Tag Archives: Math In Your Feet

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.

img_7048

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

img_7049

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

img_7046

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.

 

Math In My Feet #TMC14

After joining the Mathtwitterblogosphere two years ago, I finally got to attend Twitter Math Camp. Yay!

Meg is my TMC Bookend Buddy because we hung out together at the start and end of the conference.

Meg is my TMC Bookend Buddy because we hung out together at the start and end of the conference.

In case you aren’t aware, Twitter Math Camp is a grassroots, “for teachers, by teachers” conference put on by fellow math educators from the US, Canada, and the UK. This year the conference was hosted by Jenks High School in Jenks, Oklahoma. (Thank you, @druinok!) There is no cost to attend and none of the presenters/facilitators are paid. This is very much a DIY conference, and I think that’s why everyone loves it so much. Not to mention I finally got to meet folks I’ve been talking to on Twitter for two years!

One of the things I really enjoy about TMC is the extended learning opportunity provided by the morning sessions. The session I attended all three mornings was called “Embodied Mathematics: Tools, Manipulatives, and Meaningful Movement in Math Class”. Our facilitators, Malke Rosenfeld and Christopher Danielson, helped us begin to explore four questions:

  • What role(s) do manipulatives play in learning mathematics?
  • What role does the body play in learning mathematics?
  • What does it mean to use manipulatives in a meaningful way?
  • How can we tell we are using manipulatives in a meaningful way?

I specifically say we began to explore these four questions because I don’t feel that we came to any solid conclusions, and that’s okay!

The focus of our work together was going through an abbreviated version of Malke’s Math In Your Feet workshop. Here is a blurb about the program from her website:

First and foremost, Math in Your Feet is an integration of two separate but highly complementary paths of inquiry. Percussive dance is a sophisticated, precise, and physical expression of time and space using foot-based dance patterns. Mathematics has been called both an art as well as the ‘science of patterns’ and initially developed to understand, describe, and manipulate the physical world.

Math in Your Feet leads students through the problem solving process of creating their own dance patterns. Along the way, they increase their understanding of mathematical topics such as: congruence, symmetry, transformation, angles and degrees, attributes, pattern recognition, symbols, and mapping on a coordinate grid, as well as deep experience with mathematical practices. The mathematical content of all activities was developed in collaboration with award-winning math education specialist Jane Cooney.

And here is an introduction video because this is a program you should see, not just read about. Actually, you should experience it for yourself, but barring that…

 

One thing that I really like about Math In Your Feet is that it happens at the intersection of math and dance. It isn’t just math and it isn’t just dance. It makes me wonder what other art forms and activities intersect with mathematics, and it makes me wonder how we can leverage that in our teaching. I think this is important because working in these intersections makes math meaningful. It provides an authenticity to the work teachers and students are doing in the classroom by blurring the lines between “school” mathematics and, for lack of a better term, actual mathematics.

If you want to see some of our work during these morning sessions, I recommend reading the Storify that Malke put together. You can also read her recap of the #BlueTapeLounge, the impromptu math and dance work that continued in the evenings in our hotel lobby.

As for the four questions we started exploring, I’m going to come back to them in future posts. My thoughts on them are still churning in the back of my mind, and I want to take some more time to reflect on them.