Tuesday, October 4, 2011

Conversational Math: Part Two

In trying to capitalize on the kid's penchant for 'talking math' I recently decided to try a game with her that I found in the booklet that came with our set of Cuisenaire Rods. 

The game is called Build What I Have.  One person describes a design they are making with their rods and others try and reproduce that design by listening closely.  One of the main points in this game is to introduce and/or reinforce math vocabulary.

The suggested age range for this activity is 2nd-8th grade; even though the kid is a young six I knew we could still get something out of it.  I decided that, to start, I would capitalize on concepts she already knew (parallel, points, edges, top, bottom, sides, etc.) and introduce some new ideas (perpendicular, horizontal, vertical). 

The rest we'd muddle through somehow, I figured, but she did surprise me by knowing her lefts and rights.  "We've been doing that in ballet class, Mama," she stated mater-of-factly.  Fabulous.

To start, we hid our designs from each other.

This is the first design.  I led and she followed, trying to make her design match mine by following my instructions. I started by saying: "Lay your blue rod parallel to the bottom of our work surface."  She already knows the concept of parallel really well, often times finding and noting examples of parallel lines when we are out and about.  "Then," I continued, "take your green rod and place in perpendicular [holding the rod in the air] up and down like this, and place the end in the middle of the blue rod."  Success!  Our designs matched!
This is the game she led.  To start she told me to put my orange rod parallel to the bottom of the workspace, but about an inch up.  The second orange rod was to be 'a couple' inches above the first one, but when she told me to put the blue rods on the sides to 'make a rectangle' I clarified the distance.  "Looks more like three or four inches, to me," I said.  I asked her to clarify the placement of the blue rods -- do they go on the outside ends of the orange rods, or inside?  Notice that this design is mostly made up of parallel lines, a concept she is most familiar with.
This is the second design I led.  I said, "Take your three light green rods and put them so they are together and vertical, up and down, in your workspace...Oh look!  They make a nice little cube!"  At first she thought she needed a fourth one to make it a square, but I clarified and said we're not making the outline of a square, but a solid shape.  When we revealed our designs to each other we saw some differences! 

This is how she recreated my instructions.  The white cubes are essentially in the right areas, but I had actually challenged her to put each white block 'point to point' with each corner of the light green square.  The dark green rods are essentially in the correct place; I knew that was somewhat complicated to execute.  And, I just noticed, the light green rods are horizontal, not vertical.

This is the last design in our session, which she led.  Perfect!  She wanted to use a bunch of different rods, but everything is still parallel here.
Here is what I find fascinating:  

My daughter's designs were much simpler today than normal and I think it might be because she had to describe what she was doing as she built them.  There is an equivalent experience that I find to be true in my work with 4th and 5th graders as well.  Often times I tell those kids that they are doing complex mathematics in their bodies and grade-level math on the page; they understand more math in their bodies than they can communicate through words or symbols.  Sometimes it is impossible for them to notate their Jump Patterns because they are just too complex for their current stage of symbolic mastery.

Often kids can do, know, and understand way more than they can communicate symbolically.  If we only judge a kid by her output on paper, we're not really seeing the whole child.  There are many ways represent comprehension: we need to listen and watch carefully for other indications of understanding as well. 

It wasn't too long ago when I brought the word 'parallel' into my daughter's universe.  It will be exciting to observe her body and conversations show me she's 'got' the concepts of perpendicular, horizontal and vertical. 

1 comment:

  1. Wow, this is a lovely game. We played a version at Natural Math clubs, where groups of kids had just several 3d shapes (say, two cylinders, a cube and a prism) and explained what they did to another group. I like rods better because of freedom.

    Thank you for your kind words in Part 1 - so glad your family is playing with math!!!

    It's great your daughter is building simpler designs. Simplicity (of this sort) is a value in mathematics. A pattern is simpler than a chaotic arrangement, for example. Simplicity leads to order and analysis! So, kudos to your daughter!

    My favorite explanation about "mathematical simplicity" is here: http://en.wikipedia.org/wiki/Mathematical_beauty#Beauty_and_mathematical_information_theory


Thanks for reading. I would love to hear your thoughts and comments!


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