Moving Patterns Sneak Peek!

Moving Patterns is an active, self-directed, creative body-based game featuring patterns, footwork, friends, and math. Dancing makes life fun, and math makes the dancing more interesting! 

The Moving Patterns Kickstarter goes LIVE on July 14, 2020!  While we wait for Launch day I thought I’d give you a sneak peek of the graphics that make up the core of the game.

The orange challenge cards provide mathematical prompts for making the footwork maps more interesting and changing each pattern in some way, leading to the creation of new footwork based dance patterns. Paired together they become potent choreographic prompts where players can literally play around with both math and dance at the same time.

Why not sign up at to get a quick update in your inbox on launch day!

And don’t forget to watch the video, below!



Sign up for the Moving Patterns Game!

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Hey everyone! I hope you are all well and weathering our current situation. I am continuing to develop ways to bring math and movement together both indoors and outdoors. If you are a member of the Math on the Move Book Group or the group Moving Patterns Game Support on Facebook you will have seen some of my posts about how the game is really the first step to learning about working with math and moving bodies at the same time.


What I noticed during the game pilot at the Boys & Girls Club is that once kids get the hang of the footwork they can basically figure out how the game works. It’s at this point that they start to take ownership of the game.  I won’t be able to be back in real-life classrooms for a while but I know that the current supports in place (links above) will be a good proxy  as we move forward.  If you haven’t yet signed up for the FREE Moving Patterns Game Starter Kit why not try it out? 


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,  on Twitter,  Instagram, or Facebook.

Introducing the Moving Patterns Game!

I’ve been a little uncommunicative on this blog lately but for good reason. I’ve been hip deep in developing my new game based on my flagship program Math in Your Feet. The Moving Patterns game is an active, self directed game about about patterns, footwork, friends, and math. Dancing makes life fun and math makes the dancing more interesting!

Back in February I did a three month pilot at a local Boys & Girls club and I was completely thrilled to see the game in action and looking almost exactly the same kind of activity from the kids…EXCEPT in an even more self-directed manner than the school-based version! Program Director Lauren Hong commented on the many gains and successes  in children who participated in the Moving Patterns pilot:

The Moving Patterns game has has subtly worked its way to the heart of the Crestmont Boys & Girls Club and is transforming our members step by step. I have seen individuals on the edge of an emotional eruption be convinced to try their hands (feet) with the game and have witnessed the shift to positive engagement and pride at making up their own dance steps and accomplishing the games various mathematical challenges. The Moving Patterns game is fun, interactive and engaging.”

MP picture resizedThis playful and creative body-based game challenges players to collaboratively decode and dance a series of footwork-based “maps.” Challenge cards add a variety of mathematical challenges along the way to enhance game play and the development of original new dance patterns.​ Moving Patterns is based on a style of dance called “percussive dance” where you make rhythm and patterns with your feet at the same time. Percussive dance includes tap dance, step dance, clogging, and many other foot based styles.

An early version of the game will be out around (American) Thanksgiving. If interested, you can add your email to: for updates about the game, including when the instructional video piece is online (hopefully some time in Spring 2020.) I am also planning  a variety of teacher and parent supports. This project is the culmination my work in and around educational settings since 2002. I’m thrilled to be getting this game out in the world!

Malke 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,  on Twitter,  Instagram, or Facebook.


Whole-Body Planar Graph Investigation

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Earlier this year I was contacted by Eric Stucky who was lecturing a course for math majors at the University of Minnesota. Although I am generally in the realm of elementary mathematics, over the years I have had the pleasure of interacting with professional mathematicians and others who think expansively about both the mathematical subject matter AND the pedagogy of their instruction.

These experiences and conversations continue to show me that whole-body math learning is for everyone. This particular story is an email conversation I had with Eric that shows just how powerful whole-body math investigations can be for fourth graders AND math majors. This is also a story about coming to understand how to negotiate a whole-body math lesson. I especially appreciate Eric’s reflections later on in this post on how his lesson went.


Hello Malke,

I am a graduate student at UMN, looking for advice on an activity. I am currently a lecturer for an upper-division course for math majors; this is my first lecturing position. Class meets for two hours straight, so I’m always on the lookout for activities to break up the time.

On Wednesday, the class begins a unit on planar graphs. I had the idea to build some large physical models of graphs out of index cards [vertices] and yarn [edges], and then have them play around trying to see if they can get the edges to not cross each other.

Figuring I should know what the research is, I found your blog. Your post “A Framework for Whole-Body Math Teaching & Learning” made me consider integration of movement may not be substantial enough: they might as well lay the cards on the floor. The models should be big enough that they would have to walk/stretch to move the vertices around, but at that point, perhaps the movement becomes less of a reasoning tool and more just a nuisance? At least they would still have the experience of moving the edges physically instead of metaphorically (i.e. as they would when redrawing the graph on a worksheet), but this feels weak to me.

Unfortunately, there’s a logistical difficulty that doesn’t arise in the Rope Polygons exercise: students only have two hands, so it’s not as straightforward to make *them* the vertices of the graph because they can’t just “hold on to their edges” in a straightforward way. I really feel that if this could be done somehow, it would provide that extra something to make this activity be really special. 

If you have any thoughts, or any references to point me to, I’d love to hear them. Thank you for your hard work!



Hi Eric! Thanks for getting in touch. I’m excited that you are wanting to try a whole-body math activity with your students.  My first thought after reading about your plans for the activity is that it’s not weak at all. Movement is important but in this case I think it’s more about the change of scale and the collaborative effort to meet a series of challenges you provide (I’m assuming you might already have a specific graph or graphs in mind?)  I wonder if you could find some sturdy elastic instead of rope to make the activity more dynamic? The change of scale cannot be underestimated as a learning tool.


Sorry that I left you hanging… the activity ended up getting delayed for a few weeks because of some pressing issues that we discovered from the homework, but it did end up happening! Your kind words gave me the push I needed to do it, and you were spot-on: the collaborative aspect was definitely reinforced by the change of scale [emphasis added] and I think it worked out well all around.

I ended up using the yarn thinking that I could just use multiple strands per edge, but when I was doing some test runs I realized that this was a terrible idea because it was too much work to get the strands to stay together so they ended up being single-stranded yarn strongly taped to hard-plastic plates; definitely would do that differently next time.

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I decided to give them one non-planar graph (pictured left) to see what they would do with it. After that group worked on it for a while, and I told other people to go work on it with them, I asked the class what they thought. Half of them decided that it wasn’t possible, and half of them were not so convinced. I wonder how related those results were to how much interaction the students had with that graph. (Unfortunately, the idea was IMO undercut by the fact that one of the planar graphs I gave was a bit too complicated, and that group wasn’t able to untangle it. I didn’t tell them that it was planar— except one student who asked me about it after class. But I think everyone could see that the two groups were getting stuck in qualitatively different ways. I wonder how much the results were influenced by that graph).

The graph on the bottom right was the planar graph that the class wasn’t able to figure out.

malke-np (1)A further note from Eric: It was important to me that the graph to the left  would be fairly hard to identify for the more advanced students. In particular, if they already knew Euler’s formula and the q≤3v-6 inequality this would be useless, because it has the same number of vertices and edges as a cube, which is planar. Moreover, although it has K_{3,3} as a minor, it does not have K_{3,3} as a subgraph, so some passing familiarity with the classic 3-utilities puzzle would not be enough to immediately detect nonplanarity. In practice, although I had a few very advanced students in my class, including one who worked on this graph from the beginning, this wasn’t an issue— or perhaps it was just a success :P)

Malke 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,  on Twitter,  Instagram, or Facebook.

Inside the Whole-Body Newspaper Build Project

IMG_2906A few months ago I was asked by a school district to develop a pre-workshop workshop (yes, you heard right!) for 100 (!) 4th and 5th graders from six different elementary schools. I was brought in to design a pre-contest project that would focus on the process of collaborating in a making setting. This, in turn, would set the scene for an afternoon of collaborative Rube Goldberg Machine design and testing.

I knew exactly what I would do! For the most part, math activities and building projects are either on the page or explored with the hands. There’s nothing wrong with this, but I knew from my work developing and fine tuning Math in Your Feet that a scaled up, whole-body activity provides some mighty opportunies for talking, negotiating, learning, and working together.

We divided the kids, who, for the most part, were meeting their group members for the first time, into 20 groups of five. Each of the 10 adult chaperones were tasked with keeping tabs on two groups and providing ocassional check-ins. Once the kids were organized, I gave them a challenge:

Using the newspaper rolls and blue tape, work together with your group to build a structure that can 1) stand up independently of human support and 2)  be big enough to hold at least one or two group members, either sitting or standing inside the structure.

During the workshop I scheduled three formal moments for the groups to pause their activity and reflect with their teammates about aspects of their communication and the building process. The lesson plan has all the details.

Build 1

As part of my planning I decided that if we were going to do a project with this many kids I really wanted to have a detailed understanding of what they thought about the process. I knew that the workshop itself would go well enough because I’ve done this before at a smaller scale. However, I wanted their final activity of the build to be focused on personal written reflection. I wanted to gauge the overall dynamics and, hopefully, get some “data” on what nine and ten year olds might take away from a workshop that is intentionally focused on collaborative learning and making at the same time.

I was not disappointed! Below you’ll find their responses to three reflection prompts. The first reflection prompt was so rich I decided to break it into three parts. Responses to the final two reflection prompts follow after.

Kids are used to building with their hands. Legos, Kinex, marble mazes, etc. provide ample opportunity for literally building spatial reasoning which is the foundation of mathematical thinking. The newspaper rolls are one large sheet of newspaper rolled on the diagonal and can create a potent creative constraint requiring inginuity and collaboration. Their reflections, below, will give you a good sense of this.

What did you notice about the building process? [3 Sections]


  • I noticed in the building process that the structure was too short for Livie to fit in
  • I noticed we did not build the structure like we said we would
  • I noticed that the newspaper rolls wouldn’t stand up still [by themselves]
  • We used a lot of tape and used 25 newspaper rolls
  • The building process took a while but it didn’t take forever
  • [I noticed] that it is pretty hard to build something big
  • It was difficulat to keep the newspaper from falling down
  • We added as we built so we could fit more people [into the structure]
  • I noticed it was in stages
  • Our ideas got different throughout the building time
  • I noticed that one side wouldn’t stay up until we made the other sides
  • That a cube won’t just hold by itself
  • That it wouldn’t stand at first but then when we put more newpaper rolls and tape it finally stood up without us holding it
  • The plan changed a lot throughtout the process
  • It was very tilty and frustrating
  • I noticed that the project isn’t as easy as you think
  • It was frustrating, and hard to do
  • It was challenging but fun
  • Pretty hard until the end
  • We just added as we went


  • I saw that people did what they wanted, not what we said/suggested. It just went right over their heads.
  • We were a quiet group and we started talking near the end
  • It was bad because they kinda ignored me
  • I noticed that communicating was a HUGE step of this process
  • It was fun!


  • If teamwork worked and everybody was not goofing around our tower would have worked and it would have been a lot easier
  • I noticed that it was fast, fun, cool and nobody got mad, and I made friends
  • That having a group is very helpful
  • I noticed certain people helping, giving ideas, saving the thing that we were building [from falling down] and making new friends.
  • It was challenging and exciting
  • We made a teepee structure
  • I noticed that the building process was hard and easy depending on what we were doing
  • I noticed that everyone wanted to achieve the same thing. We worked well and let everyone do something!
  • We let everyone say what they thought should be added or fixed
  • We were working together and sharing ideas to each other
  • Everybody got the chance to help in the building process, we all built it
  • While building the structure we all agreed on things
  • What I noticed about the building process is that if you work with a team it is more fun
  • I didn’t feel heard because some of the my group kind of ignored what I said.


Would things have been easier or harder if you hadn’t been required to collaborate in a group?
  • It would be easier to do by myself because I don’t have to talk to other people
  • It would have been harder to hold  [the structure] steady while putting on the tape
  • [My role was] holding up things. I felt heard by all of the different group members because we all got a chance to talk.
  • It would have been hard to come up with the ideas, and hard to hold up stuff
  • It would  have been easier if we didn’t collaborate as a group because nobody would knock [the structure] down
  • What would’ve been harder was to tkeep it standing on its ownwhile I added supports
  • It would be easier if you did it on your own with your own creativity
  • The building structure would have looked more like what I had in mind
  • I like to work by myself
  • Harder, because without teamwork I would not have the great ideas. Everything would have been harder without a group because it’d be more work and less fun.
What was your role in the building process? Would you have liked a different role? Did you feel heard by the other group members?
  • I felt like I did everything
  • I did tape and I liked it. My group members let me choose where to put the tape and everyone had a voice in the building/design process.
  • I felt heard because everyone held where I assigned them to and let go when I asked them to.
  • I felt heard a lot because all of our thoughts were put into this
  • We sometimes changed the roles so everybody else got the chance to do something
  • My role was the tape. I felt heard by the others in the group because we were giving our opinions
  • I did not have a role because everyone else was doing everything
  • I felt bad they would not try my ideas
  • My role was to stay in the middle with or without Izzy, and we did it and built our house. I wish I was in the middle because you don’t have to do much work
  • My role was to help tape and come up with some ideas a bout how to keep it standing
  • I was building like everybody else. I felt heard by everyone. They listenend to my ideas and put them into action.
  • We actually all switched roles at different times


I’m thrilled about how seriously the students took the final written reflection because it provided great insights into what was happening inside each group. As I anticipated, some groups worked well, some didn’t; some kids felt heard, some didn’t. Some kids like working alone and others like working in a group. What’s clear to me, however, is that collaboration is pretty much a skill that needs to be intentionally developed.

On thing I wonder is how this activity would have played out if it had been a group of kids who actually knew each other. If you’re interested here is the full lesson plan.  Let me know how it goes!

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 also delights in creating rich environments for math art making in which children and adults can explore, make, play, and talk math based on their own questions and inclinations.

“What I’ve Learned (so far) About Teaching and Learning (Mathematics) in Dance Class”

“It’s hard to put your finger on the cause of a slow-burning problem. One day, you feel lucky to be paid to do something you love and the next, you’ve forgotten why you loved it in the first place. It can be even harder to put your finger on a solution. I turned to dance.”
–Ilona Vashchyshyn in her post “This one’s about dance (and burn out)”

Among many other things, Ilona is a secondary teacher in Saskatoon, Saskatchewan, and co-editor of the Saskatchewan Mathematics Teachers’ Society’s monthly periodical, The Variable. I have had the honor being interviewed by Ilona in which she heard all about my work. She posted a gorgeous, forthright story on her blog recently where I got to know more about her. In particular, I want to share her reflection on what she learned about teaching, learning, and mathematics during dance class (bolding mine)but I also encourage you to read her entire post.


What I’ve learned (so far) about teaching and learning (mathematics) in dance class, by Ilona Vashchyshyn:

Don’t underestimate the importance of routine.

Almost without fail, dance instructors begin class with a warm-up routine that engage dancers’ bodies and minds in preparation for the work ahead. At HDC (Harbour Dance Centre), most instructors kept the warm-up routine more-or-less similar from one day to the next, although new movements might be added (and some left behind) as the class gained proficiency. E.g., in ballet, a barre exercise might be repeated but with new arm movements, or with a relevé balance to finish. Of course, warm-ups are particularly important in dance because they help to prevent injury, but I found that having a common thread from class to class was valuable in other ways: notably, it gave me repeated opportunities to learn and improve the movements / pathways / exercises which, in turn, gave me the opportunity to develop my confidence as a dancer. Seeing my improvement from day to day encouraged me to continue, and experiencing small successes at the start of class offset the occasional frustration of learning new movements and combinations later on in the lesson. Not to mention, slowing down to practice movements in isolation meant that I could perform them with more ease and fluidity when it came to using them in choreography or in improvisation.

Dance is not about [learning] the choreography.

Early in the week, one of my instructors at HDC cut the music just before we began our routine to say: “Stop. Why are you here? If music is playing in dance class, you dance.” And he insisted that we did, even if it felt awkward at first. Later, referring to a complicated move: “Listen, I’m not gonna teach you that shit. You can learn it on the internet. This is dance class.”

More than any dance instructor I’ve ever had, he emphasized that dance isn’t about the choreography. Choreography, which is a sequence of memorized movements, will be quickly forgotten. A more valuable outcome of dance class is increased confidence and joy in responding with movement to music. Of course, an additional benefit of dance lessons is picking up new steps or pathways, but the value of these is not that you can perform them in a specific sequence, but rather that you can go on to combine and remix them in endless ways, in addition to creating your own. In fact, most of the dance instructors regularly set aside time during class for improvisation – even in ballet, which is generally regarded as the most rigid of the dance styles.

The connection to math class, I think, almost goes without saying: formulas, procedures, algorithms are our version of choreography. Of course, it can be fun to learn and execute the moves. There’s a great sense of accomplishment in accurately performing a complicated routine. But the main outcome of math class shouldn’t be a memorized sequence of steps; more important, I think, is increased confidence and persistence when facing new problems (the analogue of improvisation, or developing your own routine), maybe with a few more tools to tackle them.

Note that I don’t feel that there is a clash between routine (c.f. above), choreography, and improvisation – all have their place and their value. All parts of the elephant, as they say. Lest I stretch the metaphor past its usefulness, I will stop here, but the idea of dancing as problem solving (and problem solving as dancing) is something I’d really like to keep exploring.

A teacher learns.

A dance studio can be a prime location to study how great teachers differentiate and adapt instruction to meet their students’ needs. Especially in adult beginner dance classes, students tend to be very diverse in their abilities and previous experiences. While some really are starting from scratch, many are dancers returning after a long break, and still others are trying a new style but have extensive experience in another. At HDC it was instructive to watch how teachers adapted their plans for the week as they learned more about their students, as well as how they provided options in the moment for dancers with different levels of experience (“for now, just focus on the feet,” or “try lifting your hands off the bar if you’d like a challenge”).

On the flip side, the experience of being a student again was also invaluable. As teachers, we know that the struggle of learning something for the first time can be quickly forgotten, replaced by the illusion that it was easy all along. Forgetting is all the more likely when you teach the same course semester after semester, year after year. And maybe the quickest way to dismantle this illusion is to put on a pair of ballet slippers and a leotard and step into a mirrored room full of strangers who all seem to know what they’re doing while you’re still struggling to remember the difference between a frappé and a fondu and to balance with both feet on the ground. Even with the most encouraging of teachers, I sometimes found myself afraid to ask for help, hiding in the back when I felt lost, and even fighting the urge to escape to the bathroom when I started to get overwhelmed. Pushing through the frustration of just not getting it and the fear that I just never will, especially when it feels like everyone else does, can take tremendous effort. And a teacher who – in addition to providing focused feedback – takes time to remind the class that it’s okay to feel lost sometimes, that being on the verge of this is too hard is just where you’re supposed to be, can make all the difference between choosing to stay home tomorrow and showing up to try again.



Malke here again. More than anything I’d like to encourage you to think about whole- body #movingmath (whether dance or non-dance based) as a process of coming to understand not just the math but the process by which we come to know math, a topic that to many people, seems foreign and inaccessible.  Using the whole body in math class teaches us to persevere. Engaging our learners’ bodies in math class can help this process and as well as help build a community of learners. There are lots of resources on this blog for getting started. Please don’t hesitate to get in touch if you have questions!

Malke 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,  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 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,  on Twitter,  Instagram, or Facebook.

A Powerful Tool for Both Learners & Teachers



Larry Ferlazzo invited me to answer this question on his Ed Week Teacher blog: “What is an instructional strategy and/or teaching concept that you think is under-used/under-appreciated in the classroom that you think should be practiced more widely?”  I am sharing my response here but do check out the other answers!

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Every day students of all ages come to school with a powerful tool for mathematical reasoning but rarely get the opportunity to harness its full potential. When this tool, our students’ own bodies, are used, the activity is typically relegated to acts of memorization that lead no further than the next test. In contrast, taking math off the page and into the spatial, embodied realm of the whole, moving body has great potential to open up new avenues for understanding. Here are some examples of how a whole body, #movingmath approach can open up new opportunities for learning in a variety of grades and settings:

  1. Changing the scale:  When you change the scale of the math you are already exploring in your classroom you provide learners with the opportunity to get to know math from a completely new and novel perspective. Whether it’s exploring  number patterns on a scaled-up hundred chart, physically experiencing magnitude, scale, distance, and direction on an open body-scale number line, or noticing new things about polygons using lengths of knotted rope, learners collaborate, discuss, evaluate, reflect upon, record their activity, and start to connect it to other experiences in which they encounter and use these ideas. Seeing connections develops intuition,” Dan McQuillan at the University of Norwich tweeted recently. “Proofs are great; just like climbing trees, but the ability to swing from tree to tree is also great.”CH3P26
  2. Reasoning in action: During a Proving Center lesson Kindergarten students were asked to work in teams of four or five to find the center of an 11- cell structure, which looks a bit like a ladder.  Children were able to find the “center” of the object with their bodies rather quickly but their biggest challenge was to justify their physical reasoning. Lana Pavlova, an elementary teacher from Calgary, Canada told me that some of her students’ reasoning included “Because five is the same as five”, “Because these two sides are equal”, “Because it is exactly the half”.  Another student said that “not all numbers have the middle, six doesn’t. One has the middle and it’s one.” Lana told me, “I was very impressed by the kids’ reasoning. I also want to highlight how important the initial ‘explore’ stage is [and that] the movement IS the reasoning tool.”Fairhill ladder
  3. A reason to persevere: Lisa Ormsbee, a P.E. teacher at Fairhill School in Dallas,TX spent three weeks this past June running an enrichment program using movement and rhythm to explore and deepen enjoyment and understanding of math with intermediate students, many of whom exhibited what she called “math reluctance.” One of her main activities was Math in Your Feet  which requires precise physical/spatial reasoning around rotations,  categories of pattern properties, unitzing, complex patterning, equivalence, and perseverance to create original foot-based patterns. Lisa told me, “The kids were ALL so engaged in this activity! 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!”rb-5a
  4. Cognition is embodied: “Conceptualising the body, in mathematics, as a dynamic cognitive system enables students and teachers’ physical, visual, verbal, written, mental, and (in)formal activity to be taken not simply as representations  of abstract spatial concepts but…as corporeal and contextually grounded forms of cognition.” [Spatial Reasoning in the Early Years, Davis et al. 2015]

Overall, no math concept can be understood completely in one representation or modality.  Similarly, not all math can be explored with the body. Whole-body math may be a novel approach for many but it’s also clear that it can be a powerful tool for both learners and teachers.

Malke Rosenfeld is a dance teaching artist, author, editor, math explorer, and presenter coverwhose interests focus on the learning that happens at the intersection of math and the moving body. She also 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 book Math on the Move: Engaging Students in Whole Body Learning,  was published by Heinemann in 2016.

Leaving Room for Question Asking

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.





rb 10a





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.


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,  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.


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.