Teoh Poh Yew | Sep 04, 2008
Here is an example of T-shirt folding that I use when I want to demonstrate the point that ‚Äúcreativity is about making tasks/things faster/better‚Äù. The traditional way of folding a T-shirt takes about 15 seconds.
A few years ago I received a video clip showing a Japanese lady folding a T-shirt much faster, taking about 5 seconds. This is a very popular video circulated on the internet.¬† You can get it from this site¬†or you can click below for the English version of the step-by-step video explaining how to fold a T-shirt.¬†
I found it fascinating because I could never imagine that there existed such a different and creative way of folding a T-shirt. I immediately asked myself, ‚ÄúHow can I connect this interesting activity with mathematics lessons?‚Äù When I tried to force connection, I felt that I could use this activity to talk about fractions or simple algebra!
Folding a T-shirt in 5 seconds!
1.¬†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.
2.¬†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.
3.¬†Pinch the fabric at point L1 with your left hand and point R1 with your right hand.¬†
4.¬†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.¬†
5.¬†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:
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 years old kid will be able to fold a T-shirt using this machine. Teachers can make this activity a mathematics project for students.
We can ask students to work out the area of cardboards needed, cut cardboards according to the size of their T-shirts and make a machine that can fit their sizes. Recreational activities like this one can arouse curiosity, develop ability in space perception, promote discovery and stimulate mathematical creativity.
Solving difficult mathematical problems in a jiffy!
After showing students the faster ways of folding T-shirt, I tell them the story of German mathematician Gauss, Karl Friedrich (1777-1855) who calculated 1+2+3+‚Ä¶+100 very fast when he was a young boy. By reversing the order from ‚Äú1+2+3+‚Ä¶+100‚Äù to ‚Äú100+99+98+‚Ä¶+1‚Äù 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 ‚Äú1+2+3+‚Ä¶+100‚Äù, therefore the answer was 5050.
¬†¬†¬† 1 +¬†¬†¬†¬† 2 + ‚Ä¶ +¬†¬† 99 + 100
100 +¬†¬† 99 + ‚Ä¶ +¬†¬†¬†¬† 2 +¬†¬†¬† 1
101 + 101 + ‚Ä¶ + 101 + 101
100 x 101 =10100
10100 √∑ 2 =5050
This example helps students to see that if we make use of our mathematical knowledge in a creative way we can do wonders.
Then there is the formula for the sum of arithmetical progression.
Students generally find it difficult to memorize. But when I compare the formula with the story of Gauss, it helps them appreciate and understand it much better. They are then able to recall it very easily.
Baroody said very aptly: ‚ÄúThe interest of the students will be triggered if they see the relevance of the subject and have fun while learning.‚Äù¬†
There are many ways we can help children to be more creative mathematically.¬† Having been involved in helping children to love mathematics and develop creativity for the past 18 years, I realize 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 work on them. Here are my favorite meanings for creativity:
Creativity is about
‚Ä¢¬†making new connections.
‚Ä¢¬†seeing meaningful patterns.
‚Ä¢¬†making tasks/things faster/better.
‚Ä¢¬†thinking out of the box.
I believe teachers play a very important role in fostering mathematical creativity in their students. As George Polya said, ‚ÄúNobody 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.‚Äù
I also totally agree with Holden (2004) when he said, ‚ÄúTeachers 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.‚Äù
By presenting mathematical concepts in a variety of styles using a variety of materials and media, we can actually demonstrate ‚Äúcreativity at work‚Äù to our students. There are a lot of interesting happenings around us. It is our choice to force new connections and relate them to certain mathematical concepts that we wish to impart to our students. Mathematics need not be a dry and boring subject. If teachers create interesting opportunities for the development of mathematical creativity, children will revel in the magic of 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.
Teoh Poh Yew has authored three books on mathematics magic and developed m-Wizy magic cards to facilitate understanding of mathematical concepts and develop creativity in a fun and magical way.
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