ࡱ>  @*bjbj >N؝؝ :::8rL<YELR:" DDDDDDD$iGRIDD4EL"L"L"ZDL"DL"L"6@l60C P ]: lAlDl)E0YEAJ!J80C0CJDC(L"LlDD:!^: DEVELOPING MATHEMATICAL CREATIVITY BY FORCING CONNECTIONS TEOH POH YEW Abstract. By presenting mathematical concepts in a variety of styles using a variety of materials and media, we are actually demonstrating Creativity at Work to our students. There are a lot of interesting happenings around us. It is our choice to force new connections and make them related to certain mathematical concepts that we wish to impart to our students. This paper suggests some interesting T-shirt folding activities to develop mathematical creativity. INTRODUCTION There are many ways we can help children to be more creative mathematically. Having involved in helping children to love mathematics and to develop creativity for the past 18 years, I realised that one of the very effective and simple ways to develop creativity is to choose our own favorite meanings (or definitions) for creativity and constantly working on it. Here are my favorite meanings for creativity: Creativity is about making new connections variations seeing meaningful patterns making tasks/things faster/better thinking out of the box In this paper, I would like to demonstrate how we can help our students to develop their creativity by focusing on some of these meanings. HOW DO THE TEACHER, RESOURCES AND THE ENVIRONMENT AFFECT THE MATHEMATICAL CREATIVITY OF THE STUDENT? I believe teachers play a very important role in fostering mathematical creativity in their students. As George Polya said, Nobody can give away what he has not got. No teacher can impart to his students the experience of discovery if he has not got it himself. I also totally agree with Holden (2004) when he said, Teachers need to have a deep knowledge of how mathematical ideas can be presented for the students in a variety of ways, and a strong belief that all children can learn mathematics. Teachers also need to keep in mind that students have different learning strategies and thus need variation in the presentation of new mathematical concepts and themes. To be able to fulfill all these requirements, teachers need rich access to teaching and learning materials. By presenting mathematical concepts in a variety of styles using a variety of materials and media, we are actually demonstrating Creativity at Work to our students. There are a lot of interesting happenings around us. It is our choice to force new connections and make them related to certain mathematical concepts that we wish to impart to our students. CREATIVITY IS ABOUT MAKING TASK/THINGS FASTER/BETTER Here is an example of a series of activities regarding T-shirt folding that I use when I want to demonstrate the point that Creativity is about making task/things faster/better. The traditional way of folding a T-shirt takes about 15 seconds. A few years ago I received a video clip showing how a Japanese lady folding a T-shirt in a much faster way which took about 5 seconds. This is a very popular video circulated on the internet. You can get it from this site:  HYPERLINK "http://www.jengajam.com/r/shirt-folding" http://www.jengajam.com/r/shirt-folding. When I first saw it I found it so fascinating because I could never imagine that there existed such a different and creative way of folding a T-shirt. I immediately asked myself, How can I connect this interesting activity with mathematics lessons? When I tried to force connection, I felt that I could use this activity to talk about fraction or simple algebra. Detail instructions are as follows: FOLDING A T-SHIRT IN 5 SECONDS! First, lay a T-shirt flat in front of you with the front part facing up and the collar on your left as shown in the diagram below.  Imagine two lines on the T-shirt, Line 1 is drawn along one-third of the width and Line 2 is drawn along half of the length. Imagine points L1, R1 and L2 on the lines as shown in the diagram above. Pinch the fabric at point L1 with your left hand and point R1 with your right hand. Lift the fabric at point L1 and bring it to meet point L2 with your left hand, and then pinch point L1 and L2 together. With your right hand still pinching R1 and left hand pinching L1 and L2, lift the fabric and shake it and you will get the following shape:  6. Fold one more time along Line 3 and you shall get a T-shirt neatly folded.  Note: You can get an English version of detailed step-by-step video explaining how to fold a T-shirt using this approach at the following site:  HYPERLINK "http://www.youtube.com/watch?v=An0mFZ3enhM&NR=1" http://www.youtube.com/watch?v=An0mFZ3enhM&NR=1 FOLDING A T-SHIRT IN 1.5 SECONDS! A year later I received another video on T-shirt folding which is even much faster which took only 1.5 seconds! You can take a look at this video at:  HYPERLINK "http://www.youtube.com/watch?v=PKkSB1yVc1E" http://www.youtube.com/watch?v=PKkSB1yVc1E This second approach shows how we can build a T-shirt folding machine using cardboards. I was even more fascinated by this approach because even a three year old kid will be able to fold a T-shirt using this machine. Teachers can make this activity a mathematics project for students because they can make use of recycle materials and they learn how to cut the card boards according to the size of their own T-shirt. We can ask them to calculate the area and circumference of the card boards needed. We can ask them to bring a few T-shirts of their family members and make a machine that can fit all sizes. Recreational activities like this can arouse curiosity, develop ability in space perception, promote discovery and stimulate mathematical creativity. HOW DID MATHEMATICIAN MAKE TASK FASTER? After showing students the faster ways of folding T-shirt, I continue to lead them to see how mathematician could make task faster. To demonstrate this I would tell the story of how German mathematician Gauss, Karl Friedrich (1777-1855) calculate 1+2+3++100 in a very fast way when he was a young boy1. By reversing the order from 1+2+3++100 to 100+99+98++1 and added the two sets together he had every term equaled to 101. There were 100 sets of 101, so he had 10100. But the teacher just wanted one set of 1+2+3++100, therefore the answer was 5050. 1 + 2 + + 99 + 100 100 + 99 + + 2 + 1 _______________________ 101 + 101 + + 101 + 101 _______________________ 100 x 101 =10100 10100 2 =5050 This example will help students to see that if we can make use of our mathematical knowledge in a creative way we can do wonders. For secondary school students I would continue to introduce the formula for the sum of arithmetical progression.  EMBED Equation.DSMT4  By comparing this formula with the story of Gauss, students will be able to appreciate this formula and recall the formula more easily as compared to asking them to memories it. The interest of the students will be triggered if they see the relevance of the subject and have fun while learning (Baroody, 1987). CONCLUSION Mathematics needs not be a dry and boring subject. If teachers create interesting opportunities for the development of mathematical creativity, children will revel in the magic within this subject. I hope this sharing will inspire teachers to make their own connections and discover new ideas and techniques to encourage natural curiosity and stimulate mathematical creativity of their students. Note: 1. I found two versions of the story of Gauss from my reading, I prefer this version. REFERENCES Baroody, A. J. (1987). Childrens mathematical thinking: a developmental framework for preschool, primary and special education teachers. New York: Teacher College Press. Holden, I. M. (2004). How to become an excellent mathematics teacher. In Clarke, B. et. al. (Eds). International Perspectives on Learning and Teaching Mathematics. pp. 537-554. Coteborg: National Centre for Mathematics Education. Teoh, Poh Yew (2002). Mathematical Magic and Craft. Bukit Mertajam: Creative Wizard. ABOUT THE AUTHOR Teoh Poh Yew Independent Teacher Trainer Malaysian Invention and Design Society 91, Jalan Legenda 35, Legenda Heights 08000 Sungai Petani, Kedah, Malaysia Email: teohpy@tm.net.my     Developing Mathematical Creativity by Forcing Connections Teoh Poh Yew PAGE 184 DG 9: Promoting Creativity for All Students in Mathematics Education, Section 2 PAGE 185 ICME 11, Mexico, 2008 Proceedings of the Discussing Group 9 : Promoting Creativity for All Students in Mathematics Education The 11th International Congress on Mathematical Education Monterrey, Mexico, July 6-13, 2008 PAGE 180 DG 9: Promoting Creativity for All Students in Mathematics Education, Section 2 ()=>JKLMVW! 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