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I like the idea to try Minecraft in my lessons and in my learning design making children designing their zoo cage with it.
I don't like the idea to use the QR Code beacuse I think it's not so much efficient.

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It's inspiring and I really feel entusiastic thinking about all the opportunity technology can give to math teaching. In one of my class we have a IWB but in the other one we have nothing to use. That's something make me sad about the opportunity the students of that class will lost. I try to help by taking the projector and a pc, but isn't simple to use and isn't the same than the IWB.

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Conrad Wolfram: Teaching kids real math with computers

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http://www.ted.com From rockets to stock markets, math powers many of humanity's most thrilling creations. So why do kids lose interest? Conrad Wolfram says the part of math we teach -- calculation by hand -- isn't just tedious, it's mostly irrelevant to real mathematics and the real world.

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It's so hard to me to work to this skill. The one show in this video is a wounderful process but I really toil to put it in practice. I think that this kind o teaching skill can be learn only in a course with a tutor really working with you. But I don't know, this really is my Achilles heel.

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A master teacher in Anchorage, Alaska, establishes a cooperative-learning environment in an upper-elementary classroom. For more information and resources, visit http://www.edutopia.org

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Another think I really love is creating or inventing something with my children. I do this kind of activity every time I can. My learning will be about the design of a zoo cage. The ideas about the origami are the next that I will try in my class. The other project are wonderfull but for the moment I think I have no time to do such things.

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Ok, who knows me can say how much I love using story telling in math activities! And I semply LOVE all the ideas in this video. The learning design I'm working on starts with a story (L'occhio del lupo" di Daniel Pennac). Stories are an extraordinary medium to engage children.

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MakeBelieve Arts believes that children are driven to make sense of the world through story. We also believe that you can teach anything through the medium of story...even mathematics! Creative Mathematics takes the mystery out of maths and brings it to life in vivid colour.

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It cold be a way to engage my students expecially someone that really loves to move and needs to move to learn better

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By Rebecca Jacobson

Carrie Lewis and Kelly Steele's fifth grade students slide and spin across the classroom floor, doing the hustle, the robot, and the running man. While it may look at first glance like goofing off, these students are actually dancing for a higher cause...math.

Lewis, a STEM specialist for Virginia's Lynchburg city schools, and Steele, who teaches gifted education in Bedford county, Virginia, are both math enthusiasts eager to instill in their students a love of the subject. And dancing, they hoped, might be just the thing to help tackle a common fifth-grade learning deficit - number patterns.

"Dances are patterns," Lewis said. "We had identified that our students had trouble with patterns and this was a way to get them involved in it."

Both teachers are part of Sweet Briar College's STEM teacher education program, where they worked together to design "dance by numbers," a lesson plan that relies on dance to teach pattern recognition. In the video above, Lewis explains how the lesson works.
IDENTIFYING A PATTERN

The first step was to turn a dance routine into a number pattern. Students logged onto the Pillsbury Dough Boy website and watched, studied and deconstructed the cartoon mascot's six dance moves. They assigned each step a number, and charted the patterns in his dance.

"Once they translated the number to a movement, they began to see how it would be really easy to get a pattern," Lewis said. "I had them watch 'America's Best Dance Crew' so they could see that they're just doing the same thing over and over again."
MAKING THEIR OWN MOVES
The students then choreographed their own dance routines. The teachers required that each routine contain at least five moves that repeated at least once. Songs were to be set to instrumental music of the students' choice - some opted for hip-hop; others for the Mario Bros theme.

Using stopwatches to clock the average time of their routine, students were asked to then calculate how many times their pattern would repeat throughout the course of the song, and then turn the resulting data into a graph.

"If your song is 100 seconds, how many repetitions will you do of your dance?," Steele said. "If you use the extended version of your dance, 200 seconds, how many repetitions do you need to do? They are using their graph to figure that information out."
ANALYZING THE DANCE
Finally, each group performed their original routine for their classmates. And midway through the dance, they'd freeze, and the class would be asked to predict the next move in the pattern. (Lewis called these "jump-ins.")

In addition to patterns and graphing, the dance lesson helps students with averaging and calculating elapsed time, along with multiplication and division.

"If their pattern was seven [steps] long and they were asked what jump-in 23 was, rather than sit there and count, count, count, they realized they could do multiples," Lewis said. "You could almost see that light bulb go on."

"Dance by numbers" received enthusiastic feedback from a regional conference for STEM teachers, said Arlene Vinion-Dubiel at Sweet Briar College, who helped the teachers implement their lesson plan.

And inside the classroom, results were tangible. Math test scores went up. Shy students happily break-danced at the front of the class. One group performed their routine for the school talent show last year.

"They were 100% into it," Steele said, who expected the boys in her rural classes wouldn't dance in front of their peers.

"Math is such a challenge," Lewis added. "What you're trying to teach them is that what they're learning isn't isolated to a work sheet. That's what STEM is all about - letting the measurements or the math speak to you and letting it teach you something."

Watch the students in action here:

How Math is Getting Its Groove Back

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By Rebecca Jacobson Carrie Lewis and Kelly Steele's fifth grade students slide and spin across the classroom floor, doing the hustle, the robot, and the running man. While it may look at first glance like goofing off, these students are actually dancing for a higher cause...math.

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I had neve thought to this deep connection between music and math. The video linked in the article is absolutely fantastic. I sure show it to my students in the next days

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It was when hearing the sounds of hammers that Pythagoras realized the ubiquity of numbers in mathematical harmony. He would go on laying down the mathematical foundations of music, based on octave…

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A serie of books about math and real life.

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Living math books that can be used to teach or reinforce math skills. Making math meaningful, one book at a time!

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An interesting program, to use also with whiteboard, that helps students think about problems and their solution.

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Thinking Blocks is a nice site for elementary and middle school mathematics teachers. Thinking Blocks provides interactive templates in which students use brightly colored blocks to model and solve problems. As students work through the problems they are provided with feedback as to whether or not they are using the correct sequence to solve each problem. There are templates and problems for addition, multiplication, fractions, and ratios. You can also develop your own problems using the modeling tool.

Applications for Education
I learned about Thinking Blocks from James Hollis at Teachers Love SMARTBoards. James suggested that Thinking Blocks could be good site for helping students see how algebraic reasoning works. And, of course, if James is writing about it, it must be well suited to use on interactive whiteboards.

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Thinking Blocks - Model Your Math Problems

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Thinking Blocks is a nice site for elementary and middle school mathematics teachers. Thinking Blocks provides interactive templates in which students use brightly colored blocks to model and solve problems. As students work through the problems they are provided with feedback as to whether or not they are using the correct sequence to solve each problem.

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A serie of videos made by NASA about the math behind the universe.

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Real World: Comets - It's Done With Math

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NASA engineers are finding new uses for old spacecraft as a way to study comets. Find out how a repurposed spacecraft can return to a comet for a second visit to uncover secrets about the formation of the solar system. Use angular size to see just how big this comet really is!

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Another site with real math lessons and ideas.

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How to use the channel?

Educators use the Futures Channel micro-documentaries to interest and engage STEM students.

Futures Channel subscribers have access to a wide range of STEM-oriented video programs. Here's just a snapshot of what you can show your students.

Your source for STEM Videos & Lesson Plans that inspire and engage.

When your students ask the inevitable question, "When would I ever use this?" answer it with a micro-documentary from the largest STEM video library of its kind.

Videos: The library contains 140 STEM videos. They feature diverse professionals talking about use of math and science in what they do. They are 2 to 6 minutes long.

Lesson plans: There are over 200 lesson plans each containing several activities. Search and filter capabilities enables you to zero in on your lesson needs.
Teachers tell us:
"As a teacher and a media production specialist at the school district level, I am very impressed with the Futures Channel documentaries. They provide a critical link, view of the real-world application of knowledge that I want my students to strive towards as they learn about technology, art, math, and science in school. I cannot afford to take field trips to show my students all these interesting people and projects in action. Futures Channel does this in an inviting and exciting way."
-J.G

"With these videos, I can do more than tell students how math is used in the real world. I can show them what it really looks like in action. These upbeat, creative, and informative videos grab students' attention, plant a seed, and lay the groundwork for exciting and meaningful applications of mathematics in the classroom. After watching Futures Channel videos, students have a more well-defined purpose and genuine interest in the mathematics they are studying." -J. K

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How to use the channel? Educators use the Futures Channel micro-documentaries to interest and engage STEM students. Futures Channel subscribers have access to a wide range of STEM-oriented video programs. Here's just a snapshot of what you can show your students. Your source for STEM Videos & Lesson Plans that inspire and engage.

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These are other great ideas the need to be translated in italian.. That's just a little problem..

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Get The Math in Fashion ~ Introduction : Get The Math

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Chloe Dao, fashion designer and winner of season two of Project Runway, talks about her career as a fashion designer, explains how she uses math to make her designs a reality, and introduces a fashion-related algebra challenge.

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Get the Math in Music ~ Introduction : Get The Math

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Manny Dominguez and Luis Lopez of DobleFlo talk about how their duo got started, how they use math in producing hip-hop music, and set up a music-related algebra challenge.

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I don't really like sports so I'm just a bit reluctant to use this kind of resources but I know for a lot of children it is importa so...

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The Super Bowl is coming up this weekend and many classrooms will have students buzzing with their predictions for Sunday's game. This provides a good opportunity to incorporate math and science with sports. Below is a re-publishing of a review I wrote two years ago about NBC's Science of Football lesson materials.

The Science of Football is a series of ten videos from NBC Learn explaining and demonstrating math and science concepts as they relate to football. The Science of Football could be a good way to get students who enjoy sports, but don't necessarily enjoy math and science, interested in learning math and science. Lessonopoly offers lesson plans corresponding to each video to support your use of the videos in your classroom.

Here are some resources for incorporating other sports into math and science lessons.

Exploratorium's Sports Science site contains many pages on which students can explore the math and science of team sports as well as the individual sports of bicycling and skateboarding. The bicycling section has a calculator that students can use to calculate the aerodynamic drag and propulsion power of a bicyclist.

Sport Science on ESPN.com has couple of videos that are relevant as school winds-down and kids turn their attention to Little League baseball and softball. In MLB Vision Sport Science evaluates how quickly a player has to respond to a baseball thrown ninety miles per hour. Then to answer the question, can you really keep your eyes on the ball? Sport Science attaches an eye tracking device to Nomar Garciapara.

In Hitting a Softball Sport Science explains the scientific and mathematical differences between hitting a baseball and hitting a softball.

Sport Science: Distraction looks at whether or not all of those waving, screaming fans behind a basketball hoop actually make a difference in whether or not a player makes his or her free throw. You could turn this into an active survey in your school's gymnasium. Have your students shoot some hoops without distraction and tally their average rate of success. Then have them test out distractions like waving, playing music, or yelling to see if there is a change in the success rate.

Well Home offers an interesting infographic showing the energy expended by athletes performing various athletic tasks. I've seen other infographics like this and usually they only mention calories. Well Home's infographic mentions calories as well as watts and speed measurements. Well Home's infographic could be printed and displayed in health, physical education, and or mathematics classes.

Well Home's Energy in Sports infographic goes well with another resource that contains mathematics and science lessons in the context of sports. ESPN's series Sports Science looks at the mathematics and science involved in various athletic feats.

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Resources for Teaching the Math & Science of Sports

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The Super Bowl is coming up this weekend and many classrooms will have students buzzing with their predictions for Sunday's game. This provides a good opportunity to incorporate math and science with sports. Below is a re-publishing of a review I wrote two years ago about NBC's Science of Football lesson materials.

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I really love this web site! there are full problems and activity that I can do using real life objects and contests. The only problem is that I have to translate them in italian. Why we don't have something similar?

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In mid-August and early September, the Monarch butterflies begin their annual migration south to more moderate climates to hibernate and overwinter. It is an incredibly long migration and fascinating to observe. But, the populations data on Monarchs has seriously changed...

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I really love this idea and it's really a shame that the questions he created yet, are in english. I cold try to do something similar by traslating somenthing..

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When it comes to creative uses of Google tools, Tom Barrett is certainly a leader that we can all learn from. A great example of this can be found in Tom's Math Maps. Math Maps are Google Maps on which Tom and others have created placemarks which when clicked reveal mathematics questions for students to answer based on the maps. There are questions available for every elementary school grade level. The placemarks are color-coded to indicate the level of the questions. Blue = Kindergarten, Red = 1st grade, Green = 2nd grade, Light Blue = 3rd grade, Yellow = 4th grade, Purple = 5th grade. Visit Tom Barrett's Math Maps page to view the existing Math Maps and read about how to contribute to the existing Math Maps.

Embedded below is 55 Shape Activities in Paris.

View 55 Shape Activities in Paris in a larger map

Applications for Education
Math Maps could be a great way for students to see examples of mathematics in the real world. Math Maps are also have a fun scavenger hunt feel. If you work with students slightly older than elementary school, you might want to consider having them create their own Math Maps as a way to demonstrate their knowledge of mathematics in the real world.

Here are some related items that may be of interest to you:
More Real World Math
Google Maps for More than Social Studies

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Using Maps in an Elementary School Math Lesson

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When it comes to creative uses of Google tools, Tom Barrett is certainly a leader that we can all learn from. A great example of this can be found in Tom's Math Maps. Math Maps are Google Maps on which Tom and others have created placemarks which when clicked reveal mathematics questions for students to answer based on the maps.

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This site is a bit difficult too browse. It's interesting the tilling a floor expirience but with our school internet connection and old pcs we can't really use this site. I save it for the future.

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In this website you can find very interesting lesson plans based upon the connection with school math and real world. I really like the project about complex areas.

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Project-Based Learning activities offer a different approach to learning in scope and depth. PBL lessons are intended to build upon your previous knowledge and offer a unique opportunity to utilize it. Try to work with your teammates through any unexpected difficulties as they arise. Additionally, you'll often find these problems will stray from mathematics into other disciplines such as Science or Social Studies. This is encouraged and should make the project even more meaningful.

Truly, these activities should expose you to real world problem solving experiences as you rely on the work of others and face deadlines. Project Based Learning situations can provide you with important social skills that you will carry with you into the future.
The duration of these activities may range from days to weeks, or longer. The teacher acts as a facilitator of the exercise, as students work together usually in pairs or small groups. The students may have different roles to fill and gain specific expertise in these team building events. Communicating and planning with your team is an important part of the project.

In real life, problems do not always have clear solutions; there are no answers available in the back of the book. There may be several paths to choose from, each with their own advantages.

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Project-Based Learning activities offer a different approach to learning in scope and depth. PBL lessons are intended to build upon your previous knowledge and offer a unique opportunity to utilize...

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In this site I have found so much inspiring video and photos to use with my children. I can start showing a photo or a video and then we can explore a particoular math concept or create a math problem. It's interesting also that there are a lot of questions that come in people's mindsfor every picture.

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What is the first question that comes to your mind?

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I take an object in the class and I use it to make math!
I used the class clock to teach children about angles. We observed the different position of the hands every five minutes and we reproduce them on the notebooks. Then we named the different angles and measure them.

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In 5th grade my students have to study reduction scales. I can give them a picture, takes from google map, of our street and ask them to find the scale by measuring the real distance from two visible points.

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I have to try to change the textbook problems so that they become more real.

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An article about how PBL can improve Steam teaching. It makes me thinking a lot...

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Edutopia is a free source of information, inspiration, and practical strategies for learning and teaching in preK-12 education. We are published by the George Lucas Educational Foundation, a nonprofit, nonpartisan organization.

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It was really usefull to me to think about my practices and understand that there is a large work still to do.

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An article about how to use pbl learning in math teaching.

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How and why should math be taught using PBL? | MyPBLWorks

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PBLWorks National Faculty member Telannia Norfar tells how she teaches math with PBL.

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Interesting ideas to do geometry and to develope spatial skills by using wires.

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Fair at the Kinesthetic Intelligence Meeting in Ávila

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I had never thought about this difference and it'll help me a lot in evaluate students and in helping them to rise their math skills.

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Misconceptions are very different from the mistakes students make. Mistakes are not consciously made. Misconceptions are. Mistakes are usually one-off, while misconceptions, the gods forbid, could be for keeps. Mistakes are made by a few, misconceptions are made by many and, repeatedly.

Students can figure out their mistakes by themselves because mistakes are usually due to carelessness. They cannot do the same for misconceptions. Misconceptions are committed because students think they are correct.

How can misconceptions be addressed? By undressing them, carefully exposing them until the students see it. It cannot be corrected by simply marking them x because misconceptions are usually made with full knowledge.

The following are common misconceptions in arithmetic, algebra and geometry:

1. Did we not learn that multiplication is repeated addition? So, -3 x -4 = -3 + -3 + - 3 +-3 = -12?

2. Didn't we learn that to multiply fractions we simply multiply numerators and we do the same with the denominators? Didn't the teacher say multiplication is simply repeated addition so ?

3. Did not the teacher say x stands for a number? So in 3 x - 5, if x is 5, the value of the expression is 35 - 5 = 30?

4. Did not the teacher/book say to always keep the numbers and decimal points aligned? So if Lucy is 0.9 meters and her friend Martha is 0.2 taller, Martha must be 0.11 meters in height?

5. Did we not learn that the more people there are to share a cake the smaller their portion? So ?

6. Did we not learn that by the distributive law 2(a+b) = 2a + 2b? So, ?

7. Did not the teacher show us that (x-3)(x+1) = 0 implies that (x-3) = 0 and (x+1) = 0 so x = 3 and x = -1? Hence in (x-3)(x+4) = 8, (x-3) = 8 and x +4 = 8 so x = 11 and x = 4?

8. Did we not learn that the greater the opening of an angle, the bigger it is? So, angle A is less than angle B in the figure below.

9. Did we not learn that you if you cut from something, you make it smaller? Hence in the diagram below, the perimeter of the polygon in Figure 2 is less than the perimeter of original polygon?

10. Isn't it that the base is the one lying on the ground?

There's nothing a teacher should worry about mistakes. There's everything to worry about misconceptions. Good teaching practice exposes misconceptions, not hide them.

You might want to check out this book:

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Mistakes and Misconceptions in Mathematics

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Misconceptions are very different from the mistakes students make. Mistakes are not consciously made. Misconceptions are. Mistakes are usually one-off, while misconceptions, the gods forbid, could be for keeps. Mistakes are made by a few, misconceptions are made by many and, repeatedly. Students can figure out their mistakes by themselves because mistakes are usually due to carelessness.

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I want to better explore this site rich of practical activity and games.

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Math explained in easy language, plus puzzles, games, worksheets and an illustrated dictionary. For K-12 kids, teachers and parents.

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I find very difficult to personalize learning for my students. I'm not sure I know exactly all the information, about my students, that I need to do so. I want to improve this aspect this year by searching carefully all the info I need. I want to create activities that students can do in a lot of way respecting their level and preferences. My students love learning by doing and create something new. When a propose a practical problem they always are engaged. So I try to use this strategy everytime I can. The majority of them don't like to partecipate at discussion: they can't pay attention for the time necessary and they are't too good in respecting communication rules.

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A method about how to make children discuss and discover new ideas.

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Harkness refers to a method of teaching that was developed in the 1930s at the Phillips Exeter School in New Hampshire. The philanthropist Edward Harkness challenged Exeter with an offer: he would make a sizable donation of money to the school if they could originate and implement a radically student-centered method of teaching, and then use this method in all classes. After having their first proposal rejected by Mr. Harkness as "not radical enough," Exeter eventually committed to moving away from the traditional model of teaching in which the teacher lectures information to students, the students copy the information onto paper, and later, the "regurgitate" the previously instructor-fed information back onto tests and essays. In a Harkness class learning takes place through discussions held around a circular "Harkness Table." Sitting at the table, all members of the class must question, contribute, and contemplate in order to learn and succeed. Today all classes at Exeter, from English Literature to Algebra, from African History to Chemistry, are held around Harkness tables and use the Harkness method of learning.

Why Harkness?

Of the many different arguments in favor of the method, the most important may be that it goes beyond the mechanistic transmitting of information, and experientially teaches students how to learn. It is false to assume that students know how to learn. Academic learning requires a series of complex skills, such as the ability to analyze texts, verbal and written articulation of questions and ideas, listening, critical thinking, dialogue and research, to name a few. If students only learn in the traditional way, receiving information from their instructors in bite-sized chunks, and then later repeating the information onto tests, the skills they will have learned from this experience can be called little more than "parroting": a parrot can be trained to repeat what it hears, but it holds little, if any, understanding of the meanings of the words it says. Likewise, students can learn to repeat what they are told without having to actually understand what they are repeating. Furthermore, the implicit message of lecture instruction is one that ultimately disempowers students.

As "unbiased" as teachers try to be, educating is, based on the content and pedagogical approach to the curriculum chosen, a political endeavor. By maintaining their place at center stage-their classrooms filling stations for the empty-vesseled students, and they the Guardians of Truth-teacher-centered teachers convey the lesson that their students' ideas and questions have no explicit worth outside of how well they relate to the teacher's own ideas and questions. Additionally, teacher-centered classes reinforce the state of intellectual powerlessness common to most students and adults: only "qualified" authorities possess truth, and their opinions we must seek: truth is had by only "qualified" authorities, and we must seek their opinions. While the results of the teacher-centered method may be a pleasant boost to the teacher's own sense of intellectual superiority, the students are taught to distrust their individual ideas, and to rely too heavily upon the opinions of others; they learn not to trust in their own capacities to discern truth.

The Harkness class lessens students' ability to simply "parrot" information. As members of the learning group, students must engage with the class by asking questions and contributing their own thoughts. In general, Harkness teachers will minimize the amount of information and answers they give directly to their students. Instead, they will give their students' resources in which the information and ideas can be found, or at the very least, they will help their students locate the necessary resources. Because of this approach, students will experience the complex process of learning. This is a process in which they must involve themselves to a much greater degree than they may normally be required: students may not simply write down what teachers say. They must search for the ideas and information and then wrestle with that which they find. Students who engage themselves with the Harkness class will finish with a greater sense of autonomy and empowerment, knowing that they know how to learn. They will also finish the class with an increased ability to verbally articulate their questions and opinions in discussions. Additionally, Harkness students will come away with the important understanding of the power and necessity of listening, as well as the skills needed in order to be effective listeners.

What Harkness is Not

Harkness is not the Socratic method of teaching. As it is generally understood, Socratic teaching involves asking students questions about their ideas, continually pointing out weaknesses in the ideas until students "realize" the correct conclusions. The conclusions, however, are predetermined by the teacher, and the students only qualify as having realized if they agree with, or surrender to, the teacher's ideas. This type of teaching is teacher centered: the teacher is the sage on the stage, throwing forth pearls of wisdom to the flock of befuddled and bewildered minds below. Socratic teaching is excellent in terms of providing students with the experience of intensive critical thinking, of seeing an intelligent and intellectually engaged adult in action. The downside, however, is that the method focuses too much on the personality and interests of the teachers, perhaps leaving them feeling masterful and smart, but imparting feelings of subordination, stupidity, and even harassment onto their students. The Harkness class will generally have, nonetheless, a Socratic feel, in that students' ideas are questioned and commented upon. For the most part though, these questions and comments will come from the students' peers rather than the teacher.

Harkness is not just "teaching through discussion." While many teachers use class discussions in their courses, the discussions still tend to be very teacher driven: the teacher asks the questions, keeps the class focused, decides when to move on, and for the most part, still sits in the dominant role as expert holder of Truth. Conversely, some class discussions become very loose "blow-off-steam" forums in which members of the class (usually the dominant ones) shout out their opinions and argue back and forth. Unfortunately, these quasi-debate style classes almost always contain more hot air than substance-they lack the structure necessary for the type of critical inquiry that leads to substantive conclusions upon which a class may build in the future. Furthermore, these types of discussions give students a bad model of intellectual dialogue: combativeness, blind position-taking, and immaturity are the lessons learned.

Teaching a Harkness Class

Different teachers have different approaches, and many will change their techniques based on the chemistry of their particular class. For the most part, the following description accurately portrays how I run my Harkness classes.

With the nightly reading is assigned, I try to include specific and overarching questions on which the students should focus as they read; they are told to make margin notes about these specified topics and questions, and sometimes to write prepared notes on separate paper. When they come to class, I'll appoint some or all of the following roles to students: moderator, participant, observer, and note-taker. Occasionally I will notify students the day before that they will moderate the following day's Harkness. I tend to do this if I know the topic will be difficult, and thus I want the moderator to be very well prepared.

The role of moderator is the most crucial. The moderator, and I must stress this often, is not the de facto teacher. Rather, their job is to introduce topics, organize the flow of the conversation, ask participants to specify and/or provide textual references, and generally set an intellectually engaged and stimulating tone; I let the moderator decide if they want participants to raise hands, or to just speak as they wish. The participant is the student (For a good sense of the expectations of participants, see the next section in this packet on evaluating Harkness students.) The observer's role is to silently monitor the discussion. They may take notes on what works well, and what does not. They might also draw a Harkness discussion diagram: they draw a circle, put down the names of each person around the circle such that the drawing mirrors the arrangement of the people at the table, and then draw lines to and from each person as they speak. In the end this diagram offers a powerful visual reflection of how the conversation flowed. If one area is dark with lines, while others are blank, it becomes clear that the discussion was unbalanced. The note-taker's job is to take notes from the discussion about information and ideas that might be useful for future test or essay preparation; the notes are written in the communal class journal.

I will start class by clarifying any issues or questions left over from my last time with the class, and then I'll announce the moderator and the focus questions for the day's discussion. I try to pose questions and ideas that are broad enough to allow fluidity of discourse, but not so broad that students don't know what their focus should be. For very difficult readings, I will, however, often narrow my questions, being very specific so students don't feel overwhelmed by the magnitude of the piece or topic. Ultimately, I'm still very much in the development stage of learning this art form of setting up Harkness discussions.

During the discussion I intentionally sit removed from the circle. This is symbolic as well as practical: symbolically, it demonstrates that the students and their ideas are central. Practically, it weans students off of their tendencies to look and speak to me; even with sitting outside the circle, I still notice some students always looking at me when they speak. I do not remain completely silent during the discussions. Sometimes I offer an opinion, but often when I speak it will be to clarify or pose a question, assert an opinion different from the group's consensus, or provide the class with some necessary piece of historical background on the topic. I generally end the discussion five to ten minutes before the class time finishes. The rest of our time together is spent evaluating the strengths and weaknesses of the conversation-this makes explicit the lessons about academic discussion dynamics-and making plans for how to improve future discussions. I might also use this time to summarize what I heard, or to offer feedback and clarification on the content of the conversation.

Sam Shapiro, Exeter Humanities Institute Participant 2001

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History of Harkness Harkness refers to a method of teaching that was developed in the 1930s at the Phillips Exeter School in New Hampshire. The philanthropist Edward Harkness challenged Exeter with an offer: he would make a sizable donation of money to the school if they could originate and implement a radically student-centered method of...

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In this  web site you can find a lot of practical lesson plans to show real world math.

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An interesting article about how to make math more emotionally engaging for students!

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Flick/Craig Dugas

When Jacqui Young studied pre-calculus as a high school junior, she found the experience unexpectedly fulfilling. She didn't consider herself a "math person," but pre-calc came more easily to her than it did to most of her peers, and she spent a lot of time helping fellow students grasp the concepts. "It felt good to be able to understand something and then be able to walk someone else through it," she said. "It was so gratifying, and made me want to stay on top of the subject."

Satisfaction and engagement may not be the most common feelings among students studying introductory calculus. According to Jo Boaler, a professor of math education at Stanford, roughly 50 percent of the population feels anxious about math. That emotional discomfort often begins in elementary school, lingering over students' later encounters with algebra and geometry, and tainting the subject with apprehension-or outright loathing.

Professor Mary Helen Immordino-Yang, associate professor of education, psychology, and neuroscience at the University of Southern California has explored how emotions are tied to learning. "Emotions are a piece of thinking," she told me; "we think of anything because our emotions push us that way." Even subjects widely considered to be outside the realm of emotion, like math, evoke powerful feelings among those studying it, which can then propel or thwart further learning.

Is there a way to separate negative emotions from the subject, so that more students experience math with a sense of satisfaction and pleasure? Immordino-Yang believes so. "It's not about making math 'fun'," she added; games and prizes tend to be quick fixes. Instead, it's about encouraging the sense of accomplishment that comes from deep understanding of difficult concepts. "It's about making it satisfying, interesting, and fulfilling."

Adam Leaman, who teaches variations of algebra, trigonometry and calculus to high schoolers in Summit, N.J., said that a sense of awe about mathematics drew him to the subject beginning with algebra 2. "There's something satisfying about knowing there's an answer and knowing I have the ability to get it," he said. Today, he sees the same pattern with his students: they are most engaged when they're figuring out hard problems.

There are several ways teachers can replace student fretfulness over math with a sense of appreciation.

Be clear about why understanding math concepts matters. Kids who believe that they must simply endure algebra and calculus until they're through with school-and that the actual learning is pointless because they'll never use it again-should be reminded why understanding mathematical concepts is valuable. Most importantly, being able to comprehend a "symbolic, representative system," Immordino-Yang says, teaches the brain how to think theoretically and logically. "Learning how to think abstractly is a useful ability in all aspects of life," Immordino-Yang said. In fact, people who have studied complex math in high school tend to have better life outcomes, she said. Teachers who share this information may persuade reluctant math-learners to stay engaged.

Assign projects that help kids see math's usefulness. Students are more apt to participate if they see a practical application to their studies. "This goes beyond learning how to balance a checkbook," Immordino-Yang adds. By studying how fast and far vegetable oil spreads on tissue paper, for example, students can learn not only about the math concept of direct variation, but also about how oil spills are measured. Sharing stories from the news where math understanding is featured in the narrative-in a story about price fixing, say, or one on climbing interest rates-also can help students see its usefulness in the real world. Learner.org, a free educational resource from the Annenberg Center, provides such practical lesson plans for math at all levels, including the oil spill example.

Discuss mathematical role models, and share how their ideas have changed the world. Because math is the foundation of so many other fields-physics, engineering, finance, astronomy, among others-history teems with mathematical virtuosos whose creativity and curiosity shaped the modern world. In addition to the usual suspects of math icons, including Pythagoras, Rene Descartes, and Ptolemy, more contemporary role models might spark student appreciation for the subject. There are many: Alan Turing, who's code-breaking during World War II helped defeat the Axis powers; Ada Lovelace, who created the Analytical Engine, which presaged modern programming; even Nate Silver, a popular mathematician who uses statistical forecasting to predict outcomes in Major League Baseball and political elections. The humbler discoveries made by annual recipients of the Presidential Early Career Awards for Science and Engineering might also inspire.

Strive to minimize the sources of fear. Math anxiety stifles clear thinking. At those moments when students most need to marshal their intellectual resources-during a test, say, or when called up before class to work a problem-those who fear the subject are apt to panic and shut down. Sian Beilock, a professor of psychology at the University of Chicago, and author of Choke: What the Secrets of the Brain Reveal About Getting it Right When You Have To, describes the anxious over-reaction to high pressure situations as a "malfunction of the prefrontal cortex." For nervous students who feel pressure to perform well on a test, that worry causes them to execute beneath their skill level. "Anxiety is robbing you of working memory," Immordino-Yang explained. "You're wasting your thought powers," she added. Math phobic kids need help from teachers to lessen their fear.

Keeping the classroom "kid-centric," Immordino-Yang said, can help. Teachers who act as facilitators, or resident experts, rather than omniscient instructors, invite students to explore without fear of messing up in front of an authority. Freeing up fellow students to explain problems also allows for more personalized instruction. During Jacqui Young's happy year studying pre-calc, she worked with peers who struggled to keep up with the teacher's pace. "I think it was better because I'd be working one-on-one or two-on-one with my classmates," she said. Another way to tamp down dread is to set up class in a roundtable and encourage student-led give-and-take. Known formally as the Harkness Method of teaching, this collaborative approach to learning may be especially useful in math subjects.

Returning to older math processes and ideas when introducing new material also works to lessen anxiety about the new learning. While teaching synthetic division to his Algebra 2 class, for example, Adam Leaman reminds students that this "new" concept is a cousin of the factoring they did in Algebra 1. "They have something from the past to draw reference from when tackling this new subject," he said. Bringing up old material this way also helps students who might have struggled when they learned it the first time. Leaman said that some kids groan when he brings up factoring, but that they often end up understanding it better when going through it a second time, and in relation to a different concept. "Even if they have the perception that they're not good at it, when we come back to it I have students say, 'I get it now'."

How to Make Math More Emotionally Engaging For Students

Author

Linda Flanagan

Linda Flanagan is a freelance writer, researcher, and editor. Her work has appeared in The Atlantic, The Wall St. Journal, Newsweek, Running Times, and Mind/Shift, and she blogs regularly for the Huffington Post. Linda writes about education, culture, athletics, youth sports, mental health, politics, college admissions, and other curiosities. She also reviews books and conducts interviews.

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How to Make Math More Emotionally Engaging For Students

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When Jacqui Young studied pre-calculus as a high school junior, she found the experience unexpectedly fulfilling. She didn't consider herself a "math person," but pre-calc came more easily to her than it did to most of her peers, and she spent a lot of time helping fellow students grasp the concepts.

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Hi, I'm Maria Silvia. I teach Math and Science in a Primary School in Pistoia, Italy. I really want to improve my professional skills and I want to collaborate with other teacher around the world.

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In my class the students have a good motivation in studying math but they lose it year by year. A lot of them think that they can't improve in this subject because someone else have to help them. I really agree with the video assumption that our students are looking for sit com problem. They have so little patience. On the other hand so often in math, unlike in language study, you can find yourself blocked and unable to do anything. I really like these ideas to teach math in a different way, but I ask to myself: it requires a lot of time, have we enough time? And, will this cause a lack in language skills?