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.

TEDx Talk: Jump into math!

My upcoming book reminds us that the body is best positioned as a thinking tool, that math is about more than memorization, and that amazing things can happen when the body and math come together in both dance and non-dance settings.

I gave a TEDx talk in 2013 (before I had even thought to write a book!) which gives a great overview of what Math in Your Feet and whole-body math learning is all about. Math on the Move: Engaging Students in Whole Body Learning will be available in late October and is ready for pre-order.


Malke Rosenfeld delights in creating rich environments in which children and their adults can explore, make, play, and talk math based on their own questions and inclinations. Her upcoming book, Math on the Move: Engaging Students in Whole Body Learning, will be published by Heinemann in Fall 2016.

Math on the Move now ready for pre-order!

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“We want math to make sense to our students, and the moving body is a wonderful partner toward that goal.”   —Malke Rosenfeld

Kids love to move. But how do we harness all that kinetic energy effectively for math learning? In Math on the Move, Malke Rosenfeld (creator of Math in Your Feet) shows how pairing math concepts and whole body movement creates opportunities for students to make sense of math in entirely new ways. Malke shares her experience creating dynamic learning environments by:

  • exploring the use of the body as a thinking tool
  • highlighting mathematical ideas that are usefully explored with a moving body
  • providing a range of entry points for learning to facilitate a moving math classroom.

The book is filled with classroom-tested activities and detailed coaching tips, and supported with extensive online video clips.

Read more and/or pre-order by going to the Heinemann site

Join a growing community of practice around whole-body math learning on Facebook!

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Malke Rosenfeld delights in creating rich environments in which children and their adults can explore, make, play, and talk math based on their own questions and inclinations. Her upcoming book, Math on the Move: Engaging Students in Whole Body Learning, will be published by Heinemann in Fall 2016.

What it means when we say “learning through play”

Whole-body math learning should feel playful to the learner. This is a lovely short video about what it means when we say “learning through play.” Instead of building and using the “art machines” shown in this video, children can use their whole bodies as “objects to think with” in similar ways as they work to design, build, explore, and make original and mathematical foot-based dance patterns.


 

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.

Conversation: Getting started with #movingmath

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There’s a lot to think about when creating an environment for meaningful whole body math learning. Luckily, not only is the new book  filled with a wide range of information for implementing this approach in your classroom but we also have our Facebook Book Group as a space for conversations and support.

Recently a question came in on the FB group from a math teacher in the UK.  Jason Gottfried has been working on ideas for adding whole body movement into his teaching. His question and our resulting (slightly edited) conversation illustrate some of the important thinking that goes into creating and assessing activities where children’s whole bodies are engaged in making sense of math ideas.


JASON:
Hi all, I’m planning to experiment with coding and Math in Your Feet type choreography this Sunday. I will get participants to sequence dance “instructions” fairly loosely within beats in a bar and see if they or others can follow the “program”. I should be able to introduce loops and possibly conditional structures also. I’m thinking that instructions can be on cards and laid on a grid representing 4 beat bars. Any ideas about how to make this work out there? Love to hear about any activities like this that you may have done or heard about. Thanks.

MALKE:
The coding connection is a strong one! I think the thing to think about here is that children often need time to get used to the precision footwork (and benefit highly from doing so) before they can move forward toward “operations” on those patterns.  How much choice will they have in either creating or choosing the dance patterns? How much choice will they have in creating the program?

When thinking about programming in particular, and the body’s role in math learning in general, Seymour Papert’s book Mindstorms comes immediately to mind. In the book he reminds us that children have powerful ideas; his work with the LOGO turtle showed that kids will learn and thrive in an environment of exploration. It’s likely your participants will be able to follow along, but it might be way more fun for them, given some basic ideas, to create their own programs for others to “de-bug”.

JASON:
Thanks for the ideas. The idea of debugging a program is a few levels above what I had thought of. Amazing! I’ve currently produced a row of 4 cells to hold the “program” and I have instructions which are pictures of feet positions that children have to get their feet into for that beat. At the festival I’ll be at I usually get children aged 5 – 10 come and engage; I’m hoping I can get them to try to dance one of my programs and then try to arrange one themselves using cards with feet positions already on them and blank cards if needed. I don’t think I’m using actual footwork and I am not sure (but intrigued by the idea of) how to perform operations on the footwork. It’s totally experimental for me. I’ll definitely let you know how it went. Thanks again for the support.

MALKE:
So a simple way to create more exploration/agency would be to give them a program with the cards and then ask them if they want to try making a different “program” using the same cards. Which program “feels” better to execute? Is there anything they wish they could do that they don’t have a card/command for? Maybe have blank cards handy so they can create their own commands? That would be more than enough for a festival — a simple prompt/provocation and a chance to play around with making it different. Can’t wait to hear/see more!

JASON:
That’s it! Linking it to how it feels is great! That feels like the bit I was missing. Thank you. I’ll let you know how it went. Attached a picture of my son playing with the instructions. He had a couple of tries then went for the most complicated dance possible. Another angle I suppose.

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Continue reading “Conversation: Getting started with #movingmath”

At the core: Processes, strategies, and practices

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I see a lot of parallels between the work kids do in Math in Your Feet and the Maker Movement. Not only is the human body our original “technology” and the tool with which we learn about the world and develop our cognition from birth, but the “maker” philosophy aligns with my own approach to bringing math and dance together in elementary classrooms.

Mitch Resnick is the LEGO Papert Professor of Learning Research and head of the Lifelong Kindergarten group at the MIT Media Lab. Resnick recently sat down for a conversation with EdSurge. You can read the whole conversation but, below, I’ve focused on his thoughts about the process of making.

When one comes upon a whole classroom of moving bodies dancing in little blue tape squares it’s easy to to miss the forest for the trees, in the sense that it looks a lot like dance and not a whole lot like math. The reality is that math making and dance making have a lot in common. Both share a process by which the learner experiments, asks questions, revises, reflects and…often….has something tangible (an answer or some choreography) to show for it.  Resnick’s comments below resonate with the premise of the new book.


One of the things that appeals to me about the maker movement is that it’s not just about making. That’s an important part of what the maker movement is about. If you give a child a set of step-by-step instructions and build something, in one way, they’ve made something—but that’s not the spirit of the maker movement.