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p\2(344z2:=:(3=The Mathematics Education Student Associationinvites you to the colloquium:
Development of Teaching Materials using Dynamic Geometry Software: Exploration and Analysis of the Materials in Japan
Presented by:
Kaori Tabeta
Tokyo Gakugei University
Graduate School of Education
Master Course
Monday, 29 July 2002
3:00-4:00
Room 111-113Aderhold
Visit MESA online at:
HYPERLINK "http://www.ugamesa.org" http://www.ugamesa.org
INTRODUCTION
I study about teaching materials using dynamic geometry software for three years. This study started as graduate study of under graduate school. My teacher starts the seminar for graduate study for undergraduate students during the last part of 3rd year. We start own study having only a little information about the Mathematics Education, and no understanding how to study about this. Usually the students spend a half of year to find own research theme.
When I was 4th grade, I couldnt decide my theme but I was interesting in using technology in mathematic classroom. Then, my teacher gave me the dynamic software Cabri a! translated in Japanese by Tsukuba University at that time. He said, How about developing the interesting materials using this? And could you introduce how to use it for everyone? So I tried to use it. First I confuse about its manual all written in English. I worried about using it. But custom makes all things easy! I could use it gradually depending on help function. I was excited that the figures while moving dynamically kept their definition.
However my study was at a standstill soon. A good tool needs good examples, but I didnt know my way about geometry. Fortunately at that time, there were two pre-service teachers in my teachers office. They ware one-year trainees; one of them was public junior high school teacher, another elementary school. The junior high school teacher advised me often and introduced some problems in junior high school. My graduate study was greatly influenced by him. I explored those examples and we discussed some time. Especially I explored midpoints quadrangle in zeal. Exploring it continued for one year after graduation. Anyways, my graduate study, though never called academic study in Mathematics Education, was the start of my study.
After graduation I remained at my university as a one-year student, and decided to continue with study about mathematic education to try to examine graduate school. Now I am 2nd year of master course. In the meantime I have experimented teaching for one and half years. The first half year, I worked at public junior high school teaching math for 2nd and 3rd (14,and 15 years old) grades students. In this school, I allowed to use computer laboratory in my class. But these computers were 9801(made by NEC), of course not connected Internet, and I was not allowed to install any software. So I didnt use it there. Last year I worked at Attachment Secondary School of Tokyo University teaching math for 3rd, 4th, 5th (15,16,17 years old students) grade. This school is model school of junior high and high school consistently. It was good opportunity for me, because I could use handy graphic calculators in my classes, and I also couldnt practically study using Dynamic Geometry software here. I really want to know practically their activity using it.
At the same time, I was exploring about midpoints quadrangle yet. My first interest of exploring was If change the figure of quadrangle midpoint midpoints quadrangle are anytime parallelism, and proof also. It is fun for me that visual of the figure consisted a proof anytime. According to the tool scattered figures are joined, I realized proof is very economical. Gradually my concern move to What is the crooked figure like butterfly? This figure cant include quadrangle definition. If including this figure the definition is the figure of connection four points and there is universality property of midpoint quadrangle is parallelism. I tried to define the angle and area of the figure to find another common property. Finally it takes one more year until I find the figure is quadrangle on the 3D space or Complete Quadrangle it project to plane. This process was discussed with my fellow of my university. I realized pleasure of expansion, importance of definitions and counter-examples, through the communication.
Last year I presented at The National convention of JSME and discussed participants and got some advice. JSME (Japan Society of Mathematics Education) is one of the biggest associations of Mathematics Education in Japan. They have two big conventions every year The National Convention of JSME and Annual Meeting of JSME. In the first convention regularly we talk about practical study (e.g. teaching materials, lesson plan, the way of assessment), discuss with patients and are given the advice from advisers who organized professors in university, principals of public school, and the expert teacher of attachment school whom are specialist of math education. Many pre-service teachers gather there. In another convention academic papers of the year are presented. Some teachers informed me other exploring; one professor recommended a book. The most influential advice for my study was one of my advisers who was the principal of public school. He said, Your exploring activity is very interesting but you dont see classroom. How do you use this exploring in classroom? Then I didnt understand this mean because I have a little teacher experiments certainly.
Development of teaching materials companioning exploration like using dynamic geometry software necessitate developers own exploration for deep understanding about mathematic behind them. Through the exploration for long time developers find essential mathematical contents with some impression. We hope children learn the content with that feeling using the material in classroom. However, time period of one lesson is much more shorter than time period of using own exploration. The set of exploration activities need to be arranged for classroom. How is the feeling for children passed through the materials? How do we set the occasion for that? These are my main research questions.
At this time, Dr. J.W.Wilsons great lessons and ideal computer environments at UGA have helped me realized many things in my field of study. Some of them I never noticed in Japan.
Background of the study in Japan
The study concerning with dynamic geometry environment (development software and exploration, practical research) appeared in articles at 1990 in Japan. For more10 years many materials were developed and lesson studies were preceded. There are several kinds (GSP, Cabri, Geometric Constructor)of software users in Japan. Although holding the spotlight for long time, there are some serious issues in this field of study in Japan. If I say characteristic of these issues one phrase, Lack of practical, as following.
Trailing computer environments in schools
Lack of practical popularization for mathematic education
The small impact on the national curriculum
Trailing computer environments in school
The cause of another issues might be this issue. Almost school dont be maintained the computer environment. All school have at least one computer laboratory. However only a few years later it is usual that there were old computers (9801 made by NEC or FM-R/FM-TOWNS made by Fujitsu) in school, they not connect Internet, teachers not allowed to install feel free according to the capacity of their computers (Iijima, Y., 1995,2000).
In Japan there are many study about using dynamic geometry software. Focusing on practical, these researches did specific schools or areas only. Generally if one teacher is interested in using it in his/her class, he/she couldnt use it in his/her lesson feel free.
Lack of practical popularization for mathematic education
Almost mathematics educators know about dynamic geometry software, but cant use. The number of mathematic educators who can use it is small.
Students of mathematics education also know about it but havent used it. A few university which center of study about it might have, generally we dont have about using technology classes .If students interested in use it, like me, he/she have to know how to use it by him/herself. In my country, differ from other Asian countries have, there is no common software. It might be good effort to improve software each other, on the other hand it might be one issue of hard to popularize.
The small impact on the new national curriculum
In usual the Ministry of Education revises national curriculum once for about ten years. This year they force a new national curriculum (revise in 1999, enforcement in 2002). In this curriculum contents of mathematic are big cut down because of starting system of Five-day school week and innovation new subject the lesson of synthetically learning. In fact, the purpose of the new curriculum is relax education. There are some another social issues background of the curriculum.
Certainly it stress that it is bottom line from this curriculum, and refer to necessity of activity of observation, experiment. Nevertheless focus on the mathematical contents of it we feel the small impact of technology on it; the table of following is comparison of previous mathematic curriculum and new in Japan. It focuses on geometry. ;
The Comparison of previous curriculum and new focus on geometry
Mathematic ContentsGrade on
Previous Curriculum
(1987)Grade on
New curriculum
(2000)Congruence5th(elementary)
2nd(junior high)2nd(junior high)Point, Line Symmetry6th(elementary)1st(junior high)Similarity2nd(junior high)3rd(junior high)Circle3rd(junior high)1st(junior high)
and Math A
(Elect subject of high)Congruence and Similarity
TransformationMath A
(Elect subject of high)DisappearComplex PlaneMath B
(Elect subject of high)Disappear
In previous curriculum, some important mathematic contents are placed various grade based on students development. For example, Congruence and Similarity are covered all school grades but they have different purposes. In elementary school, it's to do specific operation. In junior high school, it's to make or catch system. In high school, it's to catch as mapping.
In new curriculum, each grade's contents go down 1 or 2 grades, some contents are pulled together (e.g. Congruence and Similarity) and some of important mathematic contents disappear (e.g. Transformation and Complex Plane). Educations of my country tend to be influenced by national curriculum.
If we use dynamic geometry software as a more usually tool, and if it is popularized, for example, we might think to use the contents of symmetry, transformation, and locus earlier through specific operation, and we might be remark new figure which have never used in classroom.
Some actions in Japan
Recently, there are some actions for solution to above issue of 1).
Project of Informational Education to 2005(the Ministry of Education)
Now the Ministry of education in Japan forward The project of Informational Education which is one of the governments millennium projects. This project plans as following actions to 2005 (The Minister of Education, 2000).
Two computers set at all ordinary classrooms in all school (elementary, junior high, high, public, government, private)
All school connects Internet.
All classrooms computers connected by LAN.
All teachers have one computer.
Set up the Web Site for resources of learning.
This project enables to do in classroom as following (Iijima, Y., 2000,2001)
If teacher use some software in his/her class, but use one computer and projector in ordinary classroom, it enable anytime.
Some time all students of one class enable to use one computer in computer laboratory.
The Project of Digitalization/Network Resources of Learning
The Project of Digitalization/Network Resources of Learning is one of the Projects of Informational Education. The purpose of the project is developing the way of development contents of Web Site based on textbook through the development contents. In mathematic, Professor Iijima (Aichi University of Education) are entrusted this project, Development GC Java and Construct contents of Web Site; Construct Tool Consortium based on one of textbooks (Keirin-kan) using GC Java. GC is one of the dynamic geometry software made by professor Iijima. The feature of this software enable to operate figures on the complex plane. (Iijima, Y.2000a, Iijima, Kusakabe, others, 2000) For this project, he develop new tool, GC Java. The feature of contents made by GC Java as following (Iijima, Y., 2000b, 2001a, 2001b)
They enable to open and operate the all files made by GC/DOS or GC/WIN.
They enable to use the almost functions of GC without install.
They enable to operate on Internet Explorer or Netscape Navigator (Windows)
Though textbooks of Japan dont assume using dynamic geometry software, this project will have great value for popularization using software between pre-service teachers.
Presentation/Share Information of Teaching Materials
By the grace of above projects, it will be more popular to using dynamic geometry software in ordinary classrooms. However mathematic contents of these projects are based on one textbook, but these not focus on impact of using it.
To focus on that point, we need another actions. It is according to doing mathematic by using dynamic geometry software. There are many studies about teaching materials using it. Some of studies refer to importance of record of developer's exploring activities (Iijima, Y., 1996a, 1996b), and there are many reports of records also. Usefulness of application of Internet was said (Iijima, 1997,1998), but the number of reports/researches on Internet is small in Japan.
There are a lot of reports/researches concern with this study, but they are doted various places (Iijima, Y., 2002) and they haven't assorted/analyzed yet. For collection and development of good materials using dynamic geometry, and for reflect on improvement in national curriculum by impact of it for future, Assorting/Analysis of previous studies is necessity.
My practical works for my study as following
For collection and development of good materials using dynamic geometry software, gather doted previous studies about materials, and assort/analyze them.
Development teaching materials through own exploration
The way of assorting previous studies
For development teaching materials the way of assorting previous studies should be same way of development of teaching materials. The way of development teaching materials companioning exploration like using dynamic geometry software is following.
Step 1. Finding original problem/object
Step 2. Teacher/Researchers own Explorations
Step 3. Arrangements of the material for classroom
Step 4. Practice in classroom
Original problem/object might come from some useful book, or might come from another steps. Therefore these steps have cycle.
The view points of analysis of materials: Relationship explorations and lessons
Through the exploration for a long time developers find essential mathematical contents with some impression. We hope children learn the content with that feeling using the material in classroom (Oota, S.,2002 ).However, time period of one lesson is much more shorter than time period of using own exploration. The set of exploration activities need to be arranged for classroom. How is the feeling for children passed through the materials? How do we set the occasion for that?
In a broad sense of the teaching materials include teaching tools and learning contents, however in classroom the definition of "teaching materials" are "organized the educational/learning contents to promote student's learning activities for achievement one educational purpose"(Kunimoto,K.). The Instructional Triangle is useful to consider about this definition. This figure helps us to catch the classroom. This figure represents clearly importance material to learn knowledge. Teacher supports student activity of involvement materials, but don't teach student the knowledge directly. Through activity students learn about knowledge.
Purpose
Materials
Involvement Involvement
Teacher Students
SupportFigure: Instructional Triangle
For the set of exploration activities arrange for classroom, it is need to analysis them. From Instructional Triangle, there are three view points; catch the purpose, students activity, teachers support. Those viewpoints are also useful for analysis of previous studies. Through the own exploration the developer realize these three points, especially biggest finding in set of exploring will be purpose, and a set of own exploration will be students activities.
To know teachers support it is also useful to catch aspect of discover and aspect of confirmation(Fujii, T., 1999). Middle of exploring, humans think is different clearly when he/she want to discover or to confirm.
Own Exploration of quadrangle
If change the figure of quadrangle midpoint midpoints quadrangle are anytime parallelism, and proof also.
What is the crooked figure like butterfly?
Change the definition, the figure of connection four points
Find another common character
I tried to define the angle, area of the figure
Through above exploring activity I find the figure is quadrangle on the 3D space or Complete Quadrangle it project to plane.
I could know the character of complete quadrangle of harmonically range of points; I think it use at internal and external division in high school
Some Example of midpoint quadrangle
5-1 Relationship Subsumption
Purpose: From subsumpution of parallelism decide the figures.
5-2 Quadrangle on 3D space
Purpose: From 3D space get into following Proof is common
About triangle ACB the point of P, Q are midpoint of AB, BC
Therefore AC//PQ and PQ=1/2AC (mid-segment theorem)
About triangle ACD, similarly AC//SR, SR=1/2AC
So PQ//SR and PQ=SR
Therefore Quadrangle PQR is Parallelogram.
5-3 Similar Transformation
Purpose : Find out similar transformation in mid-segment theorem.
Challenge
Sharing Information using Internet about analysis and exploration
making and using mathematics.
REFERENCES
Iijima, Y. (1995) The feature of Geometric Constructor: Dynamic geometry environment used in Japan. Tsukuba Journal of Educational Study in Mathematics, 14, pp.93-102
Iijima, Y. (1996a) From "Hold" Knowledge to "Useful" Knowledge; To send to information by Internet, proceeding, Bulletin of Data Processing Center of Aichi University of Education
Iijima, Y. (1996b), The record of exploration as one of the foundation data for presentation and sharing on Internet-Example of own record about Mr.Jibiki's "Theory of four squares", Epsiron, Aichi University of Education
Iijima, Y. (2000a) Mathematical Exploration about mapping, transformation, and complex numbers using dynamic geometry software, Proceeding of 33rd Annual Meeting of JSME, pp.205-210
Iijima, Y. (2000b) Using network in Mathematics Education to 2005. Proceeding of 33rd Annual Meeting of JSME, pp.693-696
Iijima, Y. (2001a) Development contents of Web Site Using GC/Java, Proceeding of 34th Annual Meeting if JSME, pp.193-198
Iijima, Y. (2001b) Setting up software for education and teaching materials on Internet; Report and suggestion of Construct Tool Consortium, Arithmetic Education of JSME, 83(12), pp.13-24
Iijima, Noda, Kusakabe, Ishikawa, Inagaki, &Oota (2000) Possibility for teaching complex numbers using dynamic geometry software
Please send me e-mail: HYPERLINK "mailto:tabekao@par.odn.ne.jp" tabekao@par.odn.ne.jp
The tools in general use are GSP, Cabri, and GC. GSP Ver.3 was translated by Yano-electricity; Cabri2 was translated by Tsukuba University, GC (Geometric Constructor) made by Professor Iijima (Aichi University of education). Figure Lunch Box made by Tokyo-Shoseki
For example, China and South Korea innovate GSP in junior high school. In EARCOME2002, many teachers from China participated GSP Workshop.
For example, Tsukuba University is center of study about using Cabri2, Aichi University of Education is center of study about using GC. In addition, some attachment schools (Attachment school of Yamanashi University of Education or Nara University of Education) study about using GSP.
School system in Japan is 6-3-3. 6-12 years old students learn for 6 years in elementary school. 12-15 years old students learn for 3 years in junior high. And 15-18 years old students learn in high school. Compulsory education is until junior high school. Generally there are same age students in each classroom.
In Japan, there are only 6 publishers that make textbook in elementary and junior high school based on our national curriculum.
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