Re: [IAEP] GPA Notes 7/23/09
On Sat, Jul 25, 2009 at 5:55 AM, K. K. Subramaniam subb...@gmail.comwrote: On Friday 24 Jul 2009 7:08:05 am Anurag Goel wrote: 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. The circular movement is not about geometry but differential calculus. Watch the movie clips on Talking Turtles in http://logothings.wikispaces.com, The one with the yellow turtle? particular the first part of clip 2. 732 and 12 are numerical encodings of a concept that they have to experience first using their own body movements. Subbu ___ IAEP -- It's An Education Project (not a laptop project!) IAEP@lists.sugarlabs.org http://lists.sugarlabs.org/listinfo/iaep -- Caroline Meeks Solution Grove carol...@solutiongrove.com 617-500-3488 - Office 505-213-3268 - Fax ___ IAEP -- It's An Education Project (not a laptop project!) IAEP@lists.sugarlabs.org http://lists.sugarlabs.org/listinfo/iaep
Re: [IAEP] GPA Notes 7/23/09
On Tuesday 28 Jul 2009 2:25:29 am Caroline Meeks wrote: On Sat, Jul 25, 2009 at 5:55 AM, K. K. Subramaniam subb...@gmail.comwrote: On Friday 24 Jul 2009 7:08:05 am Anurag Goel wrote: ..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. The circular movement is not about geometry but differential calculus. Watch the movie clips on Talking Turtles in http://logothings.wikispaces.com, The one with the yellow turtle? No, the BBC video Papert and Talking Turtle shown in five parts. See part 2: http://www.youtube.com/watch?v=BTd3N5Oj2jk Papert [1:37] : The essential point about the turtle is its role as a transitional object. That is, transitional between the body, self and the abstract mathematical ideas. The turtle, you can identify with it. You can move your body in order to guess how you can command the turtle. So it is related to you, your body, your movement and it is also related to mathematical ideas. Papert's genius lies in creating an environment in which children can not only experience distances, turns and geometrical shapes but also digitize them into countable numbers for operating the turtle. Pen trails help children to detect and correct any encoding errors. In this process, children use principles of differential calculus (countable offsets from current location), integral calculus (accumulate counts), arithmetic (modulo operators) and not geometry (compass-ruler constructions). The teacher in the video summarizes it very well: Teacher [4:13]: The great thing is it provides a mathematical environment for the children. While the children are working around the turtle, if you listen to what they are talking about, it's all mathematical. Verbalization in Mathematics is very important and I think that half of the problems with Mathematical teaching is that students don't communicate mathematically, talk about mathematics and experience mathematical problems... The numbers on the clock (and its shape) encode experiences that many adults take for granted but which inspire awe in children. Why deny them the wonder by jumping into encodings right away? Subbu ___ IAEP -- It's An Education Project (not a laptop project!) IAEP@lists.sugarlabs.org http://lists.sugarlabs.org/listinfo/iaep
Re: [IAEP] GPA Notes 7/23/09
On Sat, Jul 25, 2009 at 2:55 AM, K. K. Subramaniamsubb...@gmail.com wrote: On Friday 24 Jul 2009 7:08:05 am Anurag Goel wrote: 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. The circular movement is not about geometry but differential calculus. Watch the movie clips on Talking Turtles in http://logothings.wikispaces.com, particular the first part of clip 2. 732 and 12 are numerical encodings of a concept that they have to experience first using their own body movements. They all know what a 720 turn is in skateboarding or snowboarding body movements. If you don't, check out some eXtreme Sports videos on the Web. Subbu ___ IAEP -- It's An Education Project (not a laptop project!) IAEP@lists.sugarlabs.org http://lists.sugarlabs.org/listinfo/iaep -- Silent Thunder (默雷/धर्ममेघशब्दगर्ज/دھرممیگھشبدگر ج) is my name And Children are my nation. The Cosmos is my dwelling place, The Truth my destination. http://earthtreasury.org/worknet (Edward Mokurai Cherlin) ___ IAEP -- It's An Education Project (not a laptop project!) IAEP@lists.sugarlabs.org http://lists.sugarlabs.org/listinfo/iaep
Re: [IAEP] GPA Notes 7/23/09
On Thu, Jul 23, 2009 at 6:38 PM, Anurag Goelagoe...@gmail.com wrote: GPA Notes 7/23/09 Who: Walter, Caroline, Jennifer, Anurag 10:45: Set-up computers and projector. Walter worked on Clock program in Turtle Art Walter: Today we are going to use the turtle to play with clocks. (Walter shows the kids the clock program he made in Turtle Art. The kids compare Walter's clock with the other clocks in the room. Walter: Why do we use 12 numbers on the clock instead of 10 or 6 or 5? And why is the beginning hour of the day 12 and not 0 or 1? Because Leonardo of Pisa (Fibonacci) found out about Arabic numerals and published his book, Liber Abaci, during the Crusades. The Catholic Church took the position that the (Hindu/)Arabic 0 was an infidel invention, counter to the essential doctrines of Christianity. That is, that nothingness is irreligious when religion is founded on Creation. At that time clocks only existed in monasteries and cathedrals. Household clocks and pocket watches stayed with Roman numerals, and we are still stuck with this prejudice in the US. The situation is different in the sciences, in the US military, and in almost all other countries. All of them use a 24-hour clock that runs from 0:00:00 to 23:59:59 every day. This also gets rid of the ambiguity about 12 AM and 12 PM, and the resulting need to say 12 noon or 12 midnight. And the other ambiguity about 12 midnight--Which day is it? 0:00 is clearly part of the day that follows it. Clock time is the canonical example of a ring in mathematics, where you have addition, subtraction, and multiplication, but not division. -- Silent Thunder (默雷/धर्ममेघशब्दगर्ज/دھرممیگھشبدگر ج) is my name And Children are my nation. The Cosmos is my dwelling place, The Truth my destination. http://earthtreasury.org/worknet (Edward Mokurai Cherlin) ___ IAEP -- It's An Education Project (not a laptop project!) IAEP@lists.sugarlabs.org http://lists.sugarlabs.org/listinfo/iaep
Re: [IAEP] GPA Notes 7/23/09
On Mon, Jul 27, 2009 at 9:22 PM, Edward Cherlin echer...@gmail.com wrote: On Sat, Jul 25, 2009 at 2:55 AM, K. K. Subramaniamsubb...@gmail.com wrote: On Friday 24 Jul 2009 7:08:05 am Anurag Goel wrote: 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. The circular movement is not about geometry but differential calculus. Watch the movie clips on Talking Turtles in http://logothings.wikispaces.com, particular the first part of clip 2. 732 and 12 are numerical encodings of a concept that they have to experience first using their own body movements. They all know what a 720 turn is in skateboarding or snowboarding body movements. If you don't, check out some eXtreme Sports videos on the Web. Cool idea! Thanks Edward http://www.youtube.com/watch?v=B2Cg7w_8kkU http://www.youtube.com/watch?v=B_7fpFtWXCofeature=related Walter, you tube is probably blocked so you'll have to download them locally if you want to use this idea. Subbu ___ IAEP -- It's An Education Project (not a laptop project!) IAEP@lists.sugarlabs.org http://lists.sugarlabs.org/listinfo/iaep -- Silent Thunder (默雷/धर्ममेघशब्दगर्ज/دھرممیگھشبدگر ج) is my name And Children are my nation. The Cosmos is my dwelling place, The Truth my destination. http://earthtreasury.org/worknet (Edward Mokurai Cherlin) ___ IAEP -- It's An Education Project (not a laptop project!) IAEP@lists.sugarlabs.org http://lists.sugarlabs.org/listinfo/iaep -- Caroline Meeks Solution Grove carol...@solutiongrove.com 617-500-3488 - Office 505-213-3268 - Fax ___ IAEP -- It's An Education Project (not a laptop project!) IAEP@lists.sugarlabs.org http://lists.sugarlabs.org/listinfo/iaep
Re: [IAEP] GPA Notes 7/23/09
On Friday 24 Jul 2009 7:08:05 am Anurag Goel wrote: 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. The circular movement is not about geometry but differential calculus. Watch the movie clips on Talking Turtles in http://logothings.wikispaces.com, particular the first part of clip 2. 732 and 12 are numerical encodings of a concept that they have to experience first using their own body movements. Subbu ___ IAEP -- It's An Education Project (not a laptop project!) IAEP@lists.sugarlabs.org http://lists.sugarlabs.org/listinfo/iaep
Re: [IAEP] GPA Notes 7/23/09
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 ___ IAEP -- It's An Education Project (not a laptop project!) IAEP@lists.sugarlabs.org http://lists.sugarlabs.org/listinfo/iaep
[IAEP] GPA Notes 7/23/09
GPA Notes 7/23/09 Who: Walter, Caroline, Jennifer, Anurag 10:45: Set-up computers and projector. Walter worked on Clock program in Turtle Art Walter: Today we are going to use the turtle to play with clocks. (Walter shows the kids the clock program he made in Turtle Art. The kids compare Walter's clock with the other clocks in the room. Walter: Why do we use 12 numbers on the clock instead of 10 or 6 or 5? Kids: Because there are 24 hours in the day and 12 is half of it Walter: The Egyptians came up with the idea of 12 hours at day and 12 hours at night. (Walter showed kids how to count to 12 using the different parts of their fingers. Walter talked about the Babylonians and said that they liked to use the number 60.) Walter: Today we are going to use the turtle to play with hours. 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. -- Anurag Goel ___ IAEP -- It's An Education Project (not a laptop project!) IAEP@lists.sugarlabs.org http://lists.sugarlabs.org/listinfo/iaep
