The Cognitive and Intellectual Aspects of Dance (and math)

Dance Magazine recently published an interesting article titled: Don’t get It Twisted: Dance Is An Intellectual Pursuit and parts of the article really resonated with my approach to combining math and dance. Below are some excerpts from that article interspersed with related #movingmath posts from this blog (bolding mine).

People have a tendency to think of dance as purely physical and not intellectual. But when we separate movement from intellect, we are limit what dance can do for the world. It’s not hard to see that dance is thought of as less than other so-called “intellectual pursuits.” How many dancers have been told they should pursue something “more serious”? How many college dance departments don’t receive funding on par with theater or music departments, much less science departments? Perhaps that’s because dance only leaves behind traces. The words and decisions that go into making dances have a hard time being accounted for, and choreographic notes and videos cannot fully capture a dance work.

Dance depends on the presence of the body. Unfortunately, it’s difficult to explain to non-dancers how corporal movement is a means of thinking and engaging with complex ideas. That’s why it’s so important that dancers can talk or write about their work, translating the corporal knowledge into language.

When we acknowledge that our bodies think, move, translate, react—often in conjunction with linguistic thought or prior to itwe can use dance as a tool. 

Related: When the Movement IS the Reasoning Tool | What does it look and sound like when kids use their whole bodies during a math lesson? What happens prior to, during, and after the activity? Luckily Deb Torrance and Lana Pavolova have provided us with some stellar documentation so we can get a closer look at what happens when we give kids a mathematical challenge to explore with their whole bodies.

Linguistic Intelligence Has Its Place in Dance, Too
That’s not to say that language isn’t part of dance. Choreographers craft dancers’ intentions and movements with words, images and metaphors. Even in improvisation, a director dictates a score, and dancers translate the imagery into corporal form. When choreographers layer dance and words, it engages the audience in new ways. As Bill T. Jones explains, “You see one thing and you hear another thing, and then the audience puts together what they mean.”

Related: Learning Math by Ear: The Role of Language in a #movingmath classroom  | “Comprehension of a word’s meaning involves not only the ‘classic’ language brain centres but also the cortical regions responsible for the control of body muscles, such as hand movements.” To me this study explains part of why a “moving math” approach that includes a focus on math language used in context can open up new pathways for our learners.”

Dance Can Help Us Better Understand Our World
Many choreographers use dance to shed light on today’s most pressing topics. Some use dance in conjunction with social activism, like Ananya Dance Theatre’s Ananya Chatterjea, who recently created Shyamali as a tribute to women across the world who have stood up against oppression. Others explore the nuances of science: Michelle Dorrance’s Myelination, for example, translates the biological process of a myelin sheath forming around a nerve into tap dance. Not to mention artists who use their dance practice as research, focusing on the process of dance making to explore a question or subject…

Related: Leaving Room for Question Asking | “It’s these questions, arising in the moments when they’re needed, born of collaboration, that help learners notice structure and pattern and purpose in what they’re doing. From there we can move to the more formal learning. But… I think kids in general are most motivated when they are provided agency by the adults in their lives. Their work may not be technically perfect, but they are in the best part of learning (to me, anyhow): inside the flow of an investigation filled with their wonderings.”

Dancers Connect Multiple Parts of Ourselves
Dance intertwines the cerebral, physical and emotional; science tries to unravel the connections between these. Dance uses these inherent connections to delve deeper into our humanity, and create new ways of reflecting on the world. In that way, dance is a crucial tool in intellectual pursuits.

Related: Learning Without a Body |”The body is not simply a vehicle toward realizing the perceived pinnacle of abstracted knowledge housed in the mind.  The body is where learning originates. Living in a body is also the way children learn personal agency as they make decisions about how their bodies will move and act and how that power can influence and shape their world. And, in the process, learning that there are obvious consequences and responses in relation to their actions. This is literally and viscerally democracy in action.”


Malke Rosenfeld is a percussive dance teaching artist, Heinemann author, editor, math Malke Rosenfeld Croppedexplorer, and presenter whose interests focus on the learning that happens at the intersection of math and the moving body. She delights in creating rich environments in which children and adults can explore, make, play, and talk math based on their own questions and inclinations.You can find out more about her work at malkerosenfeld.com,  on Twitter,  Instagram, or Facebook.

Prepare to be Inspired! New Math & Dance Resources from a Canadian School Board to Help Guide Your Way

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During the fall and winter of the 2017-18 school year teachers and students in the Kawartha Pine Ridge District School Board (KPRDSB), Ontario, Canada took the plunge. Using Math on the Move: Engaging Students in Whole Body Learning they bravely began the process of bringing math and dance together into the same learning context. Mary Walker Hope, who spearheaded the process, invited me to observe and celebrate the final presentations of children in grades one through eight. During my video chat observations I was incredibly inspired to see how the process laid out in Chapters 4 & 5 of Math on the Move had supported both children and teachers alike.

At the very end of their math and dance project Mary created three individual e-books recounting their work, with a special emphasis on the process. She writes:

Through integrating math and the arts, we engaged our students as inquirers, collaborators, creators, problem solvers, artists, dancers and mathematicians.

We began our journey from a creatively curious stance and with humility. We inquired, persevered, and solved. We learned how to teach math through dance and dance through math. We discovered through our collaborative inquiry that math, dance, language, music, and art are as interconnected as the processes we use to understand, solve, and create.

These three e-books are divided by grade band and FULL of documentation of their math/dance making process from start to finish including:

  • Introductory activities
  • Insights and encouragement for teachers around negotiating math and dance in the classroom at the same time
  • Details about what each step of the process looks like in each grade band
  • Lots of videos illustrating a variety of student work
  • Step-by-step examples of the making process
  • Examples of what they did to apply, extend, reflect, and assess the math/dance work
  • Finally, these e-books provide an overall positive and encouraging message for teachers who might be ready to jump in to #movingmath!

These are real kids and real teachers making gorgeous math and dance.  YOU CAN TOO!

The books are linked below. You might also be interested in another post on this blog inspired by the Canadian crew called “Why Math in your FEET?” which provides an explanation of percussive dance and the different kinds of sounds you can make with your feet while dancing.


Malke Rosenfeld CroppedMalke Rosenfeld is a percussive dance teaching artist, Heinemann author, editor, math explorer, and presenter whose interests focus on the learning that happens at the intersection of math and the moving body. She delights in creating rich environments in which children and adults can explore, make, play, and talk math based on their own questions and inclinations.You can find out more about her work at malkerosenfeld.com,  on Twitter,  Instagram, or Facebook.

Why Math in Your FEET?

In Chapter One of Math on the Move: Engaging Students in Whole Body Learning I share a little of the history of how I developed Math in Your Feet and also describe how, in the years before making the connection between my dance style of percussive dance and mathematics, I worked to support children in becoming dance makers using the elements of this not-quite mainstream dance form. So what is this percussive dance and how does it connect to math and, most puzzling, why do we need to use our feet?

This question about feet came up a lot during almost weekly Skype sessions with the amazing Mary Walker Hope in Ontario, Canada. In January 2018 I was lucky enough to get a peek at the awesome Math in Your Feet patterns and footwork resulting from a 2nd through 8th grade exploration in her school board. I figure that  others may ask this “Why are we using our feet?” question from time to time so in this post I’d like to elucidate the “feet” aspect of the math and dance that we make while creating patterns with our feet in Math in Your Feet.

First of all, there many, many (MANY!) different dance styles in this world. Some of them are percussive (rhythm based) and some of them are not. Sometimes they’re a combination of both. Percussive dance is probably best known through the international performance phenomenon called Riverdance which features Irish step dancing. You might also be familiar with percussive dance through all those tap classes either you or your kid took at some point.

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The main focus of percussive dance styles is to be a rhythm maker using different parts of your feet. The Pattern Properties I created lay out the basic elements of this kind of dance, similar to what creative movement is to modern dance. To answer “why feet” look at the Movement category of the Math in Your Feet Pattern Properties chart on the left. Each movement has a clear sound associated with the movement. Making sure you produce that sound is one aspect that makes this kind of dance so satisfying. In the chart below I’ve provided some information about how these sounds are made.

Pattern Properties description FINAL
So, there you have it! Making patterns and sounds with your feet is fun and satisfying, not to mention mathematical!


Malke Rosenfeld Cropped.jpgMalke Rosenfeld is a percussive dance teaching artist, Heinemann author, editor, math explorer, and presenter whose interests focus on the learning that happens at the intersection of math and the moving body. She delights in creating rich environments in which children and adults can explore, make, play, and talk math based on their own questions and inclinations.You can find out more about her work at malkerosenfeld.com,  on Twitter,  Instagram, or Facebook.

Leaving Room for Question Asking

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NOTE: This post was originally published at my other blog  April 15, 2017.

How much of the math you do in your classroom is based on someone else’s questions? Someone far away from your classroom? Someone other than your students? Even with specter of standardized tests looming like dark, heavy clouds, how can we leave room for the most important part of learning: question asking?

“So many of the things that we do in math education — and maybe more generally in education — are giving students answers to questions that they would never think of asking. By definition, that’s what it is to be boring. If you’re sitting at a bar and someone’s telling you stuff that you’re not interested in and you would never think of asking about — what is more boring than that? That seems to be the model of our educational system: ‘Here’s the formula for the cosine of the double angle.’ ‘Well, I don’t care about that.’” —Steven Strogatz

The first time I experimented with building scaled-up geometric forms I was homeschooling my then-seven-year-old. At the time she was a “resistant” learner which basically meant she was happiest exploring her own questions, and, over a couple years of homeschooling I realized my best strategy was to influence the child by way of my own curiosities and the way I structured the environment, leaving out provocations to be discovered and, if of interest, investigated.  This was also a time when I was deep into finding answers for my own question “What is math?” and I was heavy into an investigation into Platonic Solids. I had never been a builder as a child, but I had a question and it needed to be answered.

Back in April, on Twitter, I had a conversation with Lana, a third grade teacher who is reading Math on the Move and who has been wondering about how how to “scale up” her students’ mathematical activity.  Specifically she’s been curious about my recent work with building body-scale polyhedra.  Body- or moving-scale means that the whole body/person is engaged in problem solving and mathematical thinking to investigate a mathematical challenge or project of some kind. I think Telanna’s question could be anybody’s question who is wondering how we can do math off the page.

My answer focused on how I structure a making activity and the learning environment in a way that motivates learners to collaborate and ask new questions in response to the activity in an intrinsic way.

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It’s in the process of making something with the freedom to try things out and see where it gets you that creates new questions.

It’s these questions, arising in the moments when they’re needed, born of collaboration,   that help learners notice structure and pattern and purpose in what they’re doing. From there we can move to the more formal learning. But, like my daughter, I think kids in general are most motivated when they are provided agency by the adults in their lives. Their work may not be technically perfect, but they are in the best part of learning (to me, anyhow): inside the flow of an investigation filled with their wonderings.

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To bring kids to math we need to leave room for their own questions.

What happens next? There are more questions to be asked about this kind of approach. I have  my answers and am happy to share them. But I’d love to hear your questions first!


Malke Rosenfeld is a dance teaching artist, author, editor, math explorer, and presenter whose interests focus on the learning that happens at the intersection of math and the moving body. She delights in creating rich environments in which children and adults can explore, make, play, and talk math based on their own questions and inclinations.You can find out more about her work at malkerosenfeld.com,  on Twitter,  Instagram, or Facebook.

Notes from a #movingmath Summer Classroom

I am so excited to share the work of Lisa Ormsbee at Fairhill School in Dallas, Texas  who has spent the past two weeks running a math and movement summer enrichment camp using resources from Math on the Move, the Move with Math in May lesson plans, a rhythm-based exercise program called Drumfit, and a lot of other great ideas she pulled together to meet the needs of her students through rhythm and movement. She has ten students with most of the students “learning different” (e.g. dyslexia, dysgraphia, ADHD, mild autism, and selective mutism)  not all of them fans of math, what she described as a “general math reluctance.”

Fairhill MiYF

I was thrilled to get her wonderful email updates on the first and second week of programming which showed just how much of an impact a #movingmath approach can have for all learners. I especially love the progression Lisa created to gently lead reluctant movers (and math-ers) into what has become enthusiastic engagement! Here’s some of what Lisa shared with me:

Monday:  I did a couple of ice breaker activities which involved moving around and were non-threatening (meaning no one HAD to talk in front of the  group).  I started by challenging them to put THEMSELVES into patterns during this warm up time – it was totally spontaneous but it was fun for them. We also got oriented to our class space.  I had removed all the desks and chairs and had the [Math in Your Feet] squares taped on the floor.  They had to adjust to the idea that we weren’t going to sit in desks. I also introduced Drumfit on this day and used that activity time to introduce “follow me” patterns with the drumming rhythms. These kids are fairly reluctant to move around and have pretty low physical literacy and body confidence so I wanted to be sure to take the introduction of the program slowly.  They did extremely well with the movement during the icebreakers!  The drumming is growing on them but took several days for them to feel confident and, some still do not, but I’m not pushing them in that area as it’s a “fun” time. It’s such a good fit with patterns and using your body to make them though! 

Tuesday: We did the pattern game sitting in a circle that you outline in one of your lessons [Clap Hands: A Body-Rhythm Pattern Game].  This was HARD for some of them!  They were all engaged in it though.  We could certainly do this again!  Then we went to our gym space and used the ladders to prove the center [Proving Center lesson] in teams and also to create patterns as a team using bodies and any other items they wanted to use. They were told to be as creative as they wanted with their repeatable pattern. We discussed symmetry here too.  I used my purple circle discs to have them create a game using their ladders also. The game had to have some “math” in it. It was so very, very interesting to watch them do all of this!! We discussed a lot after that and talked about what they had done and how they had thought of their games and patterns.

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After one more day of getting kids used to moving and thinking about math at the same Just turns postertime Lisa introduced the first step in the  Math in Your Feet “pattern/partner/dance process.”  Lisa wrote:

It was slow and I didn’t hurry them.  It took a while to orient them to the squares, talk about sameness (congruence), and review the movement variables. We also took a LONG time talking about the turns. That’s all we got done but I told them we’d be making a pattern with our partner the next day and we’d be concerned with precision and sameness.

On Friday they started working with their partners on creating their 4-beat patterns.

The kids were ALL so engaged in this activity!  I couldn’t believe it.  They had some trouble with cooperation and with identifying sameness. It was extremely hard for a couple of students but because they were working with a partner they were more interested in “sticking in there” where it was uncomfortable until they got it right!  AWESOME!!  I felt like it was a successful day and I can’t wait to do more. 

Next week, I want to have them write a little bit about their patterns and make a drawing etc. like you do in the book.  I also want to let them do this part again then work on combining and transforming.  When we get to the mirroring piece we will have to go pretty slowly I’m guessing. 

During the second week of summer school Lisa did the mirroring/reflection lessons and was also able to extend and connect the physical work by having them having them map their patterns and then read/decode each other’s pattern maps.

Once I added music to the activity they had a blast!  I feel we were all inspired by the Math in Your Feet program to be open to new ways to learn through movement. I was so caught up in our activities I didn’t get any pictures!

But she did eventually get some videos! Here are a couple showing the children’s awesome physical thinking around reflection. One person is keeping their rights and lefts the same as they originally designed the pattern, and the other person is dancing the pattern with opposite lefts and rights. And this is all on top of some tricky rotations. A mighty feat!

Lisa says: I hope [this account] helps others dive into the program because my kids really engaged with it and I am 100% sure that they would not have been so engaged had I chosen a more traditional program for the summer enrichment. I really hope this will help them with their understanding of math and also with their movement confidence and honestly, their joy of moving! I’ll be the P.E. teacher here next year – although I must say this might actually make me a fan of math too. Yay!

Thank you, Lisa, for sharing your work with us!


Malke Rosenfeld is a dance teaching artist, author, editor, math explorer, and presenter whose interests focus on the learning that happens at the intersection of math and the moving body. She delights in creating rich environments in which children and adults can explore, make, play, and talk math based on their own questions and inclinations.

Learning Math by Ear: The Role of Language in a Moving Classroom

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At first glance, this article about the value of reading aloud to older kids would not seem to connect to math learning. But, to me it does.  Here’s the piece that really stood out:

“The first reason to read aloud to older kids is to consider the fact that a child’s reading level doesn’t catch up to his listening level until about the eighth grade,” said Trelease [a Boston-based journalist, who turned his passion for reading aloud to his children into The Read-Aloud Handbook in 1979], referring to a 1984 study performed by Dr. Thomas G. Sticht showing that kids can understand books that are too hard to decode themselves if they are read aloud. “You have to hear it before you can speak it, and you have to speak it before you can read it. Reading at this level happens through the ear.”

Did you catch that? “You have to hear it before you can speak it, and you have to speak it before you can read it.”

I made a similar point while working with teachers and teaching artists in Minnesota in 2013 when participants noticed how the math language was woven naturally and seamlessly into our dance work. This vocabulary development, I said, was initially an attempt to help kids pay closer attention to the details of what they were doing while they created their dance patterns. I noticed that they became much better creators when they had the right words to help them identify their movement choices.

recent brain study focused on how the motor cortex contributes to language comprehension:
“Comprehension of a word’s meaning involves not only the ‘classic’ language brain centres but also the cortical regions responsible for the control of body muscles, such as hand movements.”
To me this study explains part of why a “moving math” approach that includes a focus on math language used in context can open up new pathways for our learners [bolding emphasis mine]:

“An alternative is offered by an embodied or distributed view suggesting that the brain areas encoding the meaning of a word include both the areas specialised for representing linguistic information, such as the word’s acoustic form, but also those brain areas that are responsible for the control of the corresponding perception or action. On this account, in order to fully comprehend the meaning of the word ‘throw’, the brain needs to activate the cortical areas related to hand movement control. The representation of the word’s meaning is, therefore, ‘distributed’ across several brain areas, some of which reflect experiential or physical aspects of its meaning.”

 My take away from the study overview is this:

  1. Our whole bodies are just that: whole systems working in an fascinating and astoundingly connected ways.
  2. “Knowing” something, especially the ideas and concepts on the action side of math (transform, rotate, reflect, compose,  sequence, combine, etc) is strengthened by the partnership between mathematical language and physical experience.

In Math in Your Feet we start by moving to get a sense of the new (non-verbal) movement vocabulary in our bodies. At the same time we say together, as a group and out loud, the words that best match our movement. Sometimes we also pay attention to the words’  written forms on the board so all three modalities of the idea are clear to us.  When learners are more confident with their dancing they are asked to observe others’ work and choose the the specific  words that describe the attributes/properties of the moving patterns. There are over 40 video examples of this in action in Math on the Move.

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In addition to being able to parse our patterns, we use tons of other math terminology while we choreograph in conversations with our teammates and in whole group discussions.  This approach allows learners to fully grasp the real meaning and application of these ideas which, ultimately, allows them to write and talk confidently about their experiences making math and dance at the same time. Teachers consistently notice an increase of ‘math talk’ in their classrooms when children get up to explore math ideas with their whole bodies. As in, “I couldn’t believe how much math vocabulary they were using!”

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Math is a language but it’s not just about terminology, it’s about what those words MEAN.  To do this, learners need to play with mathematical ideas, notice and talk about patterns and structure, sort and compare, and share reasoning about and understanding of mathematical relationships.

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As such, language, in partnership with the body is our tool for thinking mathematically when we are up out of our seats and moving during math time.  Ideally, this language is facilitated by an adult through conversation, play and exploration, all before bringing it to the page to explore the ideas in a different modes and contexts.


Malke Rosenfeld is a dance teaching artist, author, editor, math explorer, and presenter whose interests focus on the learning that happens at the intersection of math and the moving body. She delights in creating rich environments in which children and adults can explore, make, play, and talk math based on their own questions and inclinations. Join Malke and other educators on Facebook as we build a growing community of practice around whole-body math learning.

Beautiful Objects, Redux

[Adapted from my post Beautiful Objects, from January 24, 2014]

I’ve thought a lot about the role of physical objects in math education.  Sometimes called manipulatives or, more generally, thinking tools, I’ve discovered conflicting opinions and strategies around the use of such objects. In her book Young Children Reinvent Arithmetic, Constance Kamii helpfully sums up some of the issues with which I’ve wrestled with [bolding emphasis mine]:

“Manipulatives are thus not useful or useless in themselves. Their utility depends on the relationships children can make…” p25

“Base-10 blocks and Unifix cubes are used on the assumption that they represent or embody the ‘ones,’ ‘tens,’ ‘hundreds,’ and so on. According to Piaget, however, objects, pictures and words do not represent. Representing is an action, and people can represent objects and ideas,but objects, pictures, and words cannot.” p31

So, it is not the object itself that holds the math, but rather the process in which the learner uses the tool that creates the meaning.  But, of course, when we use this kind of language we are talking abstractly about hypothetical objects and generalized characteristics of ‘the child,’ not any specific object or individual learner in particular.

Too much generality and abstraction drives me crazy so imagine how pleasantly surprised I was when this showed up in my mailbox one day:

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What is it? Well…it’s an object. And a beautiful one, at that. An object that can be “manipulated” (the triangle comes out and can be turned). A thinking tool. It was designed and created by Christopher Danielson to investigate symmetry and group theory with his college students. Not only are parts of this tool moveable, but it also has the potential to help “facilitate [mathematical] conversations that might otherwise be impossible.” (Christopher on Twitter, Jan 17, 2014)

What was even better than getting a surprise package in my real life mailbox containing a real life manipulative (not a theoretical one) was my (real) then-eight year old’s interest in and reactions to said object. She spotted the envelope and said, “Hey! What’s that?!” I told her that a math teacher friend of mine had sent me something he made for his students to use. I took it out of the envelope for her to look at.

First thing she noticed was the smell — lovely, smokey wood smell which we both loved.  She investigated the burned edges, tried to draw with them (sort of like charcoal). This led to a discussion about laser cutters (heat, precision) and the fact Christopher had designed it. I pointed out the labeled vertices on the triangle, showed her how you can turn it, and mentioned that the labels help us keep track of how far the shape has turned. She immediately took over this process.

She repeatedly asked if she could take it to school! I asked her, “What would you do with it?”  She said, matter-of-factly: “Play around with the triangle…and discover new galaxies.” Then, she turned the triangle 60° and said, “And make a Jewish star…” Then she put the triangle behind the the opening so it (sort of) made a hexagon.  I asked, “What did you make there?” She said, “A diaper.” Ha!

I hope Christopher’s students were just as curious about and enthralled with the “object-ness” of this gorgeous thing as they were with the idea that it helped them talk and think about things that might otherwise be impossible to grasp.  I know that the objects themselves hold no mathematical meaning but watching how intrigued my daughter was with Christopher’s gift, I am left thinking about what we miss out on if we consider a tool simply a bridge to the ‘real’ goal of mental abstraction.  

Beautiful and intriguing objects, I think, have a role in inspiring the whole of us, all our senses, kinetics, and curiosities, not just our minds, to engage in the process of math learning.  An object doesn’t necessarily have to be tangible; narrative contexts are highly motivating ‘tools’ when working with children. As I blend math, dance and basic art making I see over and over again how presenting the object (idea) first pulls my learners in — they are curious about what this dance is, how they might weave their own wonderful designs using math, what does she mean “growing triangles” and why are these pennies on the table?

Learning is hard work, but my experience is that students will gladly work hard if they have even a small sense of the direction in which they’re headed. The whole, moving body is one of those beautiful objects which can create other beautiful objects (in this case a dance pattern) using the elements of time, space, and kinetic energy. This first video is from a session I did with undergraduate math majors at the University of Michigan:

And these two videos are of me and Max Ray-Riek last summer playing around a little while setting up the after-hours Blue Tape Lounge at Twitter Math Camp. The first video shows some interesting inverse and symmetry action, and the second one…can you tell what kind of symmetry is happening there?


Malke Rosenfeld is a dance teaching artist, author, editor, math explorer, and presenter whose interests focus on the learning that happens at the intersection of math and the moving body. She delights in creating rich environments in which children and adults can explore, make, play, and talk math based on their own questions and inclinations. Join Malke and other educators on Facebook as we build a growing community of practice around whole-body math learning.

A Quick Example of Body-Based Cognition: Spinning

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Yesterday I was at the library for my now monthly #makingmath sessions for kids and their parents. The ages for this event seem to trend 8 and under, probably because parents with young children are often looking for something to do on Sunday afternoons. Our youngest participant yesterday was two and a little more, and this little story is about her.

I’ve written previously on this blog about what it looks like when children think and learn mathematically with their bodies. Yesterday my new friend was there with her mom and her brother. Her brother made this delightful “Dr. Seuss house with smoke coming out of the chimney” while she made a crown and earrings for herself out of the same materials.

Another activity we had going on was playing around with these cool hexagon building blocks that I found in a big box dollar bin a couple summers ago.  A boy made an object that was just begging to be spun…

…after which my little two year old friend started rotating around in one spot exclaiming to me: “I’m spinning!”

This is just one more example of how children think and learn with their bodies. She was entranced by the toy and it’s gorgeousness.  She spent a quick moment spinning exactly like the top and then went back to making earrings for her mother.

The body is where learning originates. Children use their bodies to show us every day what they know and think and wonder. This non-verbal, physical manifestation of cognition is present every day in some way. I invite you to put on your #movingmath glasses and, when you notice something tell us about it! Here’s a few places where you can share:

In the comments to this post
On Twitter with the hashtag #movingmath
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On Facebook with privacy set to public with the hashtag #movingmath

I can’t wait to hear about (or see) what you notice!


Malke Rosenfeld is a dance teaching artist, author, editor, math explorer, and presenter whose interests focus on the learning that happens at the intersection of math and the moving body. She delights in creating rich environments in which children and adults can explore, make, play, and talk math based on their own questions and inclinations. Join Malke and other educators on Facebook as we build a growing community of practice around whole-body math learning.

 

New Year, New Tools for Making Sense of Math!

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Happy 2017!! This year harness the original “thinking tool” to help your learners make sense of math! What is this tool, you ask? Why, your students’ own bodies and creative spirits of course!

Math on the Move: Engaging Students in Whole Body Learning is now available from Heinemann. Included in the book are specific, actionable ideas for including your students’ moving bodies in the math you are already doing in your classroom!

Here is your first tip in the New Year for a simple first step in bringing Math in Your Feet and other #movingmath activities into your classroom in a low key way.  All the best to you for a new year filled with enthusiastic math making!

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You can download the Movement Variables from the Classroom Materials page.

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Will you tell us about your #movingmath adventures with us? I’d love to hear your stories. Share with us on Twitter or at the book group on Facebook.


Malke Rosenfeld is a dance teaching artist, author, editor, math explorer, and presenter whose interests focus on the learning that happens at the intersection of math and the moving body. She delights in creating rich environments in which children and adults can explore, make, play, and talk math based on their own questions and inclinations. Her new book Math on the Move: Engaging Students in Whole Body Learning was recently published by Heinemann (2016). Join Malke and other educators on Facebook as we build a growing community of practice around whole-body math learning.

A Framework for Whole-Body Math Teaching & Learning

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What is whole-body math learning? How can we be doing math if it’s not written down? What are our expectations for student work and learning math out of their seats?

My focus in Math on the Move is on how we can harness our students’ inherent “body knowledge” to help them develop new understanding and facility with mathematical ideas that often seem remote and impenetrable as presented in their textbooks. This is not to say that math is this way, but for many people, myself included, the symbolic side of math creates a barrier, at least initially, to understanding. This is why approaches like Numberless Word Problems  (“They just add all the numbers. It doesn’t matter what the problem says.”) and Notice and Wonder  were created: to help kids make sense of math.

The phrase “body knowledge” was coined by the late Seymour Papert, a protégée of Jean Piaget. In the 1980s Papert’s work at MIT focused on developing “objects to think with,” including the Logo computer programming system for children. Here are a few images of children engaged in self-initiated, body-based exploration of a math idea as they investigate the spatial aspects and physical structure of their environment.

Papert’s intention was to harness a child’s own lived experiences and natural, self-intiated explorations in the world as a way to investigate more formal mathematics via the programming of a little metal object called the “Turtle.” Much of what we do in Math in Your Feet is similar to what children do with the LOGO turtle – working independently or in teams within a specific system/constraint, investigating and creating units of commands or patterns in a spatial and geometric language and, along the way, fine tuning our intentions and results.

Similar to Papert’s work, Math on the Move is about math, but it is also about the nature of learning by actually making something and the need to develop strong pedagogy for what might be seen as a non-traditional approach. For me this means a meaningful  interdisciplinary, movement-based approach beyond the preschool years. In the first chapter I provide an overview of what meaningful whole-body math learning looks like in my own and others’ moving math classrooms. I clarify the body’s role as a thinking tool and its use within a purposeful making and learning context. I also provide a conceptual framework and pedagogical base for any educator wishing to do similar work with his/her own students at body- or moving-scale.

Because our encounters with math have been, for the most part, visual and on the page, a whole-body approach to learning math may feel foreign to both teachers and students. To quell the qualms of others who may want to try this approach in their own classroom I have spent years working to define the pedagogical elements that must be present so children can think deeply and engage in mathematical sense making with their whole bodies.  The criteria (which are explained in more detail in the book) include:

  • The lesson explores one or more mathematical ideas off the page and out of the chair.
  • The math-and-movement lesson provides a structure in which students make choices, converse, collaborate, and reflect verbally on what they did and what they noticed while they were engaged in whole-body-based activity.
  • The body activity is focused on mathematical sense making, and  often through efforts to solve a challenge of some kind, not on using the body to illustrate a math ideas as it is typically represented on the page.
  • The teacher is not the expert but acts as the facilitator of the learners’ activity by setting expectations for controlled, intentional movement, and monitoring lesson pacing and classroom discussion.
  • Students reflect on the activity as both doers and observers, learning from their own experiences and the work and thinking of their peers.
  • In partnership with the change of scale, the math-and-movement activity should be explicitly connected with the same math idea as it is experienced in other contexts, scales, or modes. 

    Just like any organized lesson, moving math needs a frame of expectations and learning goals. It may look and feel different from the norm, especially because its kinetic nature, but as long as there is an underlying structure and intent, it’s worth exploring to see what the possibilities might be.  You might be very surprised at how enthusiastically children embrace the opportunity to harness their whole selves, body and mind for a mathematical investigation!


    Malke Rosenfeld is a dance teaching artist, author, math explorer, and presenter whose interests focus on the learning that happens at the intersection of math and the moving body. She delights in creating rich environments in which children and adults can explore, make, play, and talk math based on their own questions and inclinations. Her new book Math on the Move: Engaging Students in Whole Body Learning was recently published by Heinemann (2016). Join Malke and other educators on Facebook as we build a growing community of practice around whole-body math learning.