Curriculum Study Mathematics No. 189

(Junior High School 2009 The Last Term edition)

1.         This article was written by a math teacher of a junior high school in Tokyo.

2.         The title of this article is “Using a toy to give students a clear understanding of spatial figure”; the subtitle is “Introduction of teaching materials and teaching aids”.

3.         The teacher is saying in this article that at her previous school she had a student in her classroom who was very good at math, but when it came to a study of spatial figure, he could not handle it very well. As so many other students were also struggling to understand the subject, she started looking for suitable teaching aids to assist her in making her student understand this concept. When she heard of “3D Geoshapes” from her colleague and of its superior versatility, she decided to use this toy-like teaching aid for her students. The result was more than what she had expected. Even some of her students, who had almost no interests in math, seemed excited; she could see their faces full of anticipation: “What will happen next?”. She believes that the fact that 3D Geoshapes is more like a toy than a typical educational aid might have helped raising interests among her students.

4.         The most useful functions of 3D Geoshapes, according to her, are 1) you can show developments of various types of solids, 2) you can show a three-dimensional shape by swiftly moving or turning a structure, 3) you can show the shortest diagonal line within any 3D object. This is very useful when you teach students about Pythagoras’ Theorem.

5.         The teacher was so impressed with 3D Geoshapes that she introduced it to other teachers in a math conference within her local area. Most of the teachers there had not heard of 3D Geoshapes before, however after her introduction and some demonstrations, they became quite interested in the products because it seemed very easy to build and show flat as well as 3 dimensional objects using 3D Geoshapes compared with the conventional way of cutting a piece of cardboard; they were were also amazed by its versatility.

6.         There are many students in her school who are not good at math, and she believes that it is up to her and other math teachers to make math more fun and enjoyable for their students in order to draw and keep up their interest. 3D Geoshapes certainly does a trick.

Curriculum Study Mathematics No. 190

(Junior High School 2010 The Fist Term edition)

1.         The whole article was written by a math teacher of junior high school in the Shizuoka Prefecture (west of Tokyo).

2.         The title of this article is “To realize Pythagoras’ Theorem by actual measuring”.

3.         You can see a couple of photos of students holding 3D Geoshapes at their math classroom in article 4.

4.         The teacher provided 10 Square shapes and a string per group of 2 students, and asked them to make a 3D object as shown in the article. The first question was to find out the shortest route from A to G by going through the surface of the object. There were different opinions among students; some thought that going through point M, which is in the middle of the side EF would be the shortest, and others thought that going through the point a little lower than M could be the shortest. After a while, someone made the development from the object and placed a string from A to G to find out that the shortest route should be going through point N located at one third from the bottom of the side EF. After everyone agreed with the answer, they were asked to calculate the length of AN + NG, and also, the length of AL + LG to compare the difference in lengths.

5.         The next question was to find out the length of the diagonal line inside the 3D object which is the length of AG. In order to answer this question, teacher could ask students to imagine the right-angled triangle which was to be created with a diagonal line and other 2 sides, and also, to count the number of the same right-angled triangle within the object. (the answer is 6)

6.         This exercise is for students to understand Pythagoras’ Theorem at junior high-school level. As this particular subject appears at the end of math of junior high school, the author of this article is suggesting that teachers should encourage students not only to find out answers by calculation but also to use actual objects to measure, so that students may notice that they can make use of math in more positive ways.