Sunday, April 13, 2014

[The Math We See] [The Math We Do]

There are two ways I present Math in Your Feet. The first way is to upper elementary students.  In this version, the five-day residency revolves around the creative problem solving process of making our own percussive dance patterns.  Along the way, this pattern-focused process engages students in a flurry of mathematical activity within the dance making itself.  In addition, relevant math ideas/facts are identified and/or folded in to the experience to help describe, inform and improve our creative work.

The second way I present the program is to teachers. In the current version, our 3-hour workshop revolves around giving educators an experience of making math and dance at the same time; I lead teachers through the same core Math in Your Feet lessons as I do the students. This is a program about learning while doing so it makes sense that if you're interested in teaching the program to your own students, you need to have experienced the work first hand.

I have had the thought for a year or two now that I am dissatisfied with my teacher workshop model in some subtle but important ways. There are few things in particular that have come clear since my most recent teacher workshop:

1. Three hours is enough time for experiencing Math in Your Feet, but not much more. We need another session for processing that learning and what it means for students, making connections between the dance work to other ways we do and learn math (especially on the page) and hashing out all the permutations of classroom implementation.

2. On the whole, people will see the math with which they are already familiar in the work they are doing, often geometry.

3. Math in Your Feet is not a geometry unit.

4. It's time I made this fact more explicit.

5. When I can clarify for others the core of the learning that occurs while making math and dance at the same time I will finally have the conceptual base for creating a meaningful learning experience for teachers as learners first. 

I spent the last two days mulling all this over and came up with this. I think it's a good start:


An in-depth inquiry into patterns is at the core of the program. We spend the entire first day understanding how these patterns are built and structured, and how we might go about making our own.  We begin to understand that within a single beat in a dance pattern we can describe that one moment in at least three different ways (foot position, type of movement or direction).  This is the essence of mathematical abstraction.  This program is not about any one mathematical topic or strand or subject, it is simply about how we think when we do math.

This thinking occurs when we use attributes and variables to make, compare, compose, decompose, sequence, combine and discuss our Patterns A & B. This thinking also occurs when we sort, classify, choose, name and compare the variables/attributes that make up these dance patterns.

This thinking happens in the conversations and creative work within partner teams of two and in the active observation and analysis of patterns during our sit-down group observation and discussion times.

Patterns are our focus, our purpose, and what drives us forward. This important work is informed and supported by geometry concepts as well as the use of mathematical language and spatial reasoning in context. We are also immersed in matters of equivalence:

"What does it mean to dance the same as my partner?"
"How do you know that pattern was reflected?"
"It looked like both the A and the B patterns in their Pattern C were the same, but let's take a closer look and figure out if that's so. If not, how are they different from each other?"


In the end, it all boils down to clarifying the relationship between the math we see and the math we do.

The math we see are the "mathematical objects" that can be identified, named, memorized, tested, and are often the 'things' we hold before others as proof of learning. Many of these things are important, but they in and of themselves are only half the picture of what it means to learn math.

The math we do in Math in Your Feet? Those questions that spark inquiry, noticing, wondering and new questions? This is the process side of math, the action part, the really, truly, super fun part. It doesn't matter whether it's dancing or daily number routines, or working out how many different kinds of hexagons you can make with pattern blocks, or anything else. No matter the vehicle, this is how we think when we do math.

My goal now is to make this process side explicit and to figure out how to design an inquiry for teachers that revolves around the dance making but is as intellectually engaging for the adults as the inquiry I have developed for students. And when I can figure that out, we are going to have SO. MUCH. FUN.

Friday, April 11, 2014

One Huge, Kinetic, Sonic Blur [Residency Notes Day #3]


Note #1:  Day 3 is just one huge, kinetic, sonic blur
The classroom is full of noise, sound, movement and increasing mastery of complex moving patterns, patterns which are created, observed, refined, and analyzed throughout the one-hour workshop.

Having created four-beat Pattern A on Day 2, kids are charged with creating a second dance pattern.  Pattern B needs to be as different as possible from Pattern A. This means returning to the Movement Variables chart as a resource.

Are all your movements in Pattern A jumps and slides? Pattern B should have some other kinds of movements -- steps, turns, touches.

Is your Pattern A full of turns? Try to create something new that feels and looks interesting without any turns.

How about starting and ending position?  If you start and/or end in the center of your square in Pattern A, how about changing that in your second pattern?

You get the picture, yes? What's very clear is that I generally always see much more interesting, creative work in Pattern B, in both kid and teacher workshops.

What is also clear is that giving children agency over an inventory of pattern variables is highly empowering and every class this week has been super focused, productive and engaged.

Note #2: Day 3 is about combinations too 
After creating Pattern B we talk about how to combine the two patterns to make a new 8-beat combination. The options include:

A+B | B+A | A+A | B+B

And, yes, those are simple combinations.  But only on paper.  The challenge is to see where the first pattern in the sequence ends within your dance space and how to execute your second pattern from wherever you ended your first patternMeaning, you can't go back to the starting position of the second pattern (position 0) even if you're in a tricky position or facing a new direction.  These transitions are where the really interesting spatial/math thinking and problem solving occur.

Note #3: Biggest challenge in Day 3?
Says one 4th grader: "When I started combining Pattern A and Pattern B they were separate in my brain. It took a lot of time and effort to make them into AB."

Me: "You mean it took a while before it felt like they were the new 8-count pattern, Pattern C?"

4th grader: "Yeah."

Isn't learning math and dance at the same time fun?  Yup.

[Residency Notes Day #1 | Day #2]

Wednesday, April 9, 2014

Emerging Voices [Residency Notes Day #2]


This is the day kids really start dancing.


After spending all of day one in various stages of disequilibrium, day two brings an integration of new skills.  If day one was about "Oh my gosh, look what we get to do!" day two is about "Oh my gosh, look what I can do now!" and "Look what we can make!" 

Note #1: Clarifying intent (paying attention to the attributes of moving patterns)

This is also the day we focus on sameness. As in, how can we make our dancing the same as our partner's dancing?  What exactly needs to be the same?

Type of Movement
Me, to different teams of students working on their four-beat Pattern A: "Is that a jump or a slide?"

Choice of Direction
Me, during our periodic active observations of work in progress: "Are they turning the same direction or opposite directions?  How can you tell?"

Foot Position
Me, to dancers: "Are your feet split to the sides or is that a diagonal split?" or "How does it feel to finish with your feet crossed?"

Note #2: Experiment<==>Create

Today I spend a lot of time roving around the room just observing. At the beginning of creating their four-beat Pattern A, their feet and physical intention still emerging. They have to organize and integrate the ideas they see in their heads and communicate it with their bodies.  They also have to sync up with their partner's dancing as well.  This is a fantastic, engrossing challenge. It is also fascinating to watch their dancing/moving/body voices emerging so spectacularly over the course of the hour.

As the class proceeds, they all want to show me what they've come up with. We talk. When I show up near them again, the pattern looks different than I remember. "Oh, you changed it!" I exclaim. "Yeah, we like it better this way," they grin, proud of their agency and resourcefulness. Their dancing is cleaner now too.



Note #3: Thinking bodies
(observing the research on gestural thinking, literally in action)

Teammates discuss the similarities, sameness and differences of their (blue, taped, square) dance spaces.  In one class, children noticed: "They both have four corners" and "They have four parallel lines." 

Me: "Are there really four parallel lines?"  Discussion ensues.  At one point, a boy lifts his hands and, without speaking, uses his fingers to trace two parallel lines vertically in the air, and then two parallel lines horizontally.

Me: "Good! So by that I think you mean there are two sets of parallel lines?" He nods. I say, "Okay, let's all trace those lines in the air..."

Note #4: Thinking bodies (hive mind)


Wayne McGregor is a dancer and choreographer who engages in multi-disciplinary collaborative research around how the body thinks and learns, both the individual body, and the larger thinking whole created by a larger social systems. In his 2012 TED GLOBAL talk he provides a helpful primer of what it means to think with one’s body, especially within a dance system:

“So for me, choreography is very much a process of physical thinking. It's very much in mind, as well as in body, and it's a collaborative process. It's something that I have to do with other people. You know, it's a distributed cognitive process in a way …

The work we do in teams of two to choreograph math-informed, math-infused percussive dance patterns is social learning.  Not only do ideas flow verbally and physically between student teams, but also within each class; the energy in the room while kids are making often resembles a beehive. Today, for example, about half way through my most challenging class, something clicked and everyone was working intently; I could literally feel the group working and thinking together on their individual projects. 

[Residency Notes Day #1]

Monday, April 7, 2014

Squaring the Septagon [Residency Notes Day #1]

Note #1: Squaring the Septagon

First, let me just say that I almost met my match in terms of spatial problem solving today.  Almost, but not quite. 

I arrived at the elementary school this morning where I'll be working in the LGI room for the next two weeks with some awesome 4th graders and their teachers.

The LGI room is an extremely irregular septagonal shape, with a long diagonal and without any linear referents on the floor (no patterned carpet or tiles). Add to that our taped dance spaces are square.  It was my job to square the space.

I'll let that sink in. 

Given the difficulty of the task, I think I did a pretty good job.  What do you think?


Note #2: Why do we use so much tape in Math in Your Feet?

Because we do better, more interesting work inside our own dance spaces. Because it helps us focus on the relevant structure and shape of our dancing. Because dancing in limited space is part of many traditional percussive dance styles. That's why!


Note #3: What do I look for on the first day with a new group of students?

Can they keep a steady beat?

Do they know their lefts from their rights?

After a few rounds of our 4-count patterns during warm-ups do they get that we are dancing for four beats, and resting for four beats (signified by claps)?  Do they get the essential structure of the pattern unit and stop their movement on beat 4 or do they keep dancing?

Are their bodies organized? What challenges do they have lifting their feet off the ground? Do they loose track of their personal space and bump into their neighbors or end up far away from the rest of the group? Is it just a few kids, or the whole class?

When I give them words to say while they are dancing (e.g. "Split, cross, split, together") can they talk and dance at the same time? Or does the talking throw them off?

How much new information can I give them before their attention drifts? (Some groups enjoy more words and information, others get overwhelmed with too much input at one time. This tells me how to structure future lessons. The classes that zone out with too much talking need shorter bursts of the dance/talk cycle.)


Despite differences between individual kids and even whole classes, experience has shown that marking this starting spot can help us celebrate success as defined by amount of forward movement and improvement at the end.  Here's more on that:

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