<div class="gmail_quote">On Thu, Jul 23, 2009 at 9:38 PM, Anurag Goel <<a href="mailto:agoel23@gmail.com">agoel23@gmail.com</a>> wrote: <blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;"> 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. </blockquote><div> 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: <a href="http://www.naturalmath.com/special-snowflake/index.php">http://www.naturalmath.com/special-snowflake/index.php</a> 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. <a href="http://www.naturalmath.com" target="_blank">http://www.naturalmath.com</a> social math site <a href="http://groups.google.com/group/naturalmath" target="_blank">http://groups.google.com/group/naturalmath</a> subscribe now to discuss future math culture with parents, researchers and techies <a href="http://mathfuture.wikispaces.com/" target="_blank">http://mathfuture.wikispaces.com/</a> Math 2.0 interest group home <a href="http://www.phenixsolutions.com" target="_blank">http://www.phenixsolutions.com</a> empowering our innovations </div></div>