Mathematics Classroom Innovation with Technology Japanese Movement

Abstract

In East and South East Asia, technology for classroom use has been developed and used in the world. How does Japanese use technology in their classroom? We would like to reply these questions via Japanese ways of the innovative teaching practice with technology. First perspective is technology as a learning environment. The computer supported collaborative learning system, Study Note, is one of most major system in elementary and middle school for general use. Second perspective is software developed by matheducators and distributed by free. GRAPES and Geometric Constructor have been usually used in Japanese secondary classroom. Third perspective is software developed by company. Because of freeware environment, Japanese companies have to develop better software with contents which could be used easily. Forth perspective is the website which is developed for teachers and students. Computer Supported Collaborative Leaning with Teachersf Community Tsukuba City is the most advanced municipality in Japan in terms of ICT education. An ICT education project to use a groupware and the Internet started in 1995. Now, all 53 elementary and middle schools in the city are connected to one another by optical fiber cables and a teleconference system and information sharing system aimed at promoting ICT education research. They are all outfitted with gStudy Noteh; a groupware jointly developed by Sharp System Products, Co., Ltd. and university researchers, which allows students in Tsukuba to engage in question and answer or exchange information any student or teacher in the city. Almost 40 projects are ongoing in between 3 to 32 participating schools in each project. All school subjects are included: mathematics, sciences, social studies, languages (Japanese and English), music, and physical education, etc.. Over 15,000 e-mails per year are exchanged for these projects. Students make use of ICT in various ways; for example, to receive advice from researchers who work in the cityfs research institutes and to hold discussions with other schoolsf students. In addition all students attend the Tsukubafs annual ICT education meeting. For its efforts in promoting such progression ICT education Tsukuba City was received the Prime Ministerfs Award in the 2003 Internet Use Education Contest held by the Ministry of Education, Science, and Culture Japan (MEXT). This year, the research group produced Study Note for a palm computer with digital camera. Students in Tsukuba have been using it in class. Students can observe objects, take a picture, and describe comments of their observations on it, and then immediately send their written the observation. (Fig. 2) Study Note gStudy Noteh was developed based upon the ideas of school teachers for all subjects. It has four functions: a Note book, E-mail, a Bulletin Board and a Data Base (Fig. 3). Students start off by writing a digital note book. It is used as same as a paper one.: Students can easily write sentences, draw pictures and attach pictures/figures. Moreover they can attach sounds/movies on it. They can describe the process of their ideas and report on their activities. They are able to send these Notes to others and to obtain advice from others by using the function of E-mail or the Bulletin Board. They also exchange opinions on their Note Book and revise their ideas and knowledge through the Data Base. They can easily edit or restructure their written texts. They use the Data Base for portfolios and for storing their project. Through cycling three types of activities, hands-on experience, written description of the experience, and exchange of ideas about the experience, students get new ideas and reconstruct their knowledge (Fig. 4). Example 1. Plaza of Mathematics: Let's pose a problem An example of a collaborative mathematics learning activity between schools in Tsukuba is Plaza of Mathematics@@@@@@@@@

In this project, students tackle mathematical problems posed by teachers, other adults, or students (Fig. 6). They also ask questions or present reports. Through this activity, students are expected to enjoy to create own question in mathematics. Example 2: Reports of fitting functions Students learn how to fit functions for data on a spreadsheet and then write up a report about the activity on gStudy Noteh(Fig. 7). College students also use gStudy Noteh in a statistics course to fit data by using many kinds of functions, and to estimate future data and to evaluate which function is most appropriate. They comment on their estimations each other through this system(Fig. 8). User Friendly Graphing Free Software The educational technology for mathematics teaching and learning has been developed dramatically during the past decades, such as graphing calculators (TI, Casio, etc.), dynamic geometry software (Cabri-geometre, Geometerfs Sketchpad, Cinderella, etc.), Computer Algebra System (CAS: Mathematica, Derive, Aplusix, etc.). We present here one of educational software, GRAPES (GRAph Presentation & Experiment System) developed in Japan, and its educational potential.

GRAPES

GRAPES is a graphing software that allows the graphical representations of most of the functions and relations which appear at the secondary and undergraduate levels education. It has most of functions of the graphing calculator except the numerical and algebraic calculations. GRAPES is not a CAS like Mathematica and Drive in the sense that it has been developed just for the educational purpose of functions and relations, especially for secondary mathematics education. GRAPES like other graphing software allows an immediate drawing of a graph to the given algebraic expression. This point has a potential to dramatically change the teaching and learning of functions (see Romberg et al (eds.), 1993). The traditional way of teaching dealt with only few specific types of functions represented by symbolic expressions (linear function, quadratic function, etc.) and in a specific sequence. However, the immediate drawing of graphing software allows students to explore several graphs of functions and situate the specific traditional types in an ocean of functions including those of complicated algebraic expressions. Moreover, whereas the graph was often an end point of mathematical problems in the traditional way, the approach from the graphical representation is also possible, such as finding the algebraic expression to a given graph or given phenomena. With GRAPES, in addition to the characteristics of graphing calculators, several functions are available. The use of parameters and locus makes easily visualize families of curves of functions and relations, furthermore visualize the roles of parameters and explore the graphical and analytical nature of certain families (see Figure 9). The graphs of parametric curves can be also easily drawn. The use of graphing calculator is actually not common in the Japanese classroom practice. GRAPES is one of the most used software in the ordinary mathematics class in Japan. We consider two reasons. The first is due to its usability. The highly friendly interface makes it easily integrate to the time restricted class. The second reason is due to the fact Freeware. GRAPES is developed by a high school teacher Katsuhisa TOMODA (Ikeda Senior High School Attached to Osaka Kyoiku University). He is not developing it for the commercial purpose, but just for himself and his colleagues in order to enrich and make active their mathematics class. This kind of freeware for educational use is often developed in Japan. We can also find a freeware of the dynamic geometry software for the geometry learning, Geometric Constructor (GC: http://www.criced.tsukuba.ac.jp/gc/). GRAPES is now translated in English and in Spanish and downloadable from the following website: http://www.criced.tsukuba.ac.jp/grapes/

Dynamic Geometry Free Software: GC

GC (Geometric Constructor), Dynamic Geometry Free Software, was developed by Japanese researcher Iijima Y. (1995a). GC is a dynamic geometry software (DGS) like other famous software (ex. Cabri-geometry, Geometerfs Sketchpad). Many Japanese mathematics teachers, mainly middle school, used GC in their classes and have a community in which they discuss the responses of students and more effective use. Iijima has also developed a website in which the interesting problems using GC for students are presented. Part of those contents was developed by the discussion in the community. Because the interface of GC and website are in Japanese, it is not available for teachers and researchers in foreign countries. Japanese researchers began to translate the website and contents to English. They are also planning to translate this website to Spanish. It is a way for expanding the availability for more people. Following figure 10 is an example of GC problems website (http://www.criced.tsukuba.ac.jp/gc/GCWorld.htm) which has already translated. In this website, we use JAVA applet to be able to manipulate the figure directly with mouse. It is not needed to install GC software in each computer. Teachers don't have to distribute files which are used in their lessons. Most of all people who access this website can manipulate this figure and explore this problem. In this problem, students move points A, B, C and D and try to find geometrical properties (ex. Quadrangle PQRS is always parallelogram.) Additional line, circle, polygon and so on can be also drawn with tools in this window. It will help students to explore more deeply and verify their conjecture. This website has 19 themes and there are about 20 problems in each theme. Example shown in the above is a problem from one of them. Most of problems are focused on secondary school level.

Use of Projector and E-blackboard

In Japanese program by the Ministry of Education, we are expected all schools equipped with Internet and Projectors. In these 5 years, many of new innovative tools for classrooms have been developed in commercial context for teachers enabling to use them. eMath on Projector, ee-textbook and d-book are current famous products by companies.

Math on Projector

gThe Math on Projector is a collection of mathematics teaching materials with computer for 7th to 9th grade (1st to 3rd grade in junior high school in Japan). It contains materials which can be used in ordinary lessons and also for advanced class. The data created by Cabri Geometry II can be perused and manipulated through Cabri Java. The Math on Projector has 26-29 materials for each grade. Each of them consist of a sequence of "Letfs explore", "Letfs verify", "Letfs use", and gLetfs develop", and contain 4-6 data of geometrical construction (more than 100 data for each grade). Work sheets, examples of answers, etc. are also prepared for each content. All contents are developed by Kawakami, K. and Uehara and edited by Isoda, M.. Math on Projector is awarded by Minister of Education at the year 2005.

E-textbook

The ge-textbook, created by the textbook publishers, is a teaching material for lessons using projector. By the gtextbook viewerh of e-textbook, a page of textbook displayed on a screen can be zoomed in and we can write or draw anything there. Moreover, the items created by Flash put on the text page, can be manipulated on the screen. The figures drawn with the gtextbook viewerh can be translated, rotated, reflected, and dilated. If we use an gelectronic information boardh, even the teachers and students who are not used to a computer can also write in or manipulate objects easily. "dbook" as a tool to develop e-textbook By suppressing the manufacture production costs of the basic tool of a textbook company, "dbook" was developed so that we improve quantity of digital contents and a level of quality, and many textbook publishers could gain access to the market regardless of capital power. After scanning the page of a textbook, "dbook" allows to stick Flash items teaching materials on them. In order to create these items, we have developed "GCL (Geometric Construction Language)", a description language for the Flash geometrical IT contents. GCL is based on XML. It is superior to readability and has open specification which is rich in extendibility. The viewer is developed by Flash, We can operate Flash contents and the JPEG images, and arrange animations in the background. That is why we can create the visual mathematics teaching materials with a viewer. Since editing by "dbook" is possible only by choosing and sticking thumbnail of Flash contents or GCL data. As a result, although "dbook" was developed at first for textbook publishers, it will be marketed because requests of the sale to for teachers are very strong.

Developing Website for Advanced Study beyond Curriculum

Japan has national curriculum and the lesson hours for mathematics are restricted. From the viewpoint of equity principle, each school enables to develop its own curriculum but it is not easy for school teachers to develop their own curriculum and textbooks. For supporting teachers who have a wish to develop teaching program beyond their curriculum or to teach mathematics more meaning fully, and for supporting students who want to study more, Japanese government has been offering the national grants for developing contents. But basically, developed contents should be used by free. Based on this policy, there are a lot of free contents are available on web in Japanese. In the area of middle school mathematics, GC world developed by Iijima is largest. In the high school mathematics, the website, History & Cultural Museum in Mathematics and For All project, developed by Isoda, is largest. History & Cultural Museum History & Cultural Museum in Mathematics is a virtual museum on web.

Reference

http://www.criced.tsukuba.ac.jp/gc/GCWorld.htm Iijima Y. (1995a)

The feature of Geometric Constructor : Dynamic geometry environment used in Japan', Tsukuba Journal of Educational Study in Mathemaitcs, 14,pp.93-102