Category Archives: Professional Reading

Math on the Move: Part 1

I have a tendency to devour professional books. However, in my rush to read about all these new ideas, I rarely ever slow down and take the time to stop and reflect on what I’m reading. Don’t get me wrong, I do *a lot* of thinking about what I’m reading, but I’m not doing anything to make my thoughts permanent so I can easily engage with them later.

I’ve been meaning to change that, to clarify and capture my thoughts in my blog, and what better time to do that than with my colleague Malke Rosenfeld’s long-awaited book Math on the Move: Engaging Students in Whole Body LearningToday I’d like to write about my thoughts as I read the introduction and chapter 1. I’ll follow up with posts about the other chapters as I make my way through the book.

I’d like to start with my own introduction to how I first came to meet Malke and get to know her incredible work.

Back in the summer of 2014, I had the opportunity to attend my first Twitter Math Camp. Looking at the schedule of morning sessions, my curiosity was piqued by a session called “Embodied Mathematics: Tools, Manipulatives, and Meaningful Movement in Math Class” offered by Christopher Danielson and Malke Rosenfeld. Here’s the session description:

This workshop is for anyone who uses, or is considering using, physical objects in math instruction at any grade level. This three-part session asks participants to actively engage with the following questions:

  1. What role(s) do manipulatives play in learning mathematics?
  2. What role does the body play in learning mathematics?
  3. What does it mean to use manipulatives in a meaningful way? and
  4. “How can we tell whether we are doing so?”

In the first session, we will pose these questions and brainstorm some initial answers as a way to frame the work ahead. Participants will then experience a ‘disruption of scale’ moving away from the more familiar activity of small hand-based tasks and toward the use of the whole body in math learning. At the base of this inquiry are the core lessons of the Math in Your Feet program.

In the second and third sessions, participants will engage with more familiar tasks using traditional math manipulatives. Each task will be chosen to highlight useful similarities and contrasts with the Math in Your Feet work, and to raise important questions about the assumptions we hold when we do “hands on” work in math classes.

The products of these sessions will be a more mindful approach to selecting manipulatives, a new appreciation for the body’s role in math learning, clearer shared language regarding “hands-on” inquiry for use in our professional relationships and activities, and public displays to engage other TMC attendees in the conversation.

Sounds awesome, right? It was! I can’t tell you how many times I’ve brought up this experience in conversation with colleagues over the past couple years. It gave me a new perspective about how we construct knowledge with physical things, including manipulatives and the body. And how exciting is it that two years later I get to revisit and expand on these ideas as I read Malke’s new book.

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In pairs we created 8-beat dance patterns using movement variables.

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We analyzed each other’s dances and talked about the mathematics in the dance as well as the dance itself.

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Our work bled over into the evenings as we danced and talked math in the “Blue Tape Lounge.”

Now that my introduction is over, we can move on to Malke’s.

Malke is a percussive dancer and teaching artist. During her career she has explored the relationship between dancing and mathematics through a program she developed called Math In Your Feet. Check out this TEDx video to see her do a little dancing, but mostly to hear her talk about her vision and her work.

One thing Malke does early in her book is make it clear what she is and is not saying about teaching math and dance and what she is and is not saying about the role of the body in learning. I appreciate that she takes the time to do this because as humans we have a tendency to try to fit what we’re hearing into our pre-existing worldview. By sharing examples, and more importantly, nonexamples, Malke helps create some necessary disequilibrium before readers dive more deeply into the rest of the book. Here are a couple of examples:

The first is that this is not arts integration. According to Malke, arts integration is difficult to pull off well and often the core subjects, such as math and science, are truly the focus while art is brought in as a way to “liven” things up. Rather, Malke prefers to frame her work and the ideas in this book as interdisciplinary learning.

“Both math and dance are discrete disciplines that require students to gain content knowledge, develop skills, and cultivate thinking and reasoning fluency in order to create meaning within their respective systems.” (page xvii)

The goal is not to teach math with dance or to teach dance with math. Rather, students are able to engage with and learn concepts from both disciplines simultaneously. Reading about this reminded me about Annie Fetter’s Ignite talk where she talks about the intersection of art and mathematics in her mother’s weaving and quilting. It makes me wonder in what other disciplines mathematics intertwines where someone may not even be conscious of it.

A related and important point Malke makes is that not all math can be danced and not all dance is math. But where they overlap is a beautiful place to spend some time learning about both.

The second example is probably the most important before getting into the meat of her book. If someone is going to invest the time to dive deeper and explore her message, then she needs for the reader to understand what she does and does not mean about the role of the body in learning. She does not mean using our arms to represent types of graphs, bouncing on exercise balls as we recite multiplication facts, or having students create the sides of polygons with their bodies.

“Too often the moving body is used primarily as an object for literal interpretation, illustration, and memorization of math concepts. Conceptualizing the body in this way, as a drawing or mnemonic tool, severely limits its potential in a learning setting.” (page xvii)

In contrast, Malke wants us to consider how the body can be used as a thinking tool that puts the student at the center of the reasoning and doing within a particular context. From birth, we have used our bodies to explore and make sense of our world long before we had language skills or the ability to understand someone telling us what to do. Malke wants us consider how we can provide students opportunities to use their bodies in these same ways to explore math concepts in school. I’m not going to steal her thunder, but in chapter 1 she shares three lovely vignettes of this in action in kindergarten, second grade, and fifth grade. Be sure to read and think about those,  and then contrast them with the nonexamples she provides.

Then get ready to dance! Malke doesn’t let you off the hook as a reader. Chapter 1 has two Try It Yourself! boxes that encourage you to get some masking tape and make a square on the floor – I recommend blue painters tape. Then she poses questions and challenges that give you the opportunity to try using your body as a thinking tool. You might feel a bit silly, but you just might make some new insights as well. Give it a try!

With the groundwork laid, I look forward to diving in to chapter 2.