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Embodied Mathematics

(Nov 2 – Dec 7, 2017) Our 5-7 year olds just spent five weeks experiencing math with their bodies.* You can see some footage of this circle in action on the video we produced during the course. Thanks to all the students and parents who participated.

Here’s a list/description of every activity we did.

 

Role-playing the need for math

In week 1, we acted out scenarios where no numbers were allowed. The students got around this with drawing pictures.

Week 2: no numbers, no pictures

Week 3: no numbers, no pictures, no names of shapes

Week 4: no numbers, no pictures, no names of shapes, no comparison words, and no approximations (at this point we had to use the whiteboard to keep track of all the restrictions)

Week 5: all of the above allowed.

Here were the scenarios:

  • Invite me to a party
  • Pay me for restoring your sheep’s health
  • Resolve a dispute about which army won a battle
  • Explain how to cook something (pancakes, cookies, whatever the children knew how to make)
  • Explain how to draw a snowman
  • Explain how to build a snowman
  • Explain how to plant a garden
  • Give me directions to your home or your relatives’ home

We had so much fun as students debated and even voted on which words were allowed (Point? Line? Few? Side? Shape? Herd? etc). The students decided each week how the difficulty would be ramped up the following week. They were excited that it would get harder and harder, and it was their idea to make the final week as easy as possible. I didn’t expect this activity to be as popular as it was. The students could have spent the entire 5 weeks doing nothing but this. No one ever got tired of it; they just asked for more and more.

 

Simon Says

We played the game Simon Says but with one twist: with each command, regardless of whether the Simon character said “Simon says,” you have to command the opposite. So if Simon commands “reach your arms to the sky,” the next command has to be “do the opposite of reaching your arms to the sky.” (It’s up to Simon whether to say Simon says, adding in another layer of complexity.) Over the weeks, the students discovered that

  • not every command has an opposite
  • some commands seem to have multiple opposites (so what does that mean? Does it mean they have no opposite?)
  • some commands actually are two commands embedded into one (i.e. stand on your left foot)

If you replace the word opposite with “negate” or “inverse” and replace the word command with “function” the mathematical reasoning involved here may be more apparent. We didn’t use these terms in class, though.

Over the weeks, the game evolved to include the creation of equivalent, not just opposite, expressions. Students could choose to give an opposite or equivalent command and the others had to guess which it was.

 

Mirror

The students stand in a line and the leader strikes a pose. The rest of the group has to mirror it, leading to lots of experimentation with various types of symmetry.

 

Ants Go Marching

The Ants Go Marching is a children’s song that is sung to the tune of “When Johnny Comes Marching Home.” We sang it. “How can we think about or show this idea with our bodies?” I asked, quoting Malke Rosenfeld from the sample chapter of her book Math on the Move.  The students first made their bodies into the shapes of the numbers and then wanted to act it out. Problems arose when we didn’t have the right number of people for everyone to stand in the correct formation. In other words, we were playing with divisibility.

 

Rhythm Name Patterns

We clapped the rhythm of every participant’s full name. “How is this mathematical?” I asked, as I asked for every activity during the course. Cyclical patterns, the group came up with after a discussion.

 

Sidewalk chalk addition

I drew a number line from 0 through 8 on the sidewalk. The students jumped to represent operations such as starting on 0 and adding 3, starting on 3 and adding 2, starting on 5 and taking away 4, etc. We did scenarios where the instructions landed them off the line below zero (negative). Then I asked the students to make their bodies face the opposite direction. What happens if you add 2 but you’re facing the other way? What if you take away 3?

In this activity, the wide age spread of the students became apparent. The students ranged from young 5s to a few close to 8. The older students were interested but the younger students wandered away. My original plan for this course had been to do no activities with numbers, but some of the older students begged me to work with numbers right from the start. This activity was to be my compromise. We revisited it a few times for just a few minutes when students needed a break from other activities, but it didn’t become one of our core activities.

 

Poi

I asked my helper Joanna to demonstrate the performance art of poi. “What words would you use to describe what she’s doing?” “How is what she’s doing mathematical?” I was hoping that this would facilitate student’s ability to communicate about math by naming, classifying, and describing poi patterns, and that students would notice the symmetry and periodicity in the motions. They did. Then they wanted to try it. I wasn’t prepared for this, so we couldn’t. (You can do poi with tennis balls in long socks – maybe try it at home.) I was inspired by poi artist Ben Drexler’s article “A Mathematical Approach to Classifying Poi Patterns, Introduction and Basics.”

 

Math In Your Feet

We did an activity from Malke Rosenfeld’s book Math on the Move. (On the book site, click on “Download a Sample” and then find the section “Try it yourself, part 1.”) We invited parents and siblings to do this one too. Students stood in sidewalk-chalk squares and experimented with how many ways they could do certain moves.

 

Play Doh Nim

Play the game Nim with little balls of play doh. In this version, you can smash 1 or 2 on your turn. If you smash the last one you win. This game was another place where the age spread made things difficult so we didn’t return to it on another session, but I plan to do it lots more with other groups. All of the credit for this activity goes to Lucy Ravitch, who described it when she guest-blogged on the Let’s Play Math site.

 

Pattern Function Machines

During the course, one student who had been in math circles before begged to do the activity function machines. (In function machines, students suggest an “in” number, the facilitator reports the “out” number, and the students have to discern the rule after a few examples of ordered pairs.) It took me weeks to figure out how to do this in an embodied way.

We asked the students to stand in a line. The first child was given a red block, the second a blue one, the third a red one. “What color will the next person get?” We did this repeatedly with increasing complexity of patterns and the students creating the patterns. Then we switched and gave the students puppets to hold (and operate, of course). This was tougher since puppets have many more attributes than do wooden cube blocks. The students struggled happily to discern patterns in the line of puppets. The following week we did it with blocks on the table instead of the students carrying them. Had we more time, we would have taken away all props and just had the students stand in certain positions and identify patterns. The eventual mathematical goal would be to move toward abstraction by eventually moving into words then symbols/numbers, but that was not the goal of this course.

 

Many thanks to helpers Joanna (for facilitating many of the activities) and Maria (for being an extra set of hands). Also to you parents for sharing your wonderful children with us!

Rodi

*Here’s our course description: Neuroscience has provided empirical evidence of what we intuitively knew all along: that counting on your fingers enhances learning. The discipline of embodied mathematics employs gesturing and physical interactions with the environment to develop conceptual understanding and to facilitate articulation of mathematical concepts. Year after year, young students come into Math Circle with the idea that mathematics is all about quick computation and nothing else. This course will open students’ minds to the reality that math is about more than numbers and can be explored with more than a computational approach. We’ll use our bodies and surroundings to examine symmetry, 2D and solid geometry, equivalence, measurement, spatial reasoning, and arithmetic computation.

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