Mathematics Classroom Innovation with Technology Japanese Movement
Masami ISODA msisoda@ningen.human.tsukuba.ac.jp
CRICED University of Tsukuba
Kakihana Kyoko kakihana@tsukubag.ac.jp
Infomatics & Media Studies
TSUKUBA GAKUIN University
Takeshi Miyakawa miyakawa@criced.tsukuba.ac.jp
CRICED
University of Tsukuba
Kazuhiro Aoyama aoyama@criced.tsukuba.ac.jp
CRICED
University of Tsukuba
Yoshihiko Yoden yoden@myad.jp
Faculty of Liberal Arts
Doshisha Women's Col. of Liberal Arts
Kazuo Yamanoi
yamanoi@tsukubag.ac.jp
Tsukuba GAKUIN University
Eigo Uehara
mow@mail.wind.ne.jp
Onogami elementary school
Kimiho Chino Chinok@criced.tsukuba.ac.jp
CRICED University of Tsukuba Japan
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 Teachersf 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 Noteh; 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 emails 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 cityfs research institutes and
to hold discussions with other schoolsf students. In addition all
students attend the Tsukubafs annual ICT education meeting. For
its efforts in promoting such progression ICT education Tsukuba
City was received the Prime Ministerfs 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 Noteh was developed based upon the ideas of school
teachers for all subjects. It has four functions: a Note book, Email,
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 Email 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,
handson 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 Noteh(Fig. 7). College students also use gStudy Noteh 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 (Cabrigeometre, Geometerfs
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. Cabrigeometry,
Geometerfs 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 Eblackboard
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, eetextbook and dbook 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 2629 materials for each grade. Each of them consist
of a sequence of "Letfs explore", "Letfs verify", "Letfs use", and
gLetfs develop", and contain 46 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.
Etextbook
The getextbook, created by the textbook publishers, is a teaching
material for lessons using projector. By the gtextbook viewerh of
etextbook, 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 viewerh can be translated,
rotated, reflected, and dilated. If we use an gelectronic information
boardh, 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 etextbook 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.93102
