On Thu, Jul 23, 2009 at 9:38 PM, Anurag Goel <agoe...@gmail.com> wrote:
> The kids used the following sequence to make the turtle point in different > hour directions: > > seth() --> forward(100) -- back(100) > > Note: The kids started off by experimenting with different values for > "seth" > > I feel most kids struggled with this because they had not learned too much > about geometry, particularily concepts involving degrees and radii. However, > kids experimented with a lot of different values to better predict > increments. Some kids realized that if they input a really large number they > would get the same result as importing a really small number (ex: 12 and > 732). As expected, the kids did not understand why that was. Perhaps we need > to give a brief geometry lesson before letting the kids play with heading > directions. > I had good luck with paper folding activities to go with clock activities, for example, making snowflakes with different number of segments. Clock is a highly multiplicative structure, and kids who have weak multiplicative reasoning (e.g. reunitizing) struggle with it. I have an online snowflake maker to introduce the activity: http://www.naturalmath.com/special-snowflake/index.php Just leaving 4 out of 12 clock numbers (3, 6, 9, 12) helps a lot, too, because quarters are easier cognitively, the angles are familiar and so on. However, this is the "attenuation" approach (simplifying the environment) and I don't like to attenuate too much. With paper folding, you can give kids angle experience in an interesting context. I started to sketch a Zoombini-like paper folding activity, where you need, for example, to construct (match) certain folds to build a stained glass window. You construct everything out of prime number folds. So, to make the clock (1/12th) fold, you need to use a 3-fold and a 2-fold twice. This relates to "the splitting conjecture" by Confrey et al, and the ways young kids can construct numbers multiplicatively instead of additively. However, you can't use 3-folds with paper at the start, so there is the added fun complexity here. In physical space, I use coffee filters for this work. Cheers, Maria Droujkova Make math your own, to make your own math. http://www.naturalmath.com social math site http://groups.google.com/group/naturalmath subscribe now to discuss future math culture with parents, researchers and techies http://mathfuture.wikispaces.com/ Math 2.0 interest group home http://www.phenixsolutions.com empowering our innovations
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