assist teachers in providing a myriad of opportunities for growth in mathematical reasoning and problem solving.

Author Note

The authors would like to thank Michael Bosse and Jacquie Gentile for their helpful comments on an earlier version of this paper.

References

American College Testing Program (ACT). (1997). EXPLORE technical manual. Iowa City, IA: Author.

Archambault, F. X., Westberg, K. L., Brown, S. W., Hallmark, B. W., Emmons, C. L., & Zhang, W. (1993). Regular classroom practices with gifted students: Results of a national survey of classroom teachers.

Storrs: The National Research Center on the Gifted and Talented, University of Connecticut.

Colangelo, N., Assouline, S. G., & Lu, W. (1994). Using EXPLORE as an above-level instrument in the search for elementary student talent. In N.

Colangelo, S. G. Assouline, & D. Ambroson (Eds.), Talent development II: Proceedings from the 1993 H. B. and Jocelyn Wallace National Research Symposium on Talent Development (pp. 281-297). Dayton: Ohio Psychology Press.

Greenes, C. (1981, February). Identifying the gifted student in mathematics. Arithmetic Teacher, 14-17.

Greenes, C., & Mode, M. (1999). Empowering teachers to discover, challenge, and support students with mathematical promise. In L. J.

Sheffield (Ed.), Developing mathematically promising students (pp. 121-132). Reston, VA: National Council of Teachers of Mathematics.

Heid, M. K. (1983). Characteristics and special needs of the gifted student in mathematics. Mathematics Teacher, 76, 221-226.

Howley, A. (2002). The progress of gifted students in a rural district that emphasized acceleration strategies. Roeper Review, 24, 158-160.

Lewis, G. (2002). Alternatives to acceleration for the highly gifted child. Roeper Review, 24, 130-134.

Lupkowski-Shoplik, A. E., Sayler, M. F., & Assouline, S. G. (1994). Mathematics achievement of talented elementary students: Basic concepts vs. computation.

In N. Colangelo, S. G. Assouline, & D. Ambroson (Eds.), Talent development II: Proceedings from the 1993 Henry B. and Jocelyn Wallace National Research Symposium on Talent Development (pp. 409-414). Dayton: Ohio Psychology Press.

Moon, T., Brighton, C., & Callahan, C. M. (2002). State standardized testing programs: Friend or foe of gifted education? Roeper Review, 25, 49-61.

National Council for Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. Reston, VA.: Author.

Pletan, M. D., Robinson, N. M., Berninger, V. W., & Abbott, R.D. (1995). Parents' observations of kindergarteners who are advanced in mathematical reasoning. Journal for the Education of the Gifted, 19, 30-44.

Reis, S. M., Westberg, K. L., Kulikowich, J. M., & Purcell, J. H. (1998). Curriculum compacting and achievement test scores: What does the research say? Gifted Child Quarterly, 42, 123-129.

Renzulli, J. (1977). The enrichment triad model: A guide for developing defensible programs for the gifted and talented. Mansfield Center, CT: Creative Learning Press.

Rotigel, J. V. (2000) Exceptional mathematical talent: Comparing achievement in concepts and computation. Unpublished doctoral dissertation, Indiana University of Pennsylvania.

Rotigel, J. V., & Lupkowski-Shoplik, A. (1999). Using talent searches to identify and meet the educational needs of mathematically talented youngsters. School Science and Mathematics, 99, 330-337.

Sheffield, L. J. (1994). The development of gifted and talented mathematics students and the National Council of Teachers of Mathematics Standards (Report No. RBDM 9404). Storrs: National Research Center on the Gifted and Talented, University of Connecticut. (ERIC Document Reproduction Service No. ED388011).

Sowell, E. J. (1993). Programs for mathematically gifted students: A review of empirical research. Gifted Child Quarterly, 37, 124-129.

Stanley, J. C., & Benbow, C. P. (1986). Youths who reason exceptionally well mathematically. In R. J. Sternberg & J. E. Davidson (Eds.), Conceptions of giftedness (pp. 362-387). New York: Cambridge University Press.

Tomlinson, C. A. (1995). Deciding to differentiate instruction in middle school: One school's journey. Gifted Child Quarterly, 39, 77-87.

VanTassel-Baska, J. (1995). The development of talent through curriculum. Roeper Review, 18, 98-102.

VanTassel-Baska, J. (1998a). Excellence in educating gifted and talented learners (3rd ed.). Denver: Love.

VanTassel-Baska, J. (1998b). The development of academic talent. Phi Delta Kappan, 79, 760-764.

Winebrenner, S. (2003). Teaching strategies for twice-exceptional students. Intervention in School and Clinic, 38, 131-137.

Wolfle, J. A. (1986). Enriching the mathematics program for middle school gifted students. Roeper Review, 9, 81-85.

Educator on 7/16/2014

Is there a particular math curriculum that you would suggest for mathematically gifted students who are not in need of grade acceleration, but need a more rigorous program? I'd like one program that follows the grade level curriculum throughout the year with a greater amount of depth and breadth on concepts than offered by the general classroom curriculum. Most of what I've seen needs to be piecemealed together to create one cohesive program.

The appearance of any information in the Davidson Institute's Database does not imply an endorsement by, or any affiliation with, the Davidson Institute. All information presented is for informational purposes only and is solely the opinion of and the responsibility of the author. Although reasonable effort is made to present accurate information, the Davidson Institute makes no guarantees of any kind, including as to accuracy or completeness. Use of such information is at the sole risk of the reader.

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Mathematically Gifted Students: How Can We Meet Their Needs?

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Today, as usual, Mrs. Johnson began her 3rd-grade math class by reading aloud a thinking puzzle: Charlie, the dog, was tied to a 2-meter rope. His favorite ball was lying in the grass at least 10 yards away from him. He managed to grasp the ball easily.

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Pascal’s Triangle

Fibonnaci Sequences

Decision Trees

Hidato puzzles

Shikaku puzzles

Math Contests for Kids page at the WISE Math site

Teaching your students how to play chess

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5 Tips for improving student success in Math

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5 Tips for improving student success in Math

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What does it take to improve student success and interest in math? The Philadelphia-based Society for Industrial and Applied Mathematics (SIAM) asked more than 400 U.S. high school math teachers for their advice related to teaching and learning mathematics.

"The good news is that students can have success in math class with the right effort, attitude, and behavior, regardless of a natural affinity or being 'good at math,'" said Michelle Montgomery, project director of the MathWorks Math Modeling (M3) Challenge at SIAM. "Using quantitative skills to solve real, open-ended problems by employing the mathematical modeling process is a great way to get started."

The teachers surveyed were all coaches of student teams that participated in the M3 Challenge, a national, internet-based contest with no registration or participation fees. Thousands of high school juniors and seniors spend a weekend in March coming up with a solution to a real-world problem using mathematical modeling. To add a bit of pressure, when the students download the problem, they have only 14 hours to work on it. The 2018 event was the 13th annual contest.

What the Teachers Recommend

1. Build confidence. More than two-thirds of respondents (68 percent) cited lack of confidence as a problem that prevents their students from succeeding in mathematics.

2. Encourage questioning and make space for curiosity. Sixty-six percent of respondents said their best piece of advice for students looking to do well in math was to not only pay attention in class but also ask for clarification when they need to better understand something.

3. Emphasize conceptual understanding over procedure. Three out of four respondents (75 percent) emphasized that working hard to understand math concepts and when to apply them versus simply memorizing formulas is essential to doing well.

4. Provide authentic problems that increase students' drive to engage with math. Sixty-three percent of participants pointed to students' desire, initiative, and motivation to succeed in math as being critical, and the majority of them (80 percent) said that applying math to real-world problems helps increase both student interest and understanding.

5. Share positive attitudes about math. Teachers suggest that parents avoid talking negatively about math, and especially avoid saying that it is hard or useless (74 percent)-instead they should encourage their kids not to give up, and help them find math mentors when they're not able to answer questions (71 percent).

It's no coincidence that these teaching practices are a regular part of facilitating math modeling. Through modeling, students tackle relevant, authentic, real-world problems. According to Lauren Tabolinsky, academic program manager at MathWorks, making math relevant for students and careers is the reason MathWorks sponsors the M3 Challenge.

SIAM's Montgomery adds that "inherent in modeling work are things like motivation, identification of variables that affect the issue (no spoon feeding of data or approaches), gut checking of answers, and justifying solutions offered. The result? Interest and enthusiasm for working a problem, and the understanding that being able to use skills in your math toolbox can provide insight into relevant issues facing communities and the world today."

For example, the 2018 M3 Challenge problem was called " Better ate than never: Reducing wasted food." Students addressed an issue identified by the Food and Agriculture Organization of the United Nations: Approximately one-third of all food produced in the world for human consumption every year goes uneaten.

In the first part of the problem, student teams used mathematics to predict whether the food waste in a given state could feed all of the food-insecure people living there. In the second part, teams created a mathematical model that could be used to determine the amount of food waste a household generates in a year based on their traits and habits. They were given four different types of households to consider.

Finally the teams were challenged to make suggestions about how wasted food might be repurposed. They used mathematical modeling to provide insight into which strategies should be adopted to repurpose the maximal amount of food at the minimum cost, and they accounted for the costs and benefits associated with their strategies.

Because such problems are realistic, big, and messy, student teams have plenty of opportunity to make genuine choices about how they want to go about solving them, which mathematical tools they will apply to develop and test their models, and how they will communicate their solution. There's plenty of work to go around, so all team members can contribute.

If you relate this M3 Challenge modeling problem to the advice from the teacher coaches above, you can see why participation in math modeling competitions as a team sport can help students develop more mathematical confidence, competence, and interest.

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5 Tips for Improving Students' Success in Math

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What does it take to improve student success and interest in math? The Philadelphia-based Society for Industrial and Applied Mathematics (SIAM) asked more than 400 U.S. high school math teachers for their advice related to teaching and learning mathematics.

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This lesson is planned for grade 4

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This lesson based on teaching a grade 4 level of adding and subtracting with problem solving.
It is adapted for ELL, FNMI, Dyscalculia and Gifted Learners.

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First Peoples Principles of Learning - Implications for Mathematics Classrooms

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First Peoples Principles of Learning - Implications for Mathematics Classrooms

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Dyscalculia: Tips and Tricks to Help Students

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Dyscalculia: Tips and Tricks to Help Students

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Dyscalculia: Tips & Tricks to Help Students

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Math Journals - A Record for Students and Teachers

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Math Journals - A Record for Students and Teachers

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Discussion and Supporting Materials

Thought starters

1. How could math journals be used as an assessment tool?

2. What is Ms. Lassiter's role during math journal time?

3. How could you use math journals in your classroom?

School Details

Manatee Cove Elementary School
734 West Ohio Avenue
Orange City FL 32763

Data Provided By:

Teachers

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Math Journals: A Record for Students and Teachers

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Kindergarten teacher Karen Lassiter has her students record their thinking on individual topics in math journals. Karen explains that these journals provide a record for how students' thinking has changed and developed over time. As students work in their journals, Karen rotates around the room to assess and provide feedback.

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Making kids love math is a challenge to most parents. Math is a skill that takes a lot of brain power to master, and this can be experienced by kids as hard work. A University of Chicago and Western University 2012 study even shows that for some people, doing math is similar to experiencing physical pain. Also, parents tend to tell their kids that "math is hard", as they relive their own experience as kids struggling with formulas, exponents and equations. Consequently, kids pick up this attitude and live their lives believing that math is a horrible monster that they have to face in their academic lives.

Yet being skillful, or at least, competent in math is necessary to survive in modern life. We use math to figure out personal finances, construction projects, as well as doing everyday chores such as cooking and shopping. Engineering, high technology, finance and other in-demand careers require above average math skills. Even non-math careers require that employees have sharp analytic and reasoning skills - skills that are acquired when brains are trained in math.

Many studies suggest that early math training in kids give big benefits. It create changes to the kids' brains so that the kids become adept at problem solving. The kids' brains are primed for learning advanced math concepts. Also, a 2007 study published in the journal Developmental Psychology reveals that math skill at kindergarten is a stronger predictor of later school achievement than reading skills or the ability to pay attention.

The kids' first teachers, the parents, play an important role in kids' attitude to math. According to Susan C. Levine, a professor of psychology and comparative human development at the University of Chicago, parents who engage in "math talk" provide their kid with a solid math foundation for later math achievement. Those who explain to their kids about numbers and spatial relationships by way of gestures and words tend to instill better math skills at age 4.

Since kids are more receptive to learning when it is associated more with play than with work, it is a good idea for parents to expose kids to math in fun ways. The challenge to parents is to figure out ways on how to create simple interactions and early learning activities to serve as foundation for their kids to enjoy math.

Making math enjoyable help kids grow to associate math with fun, pleasure and parental love and attention. Instead of being afraid, the kids will be excited about the subject throughout their school years. The secret to successful math education is to make it so much fun that children don't even realize they are learning something that will help them later in life.

Here are some tips for you, the parent, to make math fun for your child:

Make math a game - Make your child consider math not as work but as a game that can be played like computer games, sports or fun board games. Use digital games, apps and numerous websites as resources for making math a game. There are numerous activity books that make math fun, as well as websites where you can download fun, early learning printables. See a list of free math websites here. Non-digital games are also fun. Encourage your child to play card and board games that involve calculations (For example, Chutes and Ladders and Monopoly). A 2009 study conducted by Carnegie Mellon and the University of Maryland found that preschoolers who played Chutes and Ladders improve math skills significantly compared to those in the study who played a different board game or did non-math tasks.

Make math real and meaningful - We are surrounded by real math problems in the form of money, measurement, time and others. Point this out to your child as you go with him through life. This includes checking and comparing prices at the grocery store, driving down the street counting mailboxes, reading recipes, calculating coupons, or even measuring food or drink at the dinner table. Before approaching the checkout counter in the grocery, ask your child to estimate how much the items will cost, and if he is within a dollar or so of the right amount, he wins a prize. Encourage your child to solve real-life problems outside of school. For example, in the toy store, ask her to calculate the price of a discounted toy and how long it will take to save up her allowance to buy it. For more ideas, download a copy of of Helping Your Child Learn Mathematics, which has dozens of activities for parents of elementary school students.

Encourage "mental math" so that your child learns to appreciate "number sense," which is defined by the University of North Carolina's School of Education as "an intuitive understanding of numbers, their relationships, and how they are affected by operations." Children with strong number sense are better problem solvers; they can approach solving a problem in different ways, identify errors in their work when they occur, and be more confident and interested in math because they understand that math is more than just a series of operations to be followed. Teach "mental math" as a game.

Give a reward when your child masters math skills like counting, doing addition or multiplication. The reward does not have to be expensive. It could be a special dessert or an extra hour watching TV. Make sure rewards are attached to a specific goal or accomplishment and not used inconsistently or inappropriately.

Make math a fun competition - You can play math games with a group of kids of similar ages, making a quiz show with points given to the kid who is first to say the correct answer to a math problem. The overall winner can win a prize such as a toy or a chocolate.

Read books with mathematical themes to your child such as Big Fat Hen by K. Baker (A hen lays eggs in quantities that increase by two, up to a total of ten. This book features number comparison, object grouping, addition, and subtraction.), How Many Bugs in a Box by D.A. Carter (a book about measurements), and A. Capucilli's Mrs. McTats and her Houseful of Cats (Mrs. McTats welcomes cats into her home, often in multiples, until she has a total of 25. Using good math vocabulary, this book encourages young children to think about adding more than one item at a time.) More list of books here: http://www.naeyc.org/files/tyc/file/MathbookslistSchickedanzexcerpt.pdf . See also the benefits of reading books to children.

Start your child young - You can begin teaching your child math concepts as early as his toddler stage. The toddler stage is the best time to introduce your child to math games as play because his brain is developmentally ready for it. Importantly, anything that you do with your toddler is fun for him. Below are basic mathematical concepts that you can help your young child learn through play:

1. Patterns - Pattern is important in math and science because the ability to discover and recognize patterns help us understand how our world works in logical and predictable ways. You can jump start your baby in experiencing patterns through fun games such as patty-cake, peek-a-boo, singing, dancing, touching of the nose and toes, and feeling different textures.

2. Sequence - Sequence is the organization and order of successive events and experiences. Recognizing sequences helps your child develop a sense of order, logic, and reason. An example of a play activity with your child that involves sequencing is playing with building blocks in a step-by-step way with a goal in mind, such as building a tall block tower. Reading to your child with emphasis on how the story logically unfolds builds a mind-set for rational and logical thinking.

3. Seriation - Seriation is a math concept that involves ordering things in a logical way, in other words, making them a series. Play with your kid using toys that can be manipulated, such as different sized stacking rings or blocks. Explore nesting them together. Do this in creative ways such as telling stories about the seriated sizes of the toys.

See a list of Educational Toys and Gifts to Help Make Your Kids Smart

4. Spatial relationships - This concept involves making your baby aware of her physical self and her relation with the world. It lays the foundation for more math concepts involving directionality. Games that teach spatial relationships include navigating through a play tunnel, and climbing on structures. For your older kid, playing with jigsaw puzzles, Rubik's cubes, and anything else that involves moving, rotating, or fitting objects together teach this concept. Doing puzzles together or using gestures to help describe spatial relationships such as "taller" and "shorter," can instill spatial abilities in your child.

5. Sorting - This is when things with similar attributes are grouped together. Play with your toddler by sorting different toys.

6. Comparing - Here, your child identifies and examine specific properties of different objects or ideas and then make judgments about how they are similar or different. Play with your child games that involve comparing objects' size, number or properties. With your older kid, you can compare ideas with him, such as dark vs. bright, apple vs. carrot, etc.

7. One-to-one correspondence - This is relating one item to another one item, and is the foundation of counting. You can play with your child a game that involves associating, giving out, or partnering one object to another object like each of his toy ("This one block is for this toy, one for this toy , one for this toy, etc.") . Soon (at about age 3) your child learns to relate the concept of one-to-one correspondence to rational counting, which involves keeping track while reciting a stable order of numerals to their one-to-one count.

Integrate math into fun activities - Find out what games or activities your child enjoy, and integrate math into it. If your child loves to bake or cook with you, for example, you can have your child measure ingredients in wholes or in parts, or count and estimate objects such as number of chocolate chips. One way to integrate subtraction problem, for example, is to ask your child, "We need to put five eggs, we already placed two eggs, how many more eggs do we need?" In road trips, you can play math games. When your child asks "Are we there yet?" a math problem. Ask how many more miles or kilometer before you reach your destination. For older kids, ask travel math problems such as "If the GPS says we will arrive at 5:30 and it is 5:13, how many more minutes before we reach the destination?" or "If we are traveling 60 miles per hour, and our destination is 120 miles, how long before we reach the destination?" If your child is a sports fun, teach him about the numbers used in sports such as scores, batting average, percentage of wins, and so on.

Click here for more infant brain stimulation ideas.

Importantly, never say negative math sentiments such as "Math is hard" or "You're like me, I'm not good in math" to your kid. Avoid unconsciously impressing on your child that he should fear math and that it's the hardest school subject to master . You should show the attitude that learning math is a natural thing, and in fact, can be fun.

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Making kids love math is a challenge to most parents. Math is a skill that takes a lot of brain power to master, and this can be experienced by kids as hard work. A University of Chicago and Western University 2012 study even shows that for some people, doing math is similar to experiencing physical pain.

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Screen time is an inescapable reality of modern childhood, with kids of every age spending hours upon hours in front of iPads, smartphones and televisions.

That's not always a bad thing: Educational apps and TV shows are great ways for children to sharpen their developing brains and hone their communication skills-not to mention the break these gadgets provide harried parents. But tread carefully: A number of troubling studies connect delayed cognitive development in kids with extended exposure to electronic media. The US Department of Health and Human Services estimates that American children spend a whopping seven hours a day in front of electronic media. Other statistics reveal that kids as young as two regularly play iPad games and have playroom toys that involve touch screens.
Saturation and long-term consequences
When very small children get hooked on tablets and smartphones, says Aric Sigman, an associate fellow of the British Psychological Society and a Fellow of Britain's Royal Society of Medicine, they can unintentionally cause permanent damage to their still-developing brains. Too much screen time too soon, he says, "is the very thing impeding the development of the abilities that parents are so eager to foster through the tablets. The ability to focus, to concentrate, to lend attention, to sense other people's attitudes and communicate with them, to build a large vocabulary-all those abilities are harmed."

Put more simply, parents who jump to screen time in a bid to give their kids an educational edge may actually be doing significantly more harm than good-and they need to dole out future screen time in an age-appropriate matter.

Between birth and age three, for example, our brains develop quickly and are particularly sensitive to the environment around us. In medical circles, this is called the critical period, because the changes that happen in the brain during these first tender years become the permanent foundation upon which all later brain function is built. In order for the brain's neural networks to develop normally during the critical period, a child needs specific stimuli from the outside environment. These are rules that have evolved over centuries of human evolution, but-not surprisingly-these essential stimuli are not found on today's tablet screens. When a young child spends too much time in front of a screen and not enough getting required stimuli from the real world, her development becomes stunted.

And not just for a while. If the damage happens during these crucial early years, its results can affect her forever.

Much of the issue lies with the fact that what makes tablets and iPhones so great-dozens of stimuli at your fingertips, and the ability to process multiple actions simultaneously-is exactly what young brains do not need.

Tablets are the ultimate shortcut tools: Unlike a mother reading a story to a child, for example, a smartphone-told story spoon-feeds images, words, and pictures all at once to a young reader. Rather than having to take the time to process a mother's voice into words, visualize complete pictures and exert a mental effort to follow a story line, kids who follow stories on their smartphones get lazy. The device does the thinking for them, and as a result, their own cognitive muscles remain weak.
Trouble making friends
The brain's frontal lobe is the area responsible for decoding and comprehending social interactions. It is in this corner of the mind that we empathize with others, take in nonverbal cues while talking to friends and colleagues, and learn how to read the hundreds of unspoken signs-facial expression, tone of voice, and more-that add color and depth to real-world relationships.

So how and when does the brain's frontal lobe develop? Not surprisingly, the most crucial stage is in early childhood, during that same critical period, and it's dependent on authentic human interactions. So if your young child is spending all of his time in front of an iPad instead of chatting and playing with teachers and other children, his empathetic abilities-the near-instinctive way you and I can read situations and get a feel for other people-will be dulled, possibly for good.
Life has no on/off switch
Have you ever seen a mother chuckle as her baby tries to "swipe" a real photograph, or punch their fingers onto a poster or book as if it were a touchscreen? It may seem cute, but it points to something much deeper in the child's brain-an internalization that all actions have an immediate effect, and all stimuli elicit a quick response.

This is true in the on-screen world, but nowhere else. When every finger swipe brings about a response of colors and shapes and sounds, a child's brain responds gleefully with the neurotransmitter dopamine, the key component in our reward system that is associated with feelings of pleasure. Dopamine hits in the brain can feel almost addictive, and when a child gets too used to an immediate stimuli response, he will learn to always prefer smartphone-style interaction-that is, immediate gratification and response-over real-world connection.

This pattern mimics, in a less intense manner, the dangerous cycle psychologists and physicians regularly see in patients with drug and alcohol addictions.
Don't trash those tablets for good
Despite the danger that overexposure to smartphones can pose for young brains, there are a lot of benefits to letting little ones use technology. Once a child is over the age of two, feel free to allow limited screen time-think an hour, max, of playing with tablets and iPhones each day-to help develop coordination, hone quick reactions, and even sharpen language skills. As with all the other toys and tools available to your developing child, smartphone use should stay in moderation, and never stand in for human interaction or real-world face time.

The bottom line? Power off regularly to help your child understand the clear boundaries between the virtual world and the real one.

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What Screen Time Can Really Do to Kids' Brains

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Screen time is an inescapable reality of modern childhood, with kids of every age spending hours upon hours in front of iPads, smartphones and televisions. That's not always a bad thing: Educational apps and TV shows are great ways for children to sharpen their developing brains and hone their communication skills-not to mention the break these gadgets provide harried parents.

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A brilliant student, Jonathan sailed through grade school. He completed his assignments easily and routinely earned As. Jonathan puzzled over why some of his classmates struggled, and his parents told him he had a special gift. In the seventh grade, however, Jonathan suddenly lost interest in school, refusing to do homework or study for tests. As a consequence, his grades plummeted. His parents tried to boost their son's confidence by assuring him that he was very smart. But their attempts failed to motivate Jonathan (who is a composite drawn from several children). Schoolwork, their son maintained, was boring and pointless.

Our society worships talent, and many people assume that possessing superior intelligence or ability-along with confidence in that ability-is a recipe for success. In fact, however, more than 35 years of scientific investigation suggests that an overemphasis on intellect or talent leaves people vulnerable to failure, fearful of challenges and unwilling to remedy their shortcomings.

The result plays out in children like Jonathan, who coast through the early grades under the dangerous notion that no-effort academic achievement defines them as smart or gifted. Such children hold an implicit belief that intelligence is innate and fixed, making striving to learn seem far less important than being (or looking) smart. This belief also makes them see challenges, mistakes and even the need to exert effort as threats to their ego rather than as opportunities to improve. And it causes them to lose confidence and motivation when the work is no longer easy for them.

Praising children's innate abilities, as Jonathan's parents did, reinforces this mind-set, which can also prevent young athletes or people in the workforce and even marriages from living up to their potential. On the other hand, our studies show that teaching people to have a "growth mind-set," which encourages a focus on "process" (consisting of personal effort and effective strategies) rather than on intelligence or talent, helps make them into high achievers in school and in life.

The Opportunity of Defeat
I first began to investigate the underpinnings of human motivation-and how people persevere after setbacks-as a psychology graduate student at Yale University in the 1960s. Animal experiments by psychologists Martin Seligman, Steven Maier and Richard Solomon, all then at the University of Pennsylvania, had shown that after repeated failures, most animals conclude that a situation is hopeless and beyond their control. After such an experience, the researchers found, an animal often remains passive even when it can effect change-a state they called learned helplessness.

People can learn to be helpless, too, but not everyone reacts to setbacks this way. I wondered: Why do some students give up when they encounter difficulty, whereas others who are no more skilled continue to strive and learn? One answer, I soon discovered, lay in people's beliefs about why they had failed.

In particular, attributing poor performance to a lack of ability depresses motivation more than does the belief that lack of effort is to blame. In 1972, when I taught a group of elementary and middle school children who displayed helpless behavior in school that a lack of effort (rather than lack of ability) led to their mistakes on math problems, the kids learned to keep trying when the problems got tough. They also solved many more problems even in the face of difficulty. Another group of helpless children who were simply rewarded for their success on easier problems did not improve their ability to solve hard math problems. These experiments were an early indication that a focus on effort can help resolve helplessness and engender success.

Subsequent studies revealed that the most persistent students do not ruminate about their own failure much at all but instead think of mistakes as problems to be solved. At the University of Illinois in the 1970s I, along with my then graduate student Carol Diener, asked 60 fifth graders to think out loud while they solved very difficult pattern-recognition problems. Some students reacted defensively to mistakes, denigrating their skills with comments such as "I never did have a good rememory," and their problem-solving strategies deteriorated.

Others, meanwhile, focused on fixing errors and honing their skills. One advised himself: "I should slow down and try to figure this out." Two schoolchildren were particularly inspiring. One, in the wake of difficulty, pulled up his chair, rubbed his hands together, smacked his lips and said, "I love a challenge!" The other, also confronting the hard problems, looked up at the experimenter and approvingly declared, "I was hoping this would be informative!" Predictably, the students with this attitude outperformed their cohorts in these studies.

Two Views of Intelligence
Several years later I developed a broader theory of what separates the two general classes of learners-helpless versus mastery-oriented. I realized that these different types of students not only explain their failures differently, but they also hold different "theories" of intelligence. The helpless ones believe that intelligence is a fixed trait: you have only a certain amount, and that's that. I call this a "fixed mind-set." Mistakes crack their self-confidence because they attribute errors to a lack of ability, which they feel powerless to change. They avoid challenges because challenges make mistakes more likely and looking smart less so. Like Jonathan, such children shun effort in the belief that having to work hard means they are dumb.

The mastery-oriented children, on the other hand, think intelligence is malleable and can be developed through education and hard work. They want to learn above all else. After all, if you believe that you can expand your intellectual skills, you want to do just that. Because slipups stem from a lack of effort or acquirable skills, not fixed ability, they can be remedied by perseverance. Challenges are energizing rather than intimidating; they offer opportunities to learn. Students with such a growth mind-set, we predicted, were destined for greater academic success and were quite likely to outperform their counterparts.

We validated these expectations in a study published in early 2007. Psychologists Lisa Blackwell, then at Columbia University, and Kali H. Trzesniewski, then at Stanford University, and I monitored 373 students for two years during the transition to junior high school, when the work gets more difficult and the grading more stringent, to determine how their mind-sets might affect their math grades. At the beginning of seventh grade, we assessed the students' mind-sets by asking them to agree or disagree with statements such as "Your intelligence is something very basic about you that you can't really change." We then assessed their beliefs about other aspects of learning and looked to see what happened to their grades.

As we had predicted, the students with a growth mind-set felt that learning was a more important goal in school than getting good grades. In addition, they held hard work in high regard, believing that the more you labored at something, the better you would become at it. They understood that even geniuses have to work hard for their great accomplishments. Confronted by a setback such as a disappointing test grade, students with a growth mind-set said they would study harder or try a different strategy for mastering the material.

The students who held a fixed mind-set, however, were concerned about looking smart with less regard for learning. They had negative views of effort, believing that having to work hard at something was a sign of low ability. They thought that a person with talent or intelligence did not need to work hard to do well. Attributing a bad grade to their own lack of ability, those with a fixed mind-set said that they would study less in the future, try never to take that subject again and consider cheating on future tests.

Such divergent outlooks had a dramatic impact on performance. At the start of junior high, the math achievement test scores of the students with a growth mind-set were comparable to those of students who displayed a fixed mind-set. But as the work became more difficult, the students with a growth mind-set showed greater persistence. As a result, their math grades overtook those of the other students by the end of the first semester-and the gap between the two groups continued to widen during the two years we followed them.

Along with psychologist Heidi Grant Halvorson, now at Columbia, I found a similar relation between mind-set and achievement in a 2003 study of 128 Columbia freshman premed students who were enrolled in a challenging general chemistry course. Although all the students cared about grades, the ones who earned the best grades were those who placed a high premium on learning rather than on showing that they were smart in chemistry. The focus on learning strategies, effort and persistence paid off for these students.

Confronting Deficiencies
A belief in fixed intelligence also makes people less willing to admit to errors or to confront and remedy their deficiencies in school, at work and in their social relationships. In a study published in 1999 of 168 freshmen entering the University of Hong Kong, where all instruction and coursework are in English, three Hong Kong colleagues and I found that students with a growth mind-set who scored poorly on their English proficiency exam were far more inclined to take a remedial English course than were low-scoring students with a fixed mind-set. The students with a stagnant view of intelligence were presumably unwilling to admit to their deficit and thus passed up the opportunity to correct it.

A fixed mind-set can similarly hamper communication and progress in the workplace by leading managers and employees to discourage or ignore constructive criticism and advice. Research by psychologists Peter Heslin, now at the University of New South Wales in Australia, Don VandeWalle of Southern Methodist University and Gary Latham of the University of Toronto shows that managers who have a fixed mind-set are less likely to seek or welcome feedback from their employees than are managers with a growth mind-set. Presumably, managers with a growth mind-set see themselves as works-in-progress and understand that they need feedback to improve, whereas bosses with a fixed mind-set are more likely to see criticism as reflecting their underlying level of competence. Assuming that other people are not capable of changing either, executives with a fixed mind-set are also less likely to mentor their underlings. But after Heslin, VandeWalle and Latham gave managers a tutorial on the value and principles of the growth mind-set, supervisors became more willing to coach their employees and gave more useful advice.

Mind-set can affect the quality and longevity of personal relationships as well, through people's willingness-or unwillingness-to deal with difficulties. Those with a fixed mind-set are less likely than those with a growth mind-set to broach problems in their relationships and to try to solve them, according to a 2006 study I conducted with psychologist Lara Kammrath, now at Wake Forest University. After all, if you think that human personality traits are more or less fixed, relationship repair seems largely futile. Individuals who believe people can change and grow, however, are more confident that confronting concerns in their relationships will lead to resolutions.

Proper Praise
How do we transmit a growth mind-set to our children? One way is by telling stories about achievements that result from hard work. For instance, talking about mathematical geniuses who were more or less born that way puts students in a fixed mind-set, but descriptions of great mathematicians who fell in love with math and developed amazing skills engenders a growth mind-set, our studies have shown. People also communicate mind-sets through praise. Although many, if not most, parents believe that they should build up children by telling them how brilliant and talented they are, our research suggests that this is misguided.

In studies involving several hundred fifth graders published in 1998, for example, psychologist Claudia M. Mueller, now at Stanford, and I gave children questions from a nonverbal IQ test. After the first 10 problems, on which most children did fairly well, we praised them. We praised some of them for their intelligence: "Wow ... that's a really good score. You must be smart at this." We commended others for their process: "Wow ... that's a really good score. You must have worked really hard."

We found that intelligence praise encouraged a fixed mind-set more often than did pats on the back for effort. Those congratulated for their intelligence, for example, shied away from a challenging assignment-they wanted an easy one instead-far more often than the kids applauded for their process. (Most of those lauded for their hard work wanted the difficult problem set from which they would learn.) When we gave everyone hard problems anyway, those praised for being smart became discouraged, doubting their ability. And their scores, even on an easier problem set we gave them afterward, declined as compared with their previous results on equivalent problems. In contrast, students praised for their hard work did not lose confidence when faced with the harder questions, and their performance improved markedly on the easier problems that followed.

Making Up Your Mind-set
In addition to encouraging a growth mind-set through praise for effort, parents and teachers can help children by providing explicit instruction regarding the mind as a learning machine. Blackwell, Trzesniewski and I designed an eight-session workshop for 91 students whose math grades were declining in their first year of junior high. Forty-eight of the students received instruction in study skills only, whereas the others attended a combination of study skills sessions and classes in which they learned about the growth mind-set and how to apply it to schoolwork.

In the growth mind-set classes, students read and discussed an article entitled "You Can Grow Your Brain." They were taught that the brain is like a muscle that gets stronger with use and that learning prompts neurons in the brain to grow new connections. From such instruction, many students began to see themselves as agents of their own brain development. Students who had been disruptive or bored sat still and took note. One particularly unruly boy looked up during the discussion and said, "You mean I don't have to be dumb?"

As the semester progressed, the math grades of the kids who learned only study skills continued to decline, whereas those of the students given the growth-mind-set training stopped falling and began to bounce back to their former levels. Despite being unaware that there were two types of instruction, teachers reported noticing significant motivational changes in 27 percent of the children in the growth mind-set workshop as compared with only 9 percent of students in the control group. One teacher wrote: "Your workshop has already had an effect. L [our unruly male student], who never puts in any extra effort and often doesn't turn in homework on time, actually stayed up late to finish an assignment early so I could review it and give him a chance to revise it. He earned a B+. (He had been getting Cs and lower.)"

Other researchers have replicated our results. Psychologists Catherine Good, now at Baruch College, Joshua Aronson of New York University and Michael Inzlicht, now at the University of Toronto, reported in 2003 that a growth mind-set workshop raised the math and English achievement test scores of seventh graders. In a 2002 study Aronson, Good (then a graduate student at the University of Texas at Austin) and their colleagues found that college students began to enjoy their schoolwork more, value it more highly and get better grades as a result of training that fostered a growth mind-set.

We have now encapsulated such instruction in an interactive computer program called Brainology. Its five modules teach students about the brain-what it does and how to make it work better. In a virtual brain lab, users can click on brain regions to determine their functions or on nerve endings to see how connections form or strengthen when people learn. Users can also advise virtual students with problems as a way of practicing how to handle schoolwork difficulties; additionally, users keep an online journal of their study practices.

New York City seventh graders who tested Brainology told us that the program had changed their view of learning and how to promote it. One wrote: "My favorite thing from Brainology is the neurons part where when u [sic] learn something there are connections and they keep growing. I always picture them when I'm in school." A teacher said of the students who used the program: "They offer to practice, study, take notes, or pay attention to ensure that connections will be made."

Teaching children such information is not just a ploy to get them to study. People may well differ in intelligence, talent and ability. And yet research is converging on the conclusion that great accomplishment, and even what we call genius, is typically the result of years of passion and dedication and not something that flows naturally from a gift. Mozart, Edison, Curie, Darwin and Cézanne were not simply born with talent; they cultivated it through tremendous and sustained effort. Similarly, hard work and discipline contribute more to school achievement than IQ does.

Such lessons apply to almost every human endeavor. For instance, many young athletes value talent more than hard work and have consequently become unteachable. Similarly, many people accomplish little in their jobs without constant praise and encouragement to maintain their motivation. If we foster a growth mind-set in our homes and schools, however, we will give our children the tools to succeed in their pursuits and to become productive workers and citizens.
-Carol S. Dweck

A for Effort
According to a survey we conducted in the mid-1990s, 85 percent of parents believed that praising children's ability or intelligence when they perform well is important for making them feel smart. But our work shows that praising a child's intelligence makes a child fragile and defensive. So, too, does generic praise that suggests a stable trait, such as "You are a good artist." Praise can be very valuable, however, if it is carefully worded. Praise for the specific process a child used to accomplish something fosters motivation and confidence by focusing children on the actions that lead to success. Such process praise may involve commending effort, strategies, focus, persistence in the face of difficulty, and willingness to take on challenges. The following are examples of such communications:
You did a good job drawing. I like the detail you added to the people's faces. You really studied for your social studies test. You read the material over several times, outlined it and tested yourself on it. It really worked! I like the way you tried a lot of different strategies on that math problem until you finally got it. That was a hard English assignment, but you stuck with it until you got it done. You stayed at your desk and kept your concentration. That's great! I like that you took on that challenging project for your science class. It will take a lot of work-doing the research, designing the apparatus, making the parts and building it. You are going to learn a lot of great things.
Parents and teachers can also teach children to enjoy the process of learning by expressing positive views of challenges, effort and mistakes. Here are some examples:
Boy, this is hard-this is fun. Oh, sorry, that was too easy-no fun. Let's do something more challenging that you can learn from. Let's all talk about what we struggled with today and learned from. I'll go first. Mistakes are so interesting. Here's a wonderful mistake.
Let's see what we can learn from it.
-C.S.D.

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A brilliant student, Jonathan sailed through grade school. He completed his assignments easily and routinely earned As. Jonathan puzzled over why some of his classmates struggled, and his parents told him he had a special gift. In the seventh grade, however, Jonathan suddenly lost interest in school, refusing to do homework or study for tests.

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Great ideas for games to enhance math skills play at home on pages 6 and 7.

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Practice addition, multiplication, fractions and algebraic reasoning with our popular math games. Discover fun learning games kids love to play.

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Math and Games for Kids, Teachers and Parents. Math lessons and fun games for kindergarten to sixth grade, plus quizzes, brain teasers and more.

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60+ Websites for Teaching and Learning Math 

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60+ Websites for Teaching and Learning Math 

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The internet is full of incredible new ways to teach and learn math, from games and videos to lessons and even complete curricula. Teachers, students, and parents can all benefit from these online learning resources. This list of the best math websites has options for every skill level, from learning to count to advanced math like calculus. You're bound to find a new favorite!

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These math websites provide complete standards-based math curricula. Try them if you're looking for a new way to teach math at your school. These can be good choices for homeschoolers too.

Join the 1 million teachers already using Prodigy Math in their classrooms at no cost. This fun and engaging curriculum-aligned game lets students engage in a fun wizarding world that motivates them to practice more math than ever. It contains 1,500+ standard-aligned skills. Plus you can track student progress with a teacher dashboard that provides instant feedback on areas of progress with no grading necessary.

Info: Grades 1-8; free for teachers, and monthly memberships available for parents

From McGraw-Hill, this web-based assessment and learning system uses adaptive questioning to determine students' needs. It adapts to teach kids the topics they're most ready to learn.

Info: Grades 3-12; contact them for pricing

Along with textbooks, Art of Problem Solving has a stable of robust online resources. You'll find videos, math problems from math contests, and online classes.

Info: Grades 5-12; pricing varies by program

BuzzMath focuses on helping middle schoolers practice their math skills. It contains high-quality problems, gives immediate and detailed feedback, and lets students progress at their own pace. Randomly generated values let students retry problems to obtain mastery. Teachers also receive detailed results that help them guide and monitor student progress.

Info: Grades 1-9; free demo with subscription plans for students and families

Make free detailed charts of all kinds, including bar graphs, pie charts, scatter plots, and more.

Info: K-12; free

This resource from England provides math videos with associated math practice questions and worksheets. It's basic, but a good way to get no-cost practice.

Info: Grades K-12; free

This National Science Foundation-funded program helps students strengthen math skills. Students will learn to solve problems and explain their thinking using mathematician George Polya's four-step approach.

Info: Grades K-12; priced per teacher or school, with free trial available

A blend of paper and technology puts student ideas at the center of learning. Lessons pose problems that invite a variety of approaches, engaging kids more fully.

Info: Grades 6-8; contact them for pricing

An adaptive learning platform designed to complement classroom instruction and deliver results. Includes resources for teachers, student data reports, and instructive insights.

Info: Grades K-8; home users can sign up for individual or family subscriptions, schools pay per student or school

This site provides e-textbooks, answer keys, video lessons, and printables. Topics include algebra 1 and 2, geometry, and trigonometry.

Info: Grades 6-12; free lessons plans, homework sets, and videos; paid subscriptions include answer keys, assessments, and more

We love the friendly competition and game-based content offered by First in Math. Kids gain skills practice and fluency as they play games targeted toward fact proficiency and logical thinking.

Info: Grades K-8; subscriptions available for schools and parents, with 45-day free trial

This site allows kids to practice math at their own level and pace. It has more than 30,000 math questions, starting with a diagnostic that assigns material at just the right level. Front Row also features lessons, assessments, and reports for teachers.

Info: Grades K-12; basic use is free for teachers; premium subscriptions available

This site from the National Council of Teachers of Mathematics (NCTM) features complete lesson plans, mobile games for students, interactive activities, and brainteasers.

Info: Grades Pre-K-12; free

Get high-quality educational resources for teachers and students. Excellent math tasks, videos, lesson plans, and problem-based curriculum modules.

Info: Grades K-12; free

Formerly known as Edgenuity, Imagine Learning offers several online digital curricula for primary or supplementary instruction. Give students the support they need exactly when they need it.

Info: Grades Pre-K-12; priced per subject, per student

Istation makes personalized learning easy with computer-adaptive instruction, assessments, personalized data profiles, and teacher resources. Includes digital lessons and face-to-face teaching strategies.

Info: Grades Pre-K-8; priced per student

Make math about more than numbers with engaging items, real-world scenarios, and unlimited questions. Teachers choose the strand and then set up students to work independently.

Info: Grades Pre-K-12; free 30-day trial, pricing is per classroom or site

Khan Academy is on a mission to give a free, world-class education to anyone, anywhere. Their personalized learning resources are available for all ages, in a huge array of subjects.

Info: Grades K-12; free

Here's an online learning space that is engaging, supportive, and designed to get kids interested in math.

Info: Grades K-12; yearly subscription required; school and family pricing available

Through ongoing research, MIND Research Institute continues to investigate key questions about learning, mathematics, and how the brain works. ST Math is their pre-K-8 visual instructional program, helping teachers engage kids more deeply in math learning.

Info: Grades Pre-K-8; pricing based on total school enrollment

This award-winning program finds and fixes learning gaps with the power of personalized learning. The three-pronged approach features personalized learning, pinpoint assessments, and an interactive classroom.

Info: Grades K-8; pricing per student, school, and district

Stepping Stones 2.0, from Origo, is a unique and comprehensive curriculum that combines print and digital materials. It features problem-solving activities, strategies, and practice.

Info: Grades Pre-K-6; price varies by program

This organization is geared toward students, teachers, and families in low-income communities. The program features school workshops, instructional coaching, and professional learning communities.

Info: Grades K-12; try limited Family Playlists for free, request consultation for pricing

Enter an interactive, game-based learning world that motivates kids through rewards. Features include a daily challenge, step-by-step lessons, and parent connections.

Info: Grades K-5; 30-day free trial, then monthly subscription

Boost confidence, increase scores, and get ahead. Fun for enrichment or regular practice.

Info: Grades K-5; free for teachers and schools, monthly subscriptions available for parents

Math games make learning fun! Focus on specific skills, target interventions, and make assessment easy.

Info: Grades K-8; teachers can try six games for free, subscription unlocks more games and features

Tang Math strives to provide unparalleled math lessons for students as well as professional development for in-service teachers. Find games and puzzles, plus other resources like free downloads, worksheets/word problems, and math centers.

Info: Grades K-5; free

Woot Math offers adaptive practice for teaching rational numbers and related topics, such as fractions, decimals, and ratios.

Info: Grades 3-7; free tier for teachers, additional features available for extra cost

Personalized math curriculum that includes digital lessons and small-group instruction. Also has online modules, workbooks and answer keys, and professional development.

Info: Grades K-5; free for individual teachers and classrooms

These sites offer engaging videos and tools to use in your daily math instruction.

Engaging animated learning videos, games, quizzes, and activities to encourage kids on their unique learning path.

Info: Grades Pre-K-8; teacher, school, and district pricing available, as well as parent or homeschool options

Teachers prep an assignment, students work on their devices, everybody gives feedback, and the teacher sees it all!

Info: Grades K-12; free basic plan, Pro accounts unlock more features

A website that allows teachers to assign math practice content to their students. Students get immediate feedback as they complete the problems.

Info: Middle school+; free, with premium school and district plans available

An online graphing calculator that students can use for free. Includes a teacher-centric activity builder for creating digital math activities.

Info: Grades 9-12; free

An award-winning series of math apps that harness the power of digital tools to create a better, deeper, more fun learning experience. Blogs such as "Making Math Social" and "Saying No to Math Anxiety" are included as resources for teachers and parents.

Info: Grades K-6; priced per app, with free trials for teachers and bulk pricing for schools

Use hip-hop to teach math! Flocabulary offers songs, activities, and videos.

Info: Grades K-12; teacher, school, and district pricing available

Upload your own materials or build them from scratch, find something pre-made, act on live responses, and track student growth over time.

Info: Grades K-12; free, premium subscription unlocks additional features

Another graphing calculator for functions, geometry, algebra, calculus, statistics, and 3D math, along with a variety of math resources.

Info: Grades 9-12; free

You know it; your kids love it. Why not use it to teach math? Engage your students with this game-based classroom-response system played by the whole class in real time. Multiple-choice questions are projected on the screen, then students answer with their smartphone, tablet, or computer.

Info: Grades K-12; free, Kahoot+ AccessPass subscription offers premium content

Run by the University of Regina in Canada, this site offers free resources for math teachers and their students, including a database where users can search for the answers to math questions. Their "Mathematics With a Human Face" page includes information about careers in mathematics as well as profiles of mathematicians.

Info: Grades K-12; free

Teachers know that one of the best ways to make sure learning sticks is through song. Numberock features ad-free music videos of songs about math topics, like fractions, money, and integers, produced by an Emmy Award-winning studio. Numberock also has anchor charts, worksheets, comics, games, and more.

Info: Grades K-5; limited free videos, monthly subscription offers six-month free trial

Transform presentations into classroom conversations with Peardeck for Google Slides. Effortlessly build engaging instructional content, formative assessments, and interactive questions.

Info: Grades K-12; basic access is free, premium subscriptions unlock more features

Think of this site like YouTube but specifically for teachers and schools. Find videos created by other teachers, and upload your own to share.

Info: Grades K-12; free

These interactive math websites provide students with instruction and independent practice.

Two users play a game in which each player tries to connect four game pieces in a row (like Connect Four). The players answer math questions to connect the pieces. The teacher chooses how much time each player has to answer, the level of difficulty, and the type of math problem.

Info: Grades 2-8; free

Yes, math games can be cool! Check out the hundreds of games on this site and on Coolmath4kids.

Info: Grades K-12; free with ads, premium subscription removes ads and provides extra features

Figure This is a site designed to encourage families to practice math together. It includes fun and engaging math games and high-quality challenges. It even offers challenges in Spanish.

Info: Grades 6-8; free

Funbrain has been helping students learn key math concepts and develop crucial skills since 1997. Students can choose from a slew of games. The best part? It's all free!

Info: Grades Pre-K-8; free

Get the Math is about algebra in the real world. See how professionals use math in music, fashion, video games, restaurants, basketball, and special effects. Then take on interactive challenges related to those careers.

Info: Grades 6-12; free

Your students will love fun math games like Speed Math Deluxe, Mystery Math, Place Value Game, and more.

Info: Grades 3-12; free

A popular game-based site for online math-learning resources. It covers algebra, geometry, statistics, and more.

Info: Grades K-12; schools can contact them for a quote; parents pay per child

Play engaging games and find free printable worksheets at this site from Knowledge Adventure. Great for kids at home or teachers in the classroom.

Info: Grades Pre-K-8; free basic access with subscriptions for parents, teachers, and schools

There are dozens of games to explore here, organized by grade and subject.

Info: Grades Pre-K-7; free

In-depth lessons with videos, guided practice, interactive self-tests, and more.

Info: Grades 5-12; monthly or yearly subscription required

More than 425 math games, logic puzzles, and brain workouts for students to practice their math skills.

Info: Grades 1-6; free with ads, Premium removes ads and provides extra features

Most learners do best when they can see a problem walk-through, step-by-step. This site features multiple example problems, with walk-throughs by three separate instructors (including one in Spanish). They offer some basic math but are focused on advanced subjects from algebra on up.

Info: Grades 6-12; free

Thousands of original math games, workshops, and practice modules, as well as math printables!

Info: Grades 1-6; monthly or yearly subscription required

Need to master your multiplication facts? This is the site to try! Fun games and memory-building strategies will help students tackle this key skill.

Info: Grades 2-6; free, with Premium membership available for extra features

This interactive online tool helps students master basic facts. Set up as a whole-class or small-group competition, students earn ninja cards and track results on a ninja scoring poster. Two board games that teach operations are also available for purchase.

Info: Grades 2-8; pay per game or purchase teacher licenses

This is a free intervention tool designed to fill gaps in students' mental calculation skills and empower them with number fluency. Students can earn ninja belts of different colors for their skill level.

Info: Grades 2-8; free

From PBS Learning Media, middle schoolers will love this entertaining video blog. Not only does each episode cover Common Core Standards, it makes math learning culturally relevant with pop-culture references.

Info: Grades 6-9; free

Students can create study flash cards, play educational games, practice skills, collaborate with other students, and more.

Info: Grades 5-12; free, QuizletPlus provides additional features

Another resource to help students build fact fluency. Each game is tailored to students' ability levels.

Info: Grades 2-6; school and home licenses available

Tons of fun and educational online math games, from basic operations to algebra and geometry.

Info: Grades K-6; free

Simple math test activities for teachers and students, from beginning math operations to calculus. You set the skill level, number of problems, and time limit. A report, which tallies right and wrong answers, is provided after each quiz.

Info: Grades 3-12; free

How would your students like to learn multiplication while shooting hoops? They can do that and more at Toy Theater, which teaches early math concepts through game-based learning.

Info: Grades K-5; free

Upper-level math students will appreciate the no-frills information that's easy to find on this site. Get overviews and see examples of advanced math subjects.

Info: High School+; free

Xtramath is like a daily math vitamin. An interactive online tool that helps students practice and master basic arithmetic facts, it's quick and easy to use. Weekly emails provide progress reports for teachers and parents.

Info: Grades K-8; free, with premium licenses that offer additional features

These math websites provide lesson-planning resources and professional-development materials.

Formerly known as Mathalicious, this site provides supplemental math lessons. Experience an immersive, participatory approach that makes learning and teaching more rewarding.

Info: Grades 6-12; monthly or yearly subscriptions available

Find math worksheets for just about any area of study. Use them for planning lessons, review, and independent work.

Info: Grades K-6; free

Here's a reliable site for worksheets, games, and even lessons plans. They cover a variety of subjects, with lots of math options to choose from.

Info: Grades K-8; limited free access, monthly subscriptions unlock all content

This platform allows teachers to create technology-enhanced online math assessments from a huge question bank.

Info: Grades K-12; free teacher accounts

For teachers of pre-algebra through calculus. Create the math worksheets you need, exactly how you want them, in minutes. You can also create customizable homework, quizzes, and tests.

Info: Grades 8-12; free two-week trial, then single-user and site licenses available

A creative solution that aims to revive students' passion and interest in math. Mashup Math has a library of 100+ math video lessons as well as a YouTube channel that features new math video lessons every week. A free e-book of math challenges is also available.

Info: Grades K-8; free

Dynamically created math worksheets for students, teachers, and parents.

Info: Grades K-10; free with ads, paid membership removes ads

Tools for math teachers, including bell ringers and drills, math tools and manipulatives, question generators, printables, and puzzles.

Info: Grades K-12; free with ads

This National Science Foundation-supported project provides a large library of uniquely interactive, web-based virtual manipulatives and concept tutorials for math instruction.

Info: Grades K-12; free

Convert all of your paper assignments, quizzes, homework, etc., into digital activities delivered online.

Info: Grades K-12; free basic version, Pro plan adds multiple extra features

For a very affordable monthly fee, gain access to thousands of resources created by teachers like you. They cover every topic and every grade level.

Info: Grades K-12; monthly subscription

TopMarks is a U.K.-based site that provides a database of resources for teachers as well as online learning games for students.

Info: Grades Pre-K-8; free

The Varsity Learning Online Math Management System provides course templates, assignments, an online teacher's assistant, and thousands of practice problems so you can get organized, save assignments and videos on the web, share resources, and incorporate technology in your classroom.

Info: Grades: 7-12; free

More than 1,500 video lessons ranging from middle-grade math through algebra 2.

Info: Grades 6-12; free

What's on your list of the best math websites? Come share your ideas in our WeAreTeachers HELPLINE group on Facebook.

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75+ Awesome Websites for Teaching and Learning Math

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The internet is full of incredible new ways to teach and learn math, from games and videos to lessons and even complete curricula. Teachers, students, and parents can all benefit from these online learning resources. This list of the best math websites has options for every skill level, from learning to count to advanced math like calculus.

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Why a Growth Mindset is important for Math

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Why a Growth Mindset is important for Math

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"I'm not a math person." "I wasn't born with the math gene."
Unfortunately, as a math educator, these phrases are all too familiar to me. Kids go through school and life being bombarded with messages that imply some people are good at math and some people aren't.

This "cultural baggage" we have towards math is not based on truth about how our brains are wired. It's based on parents and teachers' years of misunderstanding or hating math and passing these negative attitudes and beliefs onto their children.

However, the great news is more and more research is proving these messages false as we learn how our brains work and how math teaching styles can impact mindset and achievement.

Before you continue, we thought you might like to download our FREE Affirmation Bracelets. It's important for children to be surrounded by loving and encouraging messages. These affirmation bracelets will boost your child's confidence and help them feel like they can do anything.

Why Having a Growth Mindset Towards Math is so Important?

The more researchers study and adjust how teachers think about math and how it's taught, the more evidence shows a link between a growth mindset and math success .

We all want kids to feel confident and successful as they learn math. Kids who have a growth mindset about their math abilities perform on standardized tests and are more engaged in the classroom.

In her research article, Carol Dweck, "Mindsets and Math/Science Achievement," delves deep into a variety of research studies that support this correlation. And although we see evidence for the advantages of a growth mindset, she also states,

"Students who have a fixed mindset but who are well prepared and do not encounter difficulty can do just fine. However, when they encounter challenges or obstacles they may then be at a disadvantage."

Every child will face math obstacles at some point, and being prepared to face them with a growth mindset and a healthy attitude toward mathematics will give them the stamina to persevere and overcome the challenge.

1. Teach Kids About the Brain's Ability to Grow

If necessary, first we need to change how kids view math and their math abilities. There are a lot of children who feel they are going to be good at math, no matter how hard they try.

By showing them how our brains work we give them hope that their brain can grow and change, as they continue to study and explore mathematics.

Here are some suggested activities:

For younger children, show fun YouTube videos like the Neuron Song to teach them about neuroplasticity.

For older children, show this brief clip from the BBC documentary 'The Human Body', which demonstrates how establishing new neural pathways between brain cells is like building a bridge to cross a ravine.

2. Model and Praise Mistakes as Opportunities for Brain Growth

Another important aspect of developing a growth mindset is to view mistakes positively.

According to Jo Boaler, in her book, Mathematical Mindsets, our brain responds to mistakes in one of two ways. First, through an ERN response, which is increased activity in our brain, which happens when there's "a conflict between a correct response and an error."

The second is a Pe response, which occurs when the brain is consciously aware a mistake has been made. Amazingly, our brains spark and grow with an ERN response. We can stretch and grow our brain by making mistakes, even if we don't realize it or work to correct it. How incredibly empowering it is to know this!

Here are some suggested activities:

Model mistakes in front of kids. Show them that you make mistakes too, and it's a good thing.

Analyze mistakes together to see what and how we learn from them. A great example for classroom teachers is to incorporate "my favorite no" , which allows the whole class to discuss mistakes together and find the value in them.

Create a mistake-welcoming home or classroom by decorating with inspiring posters and graphics.

Be sure to check out The Big Life Journal - Daily Edition (ages 5-11). This science-based journal helps children grow resilient, confident, and emotionally healthy. The daily activities inside the journal help your child focus on encouraging, self-loving thoughts and wire their brain for growth mindset, resilience, confidence, gratitude, kindness, and self-love.

3. Provide Rich, Open-Ended Math Tasks

Although changing kids' attitudes towards math and the language they use is important, no real change or progress will be made if math continues to be taught the way.

Because math is often taught as a closed, fixed subject with one goal - get the right answer - kids are often afraid to make mistakes because it feels like a failure . Their only thought is to find that one correct solution, and when they don't, they shut down and quit.

But the truth is math is about so much more than getting the right answer. It's about exploring big ideas, making connections, and learning to be creative problem-solvers .

Instead of focusing on memorizing facts, or replicating mathematical procedures, parents and teachers need to provide rich and meaningful tasks that challenge kids to think outside the box.

What does this look like? Well, as Jo Boaler says, meaningful math tasks combine the 5C's: curiosity, connection making, challenge, creativity, and collaboration.

Don't forget to download our FREE Affirmation Bracelets. The affirmation bracelets are great for boosting a child's confidence!

When presented with these types of tasks, kids are going to be more excited about math and more engaged in learning.

Challenging kids to actually think about what they're doing and WHY it works is more productive than merely completing 20 problems from a textbook.

Here are some suggested activities:

Try out a variety of tasks from YouCubed with your kids. These tasks are completed by kids all over the world and spark a deeper love of math. Learn more about the week of inspirational math .

Take traditional, closed problems and turn them into rich challenges. For example, your kids might be working on the problem, 18 x 5. This could be a straightforward problem with a single solution. But what if instead, you asked kids to solve it two different ways? Or to give a visual proof of their solution and explain their answer?

Use another engaging challenge from Boaler is the "four 4's" task. This challenge asks kids (or parents and teachers) to find all the numbers from 1-20 using 4 fours and any mathematical operation. For example, 4 + 4 + 4 + 4 = 16, 4 + 4 - 4 + 4 = 8, etc. After some basic operations, this challenge becomes a lot more difficult and engaging!

Raise the bar for kids who are finished with a given problem or task. One easy way to do this is to challenge them to create their own problem. Ask them to write a new similar question, but more difficult. This allows kids the chance to be creative and gets them excited to try and challenge their peers.

4. Remove an Emphasis on Speed

As I've already mentioned, kids often have the impression that math is about one thing and one thing only: getting the right answer quickly . But if learning and teaching math was only about getting the right answer, there would be no point in it, because calculators can do that work for us.

Evidence shows math tests increase kids' anxiety and hatred of math. The pressure of finishing within a time limit can be so stressful, some kids develop severe math anxiety, which stays with them all their lives.

Here are some suggested activities:

Teach kids the strategies they use, as well as how they talk about big mathematical ideas, are important than the final answer. And tell them the world's leading mathematicians often spend years focusing on ONE problem, proof or idea.

If you're a classroom teacher, you can assign fewer math problems. When kids see a worksheet or assignment with 20 or 30 problems, they may be more inclined to find a way to get through it all quickly. But if instead you assign fewer problems and make sure they justify their answers or look for multiple solutions, they're more likely to slow down and think about the process.

Replace a set of practice problems with reflective questions such as, "What was a big idea we learned about today?" or "What was something you struggled with today?" or "What mistake did you learn from today?" [ ]

5. Be Mindful of Your Own Attitude Towards Math

Lastly, and probably most importantly, I want to encourage you to be especially mindful of your own views of math and the you use to talk about it in front of your kids. Kids are watching and listening and learning from our example (whether we're aware of it or not) and even subtle fixed mindset messages will come across to kids.

Recently, authors of one research study concluded that mindset intervention is ineffective and a waste of money in math education. The problem with their research, however, is it ignores a key component to successful mindset intervention: the changes of a teacher and math teaching .

If the only effort made is a change in language, such as using words like "yet" or "mistakes help our brain grow," but the teacher's mindset and teaching style don't change, there will be no real change in kids.

Here are some suggestions for you:

Continue to learn and study the importance and impact of a growth mindset for yourself. This will not only help you to develop a growth mindset towards math but will be a powerful example to your kids as you show them how to persevere.

S p end time together as a family discussing some of the open math tasks shared above. You can learn new strategies together and have fun discussing big ideas. You'll be spending quality time together and engaging in meaningful math learning at the same time! It's a win-win.

If you're concerned about your own mindset towards math, complete the free course from Jo Boaler. You may also like this freemini coursefor teachers on creating rich math tasks (even if you're not a teacher).

Follow the free 4-week guide on How To Teach Growth Mindset to Children , it provides specific examples of how to model growth mindset and teach it to your children.

Given time and intentionality, even the most fixed mindsets towards math can be turned around, and the most struggling students can succeed, thrive and will love exploring mathematical ideas.

Looking for more ways to help your child with negative self-talk? We offer an on-demand How to Transform Negative Self-Talk into Self-Love masterclass for parents where you'll learn why your child has negative self-talk and effective practices to help them turn it into self-love.

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5 Powerful Ways to Help Kids Develop a Growth Mindset in Mathematics

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How can you help children develop a growth mindset in math? Here are some practical ideas to get you started at home or in the classroom.

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Picture Books that Help Foster a Love of Math

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Picture Books that Help Foster a Love of Math

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Storybooks provide a rich opportunity to build not only literacy skills, but also math understanding. Books with math concepts woven into the pictures and storylines can promote children's mathematical thinking and introduce foundational math concepts such as numbers, shapes, patterns, and measurement. Asking questions and making observations about the math found in picture books can support children's curiosity and enjoyment of math.

Like many engaging pieces of children's literature, the math picture books recommended below contain fun and interesting storylines. Many are rooted in topics kids love (like animals, dinosaurs, magic, oceans, and more!).

For example, " Quack and Count " by Keith Baker is about seven ducklings quacking, sliding, and flying in marshland. Throughout the beautifully illustrated story, the seven ducklings form different groups that can be added and always make seven. While reading, children can explore counting and addition as they practice counting a group of ducks that are not always neatly in a row and in fact may be hard to see-a challenging but enjoyable task.

The most important rule to keep in mind when selecting and reading a math picture book is to enjoy the stories and enjoy the children enjoying the stories! Read often, smile, and laugh. Learn more tips for reading math picture books with young children in this blog post. If you're a teacher educator, find tips for using math picture books in the classroom.

Explore our list of recommended picture books organized by math topic.

Adding and Subtracting

Quack and Count by Keith Baker

Rooster's Off to See the World by Eric Carle

Elevator Magic by Stuart J. Murphy

One is a Snail, Ten is a Crab by April Pulley Sayre and Jeff Sayre

Albert Adds Up by Eleanor May

Counting

Anno's Counting Book by Mitsumasa Anno

Feast for 10 by Cathryn Falwell

Eric Carle's 123 by Eric Carle

Fish Eyes: A Book You Can Count On by Lois Ehlert

Zero is the Leaves on the Trees by Betsy Franco

Mouse Count by Ellen Stoll Walsh

How Do Dinosaurs Count to Ten by Jane Yolen and Mark Teague

Hippos Go Berserk! by Sandra Boynton

Measurement and Size

Who Eats First? by Ae-hae Yoon

Just a Little Bit by Ann Tompert

Balancing Act by Ellen Stoll Walsh

Next to an Ant by Mara Rockliff

Inch by Inch by Leo Leonni

The Growing Story by Ruth Krauss

Patterns and Algebra

Anno's Magic Seeds by Mitsumasa Anno

Two of Everything: A Chinese Folktale by Lily Toy Hong

Mr. Noisy's Book of Patterns by Rozanne L. Williams

Shape

The Shape of Things by Dayle Ann Dodds

Have You Seen My Monster? by Steve Light

Circus Shapes by Stuart J. Murphy

The Greedy Triangle by Marilyn Burns

Mice on Ice by Eleanor May

Mouse Shapes by Ellen Stoll Walsh

Round is a Tortilla by Roseanne Thong

When a Line Bends, a Shape Begins by Rhonda Growler Greene

Spatial Relations

Albert is Not Scared by Eleanor May

Inside, Outside, Upside Down by Stan and Jan Berenstain

Piggies in the Pumpkin Patch by Mary Peterson

Up, Down, and Around by Katherine Ayres

Where's Spot? by Eric Hills

The Secret Birthday Message by Eric Carle

Changes, Changes by Pat Hutchins

Over, Under, and Through by Tana Hoban

Rosie's Walk by Pat Hutchins

Taking Apart Numbers

12 Ways to Get to 11 by Eve Merriam

Ten Friends by Bruce Goldstone
View this list on Goodreads or download in PDF format to take with you to the library or bookstore.

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40 Children's Books That Foster a Love of Math - DREME

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Picture books offer many opportunities to explore and develop children's mathematical thinking. Discover educational and entertaining picture books for early math learners with our recommended reading list.

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I was a math kid. I did well in class, but the type of math I loved came from doing things I enjoyed. I loved reading the stats on the back of my baseball cards (I understood how great Mickey Mantle's .298 lifetime batting average was). I helped my father measure down to the sixteenth of an inch as we worked on projects. I liked figuring out discounts at comic book stores. Only later, when I began teaching, did I realize that my most meaningful understanding of math came when it was part of other things that interested me. After all, that's how math occurs in real life.

Teachers who intentionally bring math into other subject areas, or who bring other subjects into math, love the results. Audrey Trapolsi, an early childhood teacher in Chapel Hill, North Carolina, says, "I love cross-curricular integration. I think it strengthens all the areas of study by applying them in new ways. Applying a new skill within a different content area strengthens and deepens the skill."

Kevin Costley, an associate professor of early childhood education at Arkansas Tech University, agrees. In his recent research, he found that "students in integrated curriculum courses perform better than [those] in nonintegrated courses...[showing] increased critical thinking skills, self-confidence, and love for learning."

And what about math achievement specifically? In a 2015 article on Mindshift, KQED's education news site, Katrina Schwartz found that great things were happening with math and the arts at the Integrated Arts Academy at H. O. Wheeler School in Burlington, Vermont. The school was failing before it became an arts-integrated magnet school in 2009, Schwartz reported, with only 17 percent of its third graders proficient in math. But by 2014, "66 percent met and achieved the standards."

"Not only is achievement better," says IAA principal Bobby Riley, "but students' ability to collaborate and cooperate is enhanced. During integrated arts times, discipline referrals drop to basically zero."

Both the research and educators' personal experience make one thing clear: Integration helps to make math meaningful. Kids can relate to it, and may even decide it's fun. Read on for tips on how to make math a companion to any subject, from writing to social studies to music.

Social Studies Loves Stats

Jo-Ann Trifiro, a fourth-grade teacher at Millstone Township Elementary School in New Jersey, uses math to help her students better appreciate and understand the differences between life in the 1800s and today. She does this by creating a simple chart or table in which key facts tell an important story about what life was like more than 130 years ago: Using multiplication, students figure out how much money a typical worker would make in a week, a month, or a year. The numbers help them better understand just how hard life was back then.

Planners and architects creating spaces for communities also use math in their work. Michael Jackson, a social studies teacher at Community Middle School in Plainsboro, New Jersey, helps students experience this in a project where they design schools that meet the needs of their community. Using centimeter graph paper and Cuisenaire rods, they determine a perimeter and then manipulate the rods to explore all of the possible arrangements to meet the area requirements while accommodating the needs of the school community.

The Art of Mathematics

Judy Klima, the integration arts coach at IAA, brings math into a study of famous artists. She begins by showing kindergartners Vincent van Gogh's painting of sunflowers. They discuss their observations of the painting, including the colors, composition, and parts of the flowers. They then count the petals. Next, using large art paper and tempera paints, students create their own sunflower paintings and check to see if their number of petals match up with the original.

Another early elementary activity that brings together math, art, and, yes, space aliens comes from my book Special Delivery: Putting Math to Work. Shapey is an alien who wants kids to help him make a portrait of himself for his mom. He describes himself as symmetrical, made up of four rectangles, five triangles, and so on. Students create a portrait of Shapey out of construction paper, using their geometry knowledge and their own creativity. The complete lesson plan, including a letter from Shapey, can be found here.

Writing Math

To really empower kids in math, have them write their own math word problems. First, lay out specific criteria. In a second-grade class they might be: "Write a word problem that makes us add, makes us regroup, uses two double-digit numbers, and has one distractor." (A distractor is an incorrect answer on a multiple-choice test.) Students write the problem and the solution. Emphasize that they should take care with punctuation, clarity, spelling, and other ELA standards.

Explaining one's thinking in math is difficult for many students. Often they don't know how to begin, so ask them to imagine that a new student has joined their class and doesn't know anything about the topic they're studying (e.g., adding with regrouping). They're to write down a step-by-step instruction guide or how-to booklet on whatever the math concept is, or another of their choice. These are fun to publish and can be saved in a math resource writing center.

Music and Numbers

Patterns are foundational for math and for systems of notation, like those found in music.

To demonstrate the power of patterns, take your kids to the theater with Cyberchase for Real, a video showcasing the off-Broadway production Stomp, where the dancer-drummers make rhythm-infused music with everyday objects like brooms, garbage can lids, and tin cans. After students watch the video, have a volunteer clap out a pattern and then invite other students to repeat it. Challenge everyone to record and explain the pattern using letters, numbers, or symbols, then try other clapping patterns and compare notation systems with others.

To practice ordinal numbers and serial order with young students, recite "There Was an Old Lady Who Swallowed a Fly" together. Make simple cutouts of the items the old lady swallows. As you sing, pause at each new item and have volunteers place the cutout on the board in linear order. Number the items, and write the ordinal words first, second, third, and so on beside each item.

Reading Grids and Graphs

Diana Kaiser, a fifth-grade teacher at John F. Kennedy Elementary School in Jamesburg, New Jersey, uses a variety of charts for organizing data about book characters. For example, Kaiser has students create a grid for analyzing character traits while reading Because of Winn-Dixie, by Kate DiCamillo. "After analyzing their findings," she says, "I encourage them to write a composition comparing these characters by citing examples from the book."

Trapolsi, the early childhood teacher, uses chart paper to record events in fairy tales and fables. (Older kids can do this themselves.) She draws a line graph and annotates it as she reads. As the tension in a plot rises, so does the line on the graph. At the resolution of the story, the tension is gone, and the line returns to 0. Students see change over time recorded in a simple, understandable form, and they see how a line graph can describe how a favorite story is constructed.

Getting Physical With Math

Beverley Lynk, a first-grade teacher at Town Center Elementary School in Plainsboro, New Jersey, helps her students learn about shapes by physically experiencing them. When a shape-for example, a triangle-is introduced, students use their bodies to form it. The characteristics of the shape are reviewed on the board (closed figure, three straight lines, three corners), and students check their "work" (i.e., bodies) to make sure the shapes they're making meet the criteria. She takes photos of the student shapes and compiles them in a class geometry book.

To build on Lynk's idea, IAA's Riley shares a lesson called "dancing geometry." Fourth graders come up with singular moves for geometry terms: polygon, perpendicular, intersecting, obtuse angle, quadrilateral, and so on. Teachers choose one or two moves to combine to create one dance move for each word. Later, students find three or four terms to combine with transitions into a movement phrase that has individual and group moves. Now that's truly math in action!
Bob Krech is a math consultant and author. He is a former elementary teacher and math supervisor and a recipient of the Presidential Award for Excellence in Math and Science Teaching.
Photo: Courtesy of Judy Klima
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I was a math kid. I did well in class, but the type of math I loved came from doing things I enjoyed. I loved reading the stats on the back of my baseball cards (I understood how great Mickey Mantle's .298 lifetime batting average was).

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Integrating Math into other subject areas

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Integrating Math into other subject areas

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Are you having trouble integrating math with literature, geography, art, or music? Discover how one teacher brought her love of running into the classroom and, in the process, integrated all areas of her curriculum. Also: Internet sites for integrating math with literature, history, science, geography, health, art, and music!

Educational research -- not to mention experience and common sense -- tells us that students learn best and make better sense of what they're learning when they can make connections with previous learning or with different areas of learning...
Carol Goodrow, a first grade teacher and an avid runner, knows about the value of making connections. She has connected her curriculum by integrating running into almost every subject area -- and her students are reaping the benefits.

Mrs. Goodrow's first graders at Parker Memorial School in Tolland, Connecticut, took off running in September. By May, Goodrow told Education World, all the students could run a mile, had completed a mile fun run, and loved to write about running. According to Goodrow, many of the students started writing in their journals after running practice. Even those who had been reluctant writers loved the running practices so much they wanted to write about them.

"Also," Goodrow added, "they couldn't have any Gatorade until they wrote in their journals."

But, as Goodrow told Education World, the benefits weren't limited to physical fitness and writing. She saw improvement in math skills as well. For example, during year-end benchmark testing, the class completed sections on numeration more quickly, yet scored as well or better, than past classes.

In addition, Goodrow reported that many students demonstrated a better understanding of fractions. "My fraction committee, a group of the most capable math students, computed the class's [running] mileage on their own, working with 1/2's, 1/4's and 3/4's. They represented the fractions by models, but they could also compute them in their heads."

One of the class's favorite activities, however, was their ongoing "Trek Across America." In this project, Goodrow, her class, their families, and runner Don Allison set off on a virtual race from Boston to San Diego. Each time the participants ran, they kept track of their distances in personal mileage logs. As they progressed along the trek's 3,252 miles, the students traced the route, exploring 14 key cities.

Reports of the trek, as well as many other class activities, can be found on the class's Web site, Kids Running.com. According to Goodrow, this site is built so that kids can be authors, columnists, and more. There are sections where teachers can use running-related data, such as the voting booth data bank, to build math lessons. "It's also a site," she said, "where kids can practice reading stories written by other kids. And of course it encourages fitness and healthy attitudes."

Education World asked Goodrow if she had any suggestions to offer other teachers on how they can make learning more relevant. "Choose something you love," she said, "and integrate it into your curriculum."

But first, you might want to choose some of the activities below and use them to integrate Math across your curriculum.

MATH AND YOUR CURRICULUM

Math and Literature

Another good source for ideas on integrating math is Carol Hurst's Math and Children's Literature site. Though geared toward students in Pre-K through Grade 2, many of the activities here can be adapted for use with older students. For example, the article Time and Time Travel Fantasies, reprinted from Teaching K-8 Magazine, recommends setting up a classroom clock display and allowing students to take the clocks apart (and, hopefully, put them back together again) as they learn to tell time. The site includes a list of books with time-related themes, which you can use to accompany and/or inspire the activities.

Extension: You might extend the activities with older elementary students by setting up a clock repair shop, rather than a display, and having students prepare estimates and invoices for needed repairs. Students might also prepare written reports about the ways in which people have told time throughout history. One interesting site about gnomonics, the art of telling time using the sun's shadow, can be found at Cannon-Mania. Scroll down and click Sundial to learn about the sun dial cannon.

Math and History

At Mathematicians Commemorated on the Eiffel Tower, students in grades 3-12 will discover the names of French scientists and mathematicians that were placed on plaques in the Tower more than 100 years ago. Encourage students to visit The Official Site of The Eiffel Tower to learn more about this historic French landmark.

Extension: Following the tour, have each student return to the Mathematicians Commemorated on the Eiffel Tower site to read the biography of one of the mathematicians whose name is on the tower. Create a chart listing the name and major accomplishment of each mathematician. You might also encourage students to add to the chart the names of other mathematicians, some of whom might be found at Biographies of Woman Mathematicians.

Math and Science

After your middle- and high school students have toured the Eiffel Tower (see "History and Math" above) and perhaps helped build the Tower of the 3rd millenium, they may be ready to participate in Hands-On Bridge Building. This project, in which students use spaghetti, glue, and their knowledge of science and math to construct a weight-bearing bridge, begins with a lesson on scientific and mathematical vocabulary. Then, students create designs, reduce them to scale, prepare cost analyses, and build and test their bridges. The site includes quizzes, worksheets, and bonus and extension activities.

Math and Geography

At The Stowaway Adventure, "stowaways" in grades 6-12 can plot latitude and longitude to locate the route of the ship they're hiding on. They use that information, along with their math knowledge, to determine the ship's speed, distance traveled, and projected destination. Those stowaways who enjoy their voyage can move on to the second leg of their voyage, where they use what they have learned to determine future destinations and view satellite images to predict weather and ocean conditions.

Extension: When students return from their sea voyage, ask them to plan a trip on land or in the air. Students should use a map to set their starting point and destination, decide on an appropriate mode of transportation, and determine a reasonable speed. Then have them calculate the distance they'll travel and the time the trip will take. You might also encourage students to identify some landmarks along the way and to write postcards about the places they "visit."

Math and Health

At Fat Counting, students in grades 1-6 study and discuss the food pyramid. Then they compare the foods on the pyramid to the foods they eat, keep a fat-counting diary, calculate the number of calories from fat they eat in a week, find their daily average of fat, and compare their fat intake with that of other students. The lesson is less self-sufficient than many others, but the site does provide links to all the necessary information and resources.

Math and Art

At Greeting Card Geometry Math, a unit you can use to teach geometry to students in grades 2-5, students learn to identify and create congruent, similar, and equivalent shapes and then they use those shapes to make a holiday greeting card. The lessons are simple, yet effective, and include creative extension activities.

Extension: As a follow-up, you might encourage older students to use geometric shapes, and any medium, to create a poster showing the relationship between math and art. Then invite them to visit the National Museum of American Art or another online museum or art gallery, and identify examples of math in the art they find.

Math and Music

The Music section of Online Math Applications is one of the best sites available for introducing students to music and its relationship to math. The rhythm page explains how different musical notes represent the rhythm, or time, of a piece of music, while pages on tone and tune provide a thorough discussion of pitch, frequency, and amplitude. The site explains the mathematical relationship of adjacent notes on a keyboard and the theory that ratio is essential to harmony. Here, students can rediscover the discoveries of Pythagoras and listen to the music of Mozart. The clearly written, easy-to-read information makes this is a site that's appropriate for students of all ages.

Extension: After students have explored the site, taken some of the quizzes, or submitted quizzes of their own, give them an opportunity to listen to a variety of musical styles. Discuss the rhythm, tone, and tune of each selection, then ask students to compose a tune of their own. You might also encourage older students to research the lives of some classical musicians to discover how many were also mathematicians. Students of all ages will enjoy making, and experimenting with, a monochord.

Fun and Games

Finally, invite students to explore the activities at Fermi Questions. These problems, which encourage multiple approaches to problem solving and emphasize process over product, involve water balloons and jelly beans. Does it sound like fun? Does it sound like math? Check out this site and see what you think. But save it for the end of a very warm day!

ADDITIONAL RESOURCES

Article by Linda Starr
Education WorldÂ®
Copyright Â© 1999 Education World

Updated 04/26/2010

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You're Not in Math Class Anymore: Integrating Math Across th... | Education World

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Are you having trouble integrating math with literature, geography, art, or music? Discover how one teacher brought her love of running into the classroom and, in the process, integrated all areas of her curriculum. Also: Internet sites for integrating math with literature, history, science, geography, health, art, and music!

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Teaching Math Through a Social Justice Lens

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Teaching Math Through a Social Justice Lens

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WELCOME
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Sumdog's maths and spelling adaptive learning games for children aged 5-14 boost engagement and fluency. See how Sumdog can have an impact in your school!

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