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Math workshop is way less differentiated. Kids don't know their goals and what they are working on. Grouping kids based on data hasn't happen. 3rd grade has been responsive to student work. Check ins and reteaching. Using it during math time as well. Using schoolrunner somewhat to help. How could students be owning that. Lots of examples. Here's the wrong answer, here's an example. Kindergarten has more relevance.

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A: I want to know my child is reading for testing in 3rd grade.

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Interviewing the user: KIDS, parents, administrator

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Interviewing the user: KIDS, parents, administrator

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Q: What do you wish your child's school provide to teach math?
A: More online programs. I don't have time to teach my kid math, but I think they should get more practice at home. They get competitive about things like video games and I think that's really helpful.  I don't know why we don't have more.

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Bedtime Math – We inspire kids to love math so they embrace and excel at it.

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Code.org sums up the situation nicely:

Computer science drives innovation in the U.S. economy and society. Despite growing demand for jobs in the field, it remains marginalized throughout the U.S. K-12 education system.

There are many reasons for this. As you well know, teachers are already stretched pretty thin, and often it seems like there's just no bandwidth to add something new to a very full schedule. Additionally, some schools have few or no computers and/or tablets for classroom use.

But the earlier we introduce children to coding, the more comfortable they will be when presented with more in-depth learning opportunities in middle and high school. Also, early exposure to coding helps teach children how important it is to understand computers as the valuable tools they are rather than merely fun playthings.

Kids Want to Code

Even if you don't have a classroom full of future computer programmers, learning the fundamentals of coding provides students with skills that will serve them well in virtually any career they choose. Plus, there are few things that ignite and excite a room full of learners like a coding class.

In my work as the technology chair of our PTA board, I've participated in organizing the Hour of Code for the past two years at my children's school, and Computer Science Week generates a lot of buzz. I've seen firsthand how excited both kids and their parents get over learning to code, but it's really the kids who enjoy the experience the most. (To see that enjoyment, look at the picture above -- it's a second grade coder right after she grasped a new computational thinking task.)

Children want to learn how to code. They want to learn how to make tablets and computers do useful things. They want to learn how to build websites. It's actually a very cool thing to them.

And while "cool" is nice, what really matters are the lasting benefits of building these skill sets:

Logical thinking

Problem solving

Persistence

Collaboration

Communication

So how do we get there? There are many great online resources to help you find the right coding tools for your particular curriculum, including those provided by Code.org and right here on Edutopia. For example:

But what I want to focus on is breaking down the barriers to getting started in your classrooms. . . not some day, but right now.

5 Steps to Start Coding

At J.Y. Joyner Elementary School, we're lucky to have Jen Bell, our amazing technology teacher. Together, we've put together some advice to help you introduce coding to your curriculum, regardless of your budget or specific circumstances.

1. Get connected.

There are so many educators and organizations that promote computer science. The resources available through Code.org alone are amazing. They offer curriculum and content, live chat or Skype sessions with professionals, and workshops that focus on teaching coding to young children. If you do one thing after reading this, go join the Code Studio for grades K-5 and try to attend a workshop ASAP.

2. Creating a 1:1 classroom isn't necessary.

Don't be hindered by the misconception that every child needs his or her own device. Coding is a language which involves logic and problem solving, so working in pairs is actually a great way to increase production, develop collaboration skills, and allow children the opportunity to take on different roles in a partnership. In fact, there are many "unplugged" activities offered that don't use a device at all.

3. Trust the kids.

Don't underestimate what young children are able to accomplish when educators let go of the wheel and allow students to become the drivers. Just adding one piece of computer science to your curriculum will get the ball rolling, and you'll get the feedback you need from your students to make it even better.

4. Don't go it alone.

If you're a teacher reading this post, there are certainly others like you who will want to implement something and maybe even work with you at your school. And of course, you can reach out to your students' parents and see if there are any geeks (like me!) who would be willing to help out and maybe even come into the classroom. Get those parents involved immediately! Speaking from experience, I can assure you that they will be tremendously excited when asked to share what they know.

5. Make it fun.

Choose age-appropriate resources that allow kids to progress and grow. Apps like Kodable, The Foos, LightBot, Run Mario Run, and Daisy the Dinosaur guide children through a series of puzzles and tasks that allow them make connections with minimal adult intervention, even without a computer (refer back to the Vicki Davis piece mentioned above for more ideas).

Teaching young learners how to code on a large scale will help change the paradigm of children, and ultimately adults, from being technology consumers to technology producers. And that's precisely what our students -- and our country -- need right now. Don't wait for conditions to be perfect, or for that new batch of classroom tablets to arrive. Just jump in and take action today.

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Add Coding to Your Elementary Curriculum. . . Right Now

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Code.org sums up the situation nicely: Computer science drives innovation in the U.S. economy and society. Despite growing demand for jobs in the field, it remains marginalized throughout the U.S. K-12 education system. There are many reasons for this.

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When you conjure your stereotype of Seattle's Amazon high-tech workers, what do you see?

If your mental picture of the Amholes/Amabots/Amazombies changing our city is a transplant, rather thana native Seattleite, you'd be mostly right.

You'd certainly be hard pressed to find a black person born and raised in Seattle working as high-tech employee for the South Lake Union company (or any other local tech giants, for that matter).

But the sad truth is, part of the reason is the way we're educating our young people.

There has ben an alarming ethnic and racial disparity in math achievement in Seattle Public Schools, even as Seattle marches at the forefront of education reforms.

Between 2010 and 2014 more than sixty percent of black students failed their end-of-course (EOC) algebra exams (compared with less than 20 percent of white students). Performance on the EOC geometry test was only slightly better.

Even with the new "Smarter Balanced" exams, which are based on recently implemented Common Core Standard, this "achievement gap" doesn't seem to have narrowed. It exists for other demographic groups like Latinos, American Indians and migrants as well. And it's not just SPS. The achievement gap is replicated in school districts across the state.

So what's wrong?

At the classroom level, it has to do with inequitable teaching practices, says a revolutionary math education researchers at Stanford University.

Jo Boaler, author of a new book Mathematical Mindsets, envisions an academic world where everyone can learn math equitably regardless of their skin color, gender, sexual orientation or income.

I got the chance to see Boaler, a professor of mathematics education at Stanford University, and her colleague Carol Dweck, present their work at a seminar titled: "New Lens on Learning: The Hidden Value of Motivation, Grit and Engagement" put together by Education Writers Association.

At the conference, I was shocked to learn how gentrified and racialized math education in the U.S. is.

There's a thinly veiled belief in the U.S. that white male students from rich backgrounds just happen to have the "math gene."

Personally, I found this chauvinism amusing, given my background in public schools in Ethiopia, where the "math geniuses" weren't typically the rich students, and often came from economically disadvantaged backgrounds.

I believe Boaler, who's British, found this exclusivity perpetuated in American culture equally shocking.

As a mother of two daughters, she mentioned being extremely dissatisfied with a Disney show that portrayed girls as being particularly bad at math. But she suggests there's something even more insidious behind the stereotypes:

" Some people revel in the inaccessibility of mathematics as it's currently taught, especially if their own children are succeeding, because they want to keep clear a societal advantage... Mathematics has the greatest and most indefensible differences in achievement and participation for students of different ethnicities, genders, and socioeconomic income levels for any subject taught in the United States."

And this disparity really matters, because math education is such a powerful predictor of future success.

Most universities require at least three years of high school math for college entrance, determining the opportunities available for the rest of student's lives.

Earnings can also be predicted by amount, type and level of math course taken in high school. In 2004, Rose and Betts found that the more math classes students take in high school, especially in algebra and geometry, the higher their earnings were ten years later. Moreover, taking advanced math courses predicted an increase in salary as high as 19.50% ten years later.

According to her research, Boaler says there are some extremely successful strategies for producing more equitable math outcomes. She can frequently be heard calling for a "math revolution" to implement these approaches and narrow the achievement gap.

Here are 5 things Seattle teachers, schools and parents do to teach math more equitably. (Okay, really there's six - and the last one is the most important):

1. Offer high-level content to all students

"Put simply, if students spend time in class where they are given access to high-level content, they achieve at higher levels," Boaler writes. So why not g ive all students access to advanced math courses?

Rainier Beach High School took this sort of gamble recently, introducing all students to International Baccalaureate Curriculum, and has since topped the district in graduation rates, according to the Seattle Times. These results are pretty stunning. Only three years ago (before the introduction of the IB program) Rainier Beach was considered one of the worst high schools in Seattle.

According to Boaler, radical teachers have achieved similar results by offering advanced math classes to all students, dismissing the myth of "gifted child" which has been used to separate into those with and without math gene into separate courses (an injustice that was actually the subject of a class action lawsuit in California).

2. Dump the myth about the "math gift"

As in most STEM fields, in math education there tends to be a belief that aptitude for learning math is something genetically owned and not modifiable.

Boaler describes this "fixed mindset" as "the heart of inequity problems in Mathematics".

"Although I am not saying that everyone is born with the same brain, I saying that there is no such thing as a 'math brain' or 'math gift' as many believe," Boaler wrote.

During the her presentation at the Stanford conference, I grilled Boaler on this: While I consider my own math stellar, I have a friend who is a math overachiever who always leaves me in the dust both in his speed and ability to solve difficult problems.

She told me the percentage of such people is negligible, and normally they fail when they start to believe their math ability is a given and start studying less, which is damaging in the long-run.

Boaler suggests moving from that "fixed mindset to a "growth mindset."

Communicating that change to students in the classroom is both about what you say and don't say: Don't tell students they are "smart" when they get perfect score. Parents should never say they are "bad in math" in front of their children - especially girls. Both things just reinforce that "fixed mindset."

Don't praise students when they are achieving lower, but do c elebrate mistakes. Research has found that the brain grows and a "spark" occurs when students make mistakes, even if they are not aware they've done so.

Boaler listed a few values she reiterates over and over to students in her the classroom to reinforce the "growth mindset":

That she believes in every one of them.

That the math gene doesn't exist and she expects all of them to achieve higher.

That mistakes are valuable and she loves them. Failure and struggles are the most important part of math and learning, and they don't mean her students can't do math.

That she doesn't value students' working quickly. She values depth.

That she loves student questions and will share them on posters for other students to think about.

3. Encourage students to think deeply about mathematics

Students achieve higher when they are exposed to the kind of deep understanding that's typically unavailable in math classrooms.

This is especially true for girls who studies show tend to be put off by procedural math. Boaler suggests getting at deep understanding by using project-based curriculum with real-life applications, giving students lots of opportunities to work together and get hands-on experience.

Boaler explains in her book that if math is taught using deep learning, instead of as performance subject, students can start to see it as important knowledge that empowers them to think quantitatively to solve problems in their work and lives.

4. Teach Students to work together

"Group work is a strategy I regard as critical to good mathematics work," Boaler wrote, "But a fascinating study showed that group work may also be critical in countering racial inequities in mathematics achievement and course taking."

Research shows that black students' results were better when working together. Back in the '70s, Uri Treisman of the University of California, Berkeley was alarmed to find 60% of black students failing required calculus courses, despite coming with good GPA's from high school. Treisman introduced a new approach in which students were offered collaborative workshops so they could work mathematics together. The failure rates dramatically dropped to zero in two years.

More recent research studies by Boaler and others confirm this result.

"When students work on mathematics collaboratively, which also gives them opportunities to see and understand mathematics connections - equitable outcomes results," she wrote.

5. Give girls and students of color additional encouragement to learn math and science

Due to the severely damaging stereotypes that they'll underperform at math, girls and students of color need more encouragement than other students.

"Both girls and students of color - particularly underrepresented minorities - need thoughtful and positive messages to be given to them, about their valued place in mathematics," Boaler wrote.

She gives a few examples how positive messages can be delivered to girls and students of color:

Highlighting the achievements of women and underrepresented minorities in mathematics and STEM.

Structuring classrooms so students are asked to become an expert on a subject and share their findings with other students.

Increasing diversity of teachers to present role models to students of color.

"My main point is that it may not be enough, as a math teacher, to treat students equally in the pursuit of equity," she wrote. "Some students face additional barriers and disadvantages, and we must work to address those quite deliberately if we are to achieve a more equitable society."
Professor Jo Boaler is a part of this math parody mashup of Taylor Swift's "Shake it Off" and Nicki Minaj's "Anaconda"
6. Eliminate homework! (or at least change the nature of it)

Great news kids! PISA ( The Program for International Student Assessment) conducted a survey of 13 million students to study the relationships between homework, achievement and equity, and found that homework is inherently inequitable, and that it "didn't seem to raise achievement for students."

"This is not an isolated finding; academic research has consistently found homework to either negatively affect or not affect achievement," Boaler wrote.

Why? Students from less-privileged families rarely have quiet place to study or do homework at night, and their parents are more likely to be at work and unable to help). T hey also have fewer study materials such as books and devices with Internet access.

"When we assign homework to students, we provide barriers to the students who need our support," Boaler wrote, "This fact, alone, makes homework indefensible to me."

She suggests that teachers and school leaders who want to promote equity by eradicating homework arm themselves with resources like "The Case Against Homework" by Alfie Kohn and "The One World School House" by Sal Khan, which reinforce these conclusions.

But old habits die hard, and the quantity of homework is often seen as a measure of a curriculum's rigor.

"If you want to retain a homework, then I recommend changing the nature homework," Boaler suggests. "Instead of giving questions students need to answer in a performance orientation, give reflection questions to encourage students to think back on mathematics lesson and focus on the big ideas."

There's a widespread assumption is that " social-cultural context" is to blame for the math achievement gap. But there's still shockingly little academic research on how context actually affects engagement in students of color (here's the one example I found, based on a survey of studies conducted by ).

Regardless, Boaler's six strategies are all designed to mitigate those contexts and challenge education inequity.

Her recommendations are all things teachers can start to do right now, even without a much-needed overhaul of the way school districts approach math education.

Because even if teachers are not able to change the socio-cultural context impacting their students, they can change the classroom context.

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5 + 1 things teachers can do to close the math achievement gap

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When you conjure your stereotype of Seattle's Amazon high-tech workers, what do you see? If your mental picture of the Amholes/ Amabots/ Amazombies changing our city is a transplant, rather thana native Seattleite, you'd be mostly right.

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A few weeks ago I (Jo Boaler) was working in my Stanford office when the silence of the room was interrupted by a phone call. A mother called me to report that her 5-year-old daughter had come home from school crying because her teacher had not allowed her to count on her fingers. This is not an isolated event-schools across the country regularly ban finger use in classrooms or communicate to students that they are babyish. This is despite a compelling and rather surprising branch of neuroscience that shows the importance of an area of our brain that "sees" fingers, well beyond the time and age that people use their fingers to count.

In a study published last year, the researchers Ilaria Berteletti and James R. Booth analyzed a specific region of our brain that is dedicated to the perception and representation of fingers known as the somatosensory finger area. Remarkably, brain researchers know that we "see" a representation of our fingers in our brains, even when we do not use fingers in a calculation. The researchers found that when 8-to-13-year-olds were given complex subtraction problems, the somatosensory finger area lit up, even though the students did not use their fingers. This finger-representation area was, according to their study, also engaged to a greater extent with more complex problems that involved higher numbers and more manipulation. Other researchers have found that the better students' knowledge of their fingers was in the first grade, the higher they scored on number comparison and estimation in the second grade. Even university students' finger perception predicted their calculation scores. (Researchers assess whether children have a good awareness of their fingers by touching the finger of a student-without the student seeing which finger is touched-and asking them to identify which finger it is.)

Evidence from both behavioral and neuroscience studies shows that when people receive training on ways to perceive and represent their own fingers, they get better at doing so, which leads to higher mathematics achievement. The tasks we have developed for use in schools and homes (see below) are based on the training programs researchers use to improve finger-perception quality. Researchers found that when 6-year-olds improved the quality of their finger representation, they improved in arithmetic knowledge, particularly skills such as counting and number ordering. In fact, the quality of the 6-year-old's finger representation was a better predictor of future performance on math tests than their scores on tests of cognitive processing.
Many teachers have been led to believe that finger use is useless and something to be abandoned as quickly as possible.
Neuroscientists often debate why finger knowledge predicts math achievement, but they clearly agree on one thing: That knowledge is critical. As Brian Butterworth, a leading researcher in this area, has written, if students aren't learning about numbers through thinking about their fingers, numbers "will never have a normal representation in the brain."

One of the recommendations of the neuroscientists conducting these important studies is that schools focus on finger discrimination -not only on number counting via their fingers but also on helping students distinguish between those fingers. Still, schools typically pay little if any attention to finger discrimination, and to our knowledge, no published curriculum encourages this kind of mathematical work. Instead, thanks largely to school districts and the media, many teachers have been led to believe that finger use is useless and something to be abandoned as quickly as possible. Kumon, for example, an after-school tutoring program used by thousands of families in dozens of countries, tells parents that finger-counting is a "no no" and that those who see their children doing so should report them to the instructor.

Stopping students from using their fingers when they count could, according to the new brain research, be akin to halting their mathematical development. Fingers are probably one of our most useful visual aids, and the finger area of our brain is used well into adulthood. The need for and importance of finger perception could even be the reason that pianists, and other musicians, often display higher mathematical understanding than people who don't learn a musical instrument.

Teachers should celebrate and encourage finger use among younger learners and enable learners of any age to strengthen this brain capacity through finger counting and use. They can do so by engaging students in a range of classroom and home activities, such as:

Give the students colored dots on their fingers and ask them to touch the corresponding piano keys:

Give the students colored dots on their fingers and ask them to follow the lines on increasingly difficult mazes:

(The full set of activities is given here.)

The finger research is part of a larger group of studies on cognition and the brain showing the importance of visual engagement with math. Our brains are made up of "distributed networks," and when we handle knowledge, different areas of the brain communicate with each other. When we work on math, in particular, brain activity is distributed among many different networks, which include areas within the ventral and dorsal pathways, both of which are visual. Neuroimaging has shown that even when people work on a number calculation, such as 12 x 25, with symbolic digits (12 and 25) our mathematical thinking is grounded in visual processing.

A striking example of the importance of visual mathematics comes from a study showing that after four 15-minute sessions of playing a game with a number line, differences in knowledge between students from low-income backgrounds and those from middle-income backgrounds were eliminated.

Number-line representation of number quantity has been shown to be particularly important for the development of numerical knowledge, and students' learning of number lines is believed to be a precursor of children's academic success.

Visual math is powerful for all learners. A few years ago Howard Gardner proposed a theory of multiple intelligences, suggesting that people have different approaches to learning, such as those that are visual, kinesthetic, or logical. This idea helpfully expanded people's thinking about intelligence and competence, but was often used in unfortunate ways in schools, leading to the labeling of students as particular type of learners who were then taught in different ways. But people who are not strong visual thinkers probably need visual thinking more than anyone. Everyone uses visual pathways when we work on math. The problem is it has been presented, for decades, as a subject of numbers and symbols, ignoring the potential of visual math for transforming students' math experiences and developing important brain pathways.

It is hardly surprising that students so often feel that math is inaccessible and uninteresting when they are plunged into a world of abstraction and numbers in classrooms. Students are made to memorize math facts, and plough through worksheets of numbers, with few visual or creative representations of math, often because of policy directives and faulty curriculum guides. The Common Core standards for kindergarten through eighth grade pay more attention to visual work than many previous sets of learning benchmarks, but their high-school content commits teachers to numerical and abstract thinking. And where the Common Core does encourage visual work, it's usually encouraged as a prelude to the development of abstract ideas rather than a tool for seeing and extending mathematical ideas and strengthening important brain networks.

To engage students in productive visual thinking, they should be asked, at regular intervals, how they see mathematical ideas, and to draw what they see. They can be given activities with visual questions and they can be asked to provide visual solutions to questions. When the youcubed team (a center at Stanford) created a free set of visual and open mathematics lessons for grades three through nine last summer, which invited students to appreciate the beauty in mathematics, they were downloaded 250,000 times by teachers and used in every state across the U.S. Ninety-eight percent of teachers said they would like more of the activities, and 89 percent of students reported that the visual activities enhanced their learning of mathematics. Meanwhile, 94 percent of students said they had learned to "keep going even when work is hard and I make mistakes." Such activities not only offer deep engagement, new understandings, and visual-brain activity, but they show students that mathematics can be an open and beautiful subject, rather than a fixed, closed, and impenetrable subject.

Some scholars note that it will be those who have developed visual thinking who will be "at the top of the class" in the world's new high-tech workplace that increasingly draws upon visualization technologies and techniques, in business, technology, art, and science. Work on mathematics draws from different areas of the brain and students need to be strong with visuals, numbers, symbols and words-but schools are not encouraging this broad development in mathematics now. This is not because of a lack of research knowledge on the best ways to teach and learn mathematics, it is because that knowledge has not been communicated in accessible forms to teachers. Research on the brain is often among the most impenetrable for a lay audience but the knowledge that is being produced by neuroscientists, if communicated well, may be the spark that finally ignites productive change in mathematics classrooms and homes across the country.

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Using Fingers to Count in Math Class Is Not 'Babyish'

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A few weeks ago I (Jo Boaler) was working in my Stanford office when the silence of the room was interrupted by a phone call. A mother called me to report that her 5-year-old daughter had come home from school crying because her teacher had not allowed her to count on her fingers.

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still isn't enough. How do we close the achievement gap in our own classrooms?

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Norman Rockwell's painting "The Problem We All Live With" depicting Ruby Bridges - the first black child to attend an all white elementary school in the South. Image from the website of the Norman Rockwell Museum.

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