Trail of a curriculum for Super Science High school

							        th
 The 10 International Congress on Mathematical Education, July 4-11, 2004, Copenhagen, Denmark
                      TSG4: Activities and Programs for Gifted Students


   ACTIVITIES IN NEW CURRICULUM FOR GIFTED STUDENTS
    -TRIALS IN SUPER SCIENCE HIGH SCHOOLS IN JAPAN-
                                Kyoko Kakihana, Suteo Kimura
      Abstract: The Super Science High school (SSH) project was set up by the Ministry of Education,
Cultural, Sports, Science and Technology (MEXT) in 2002 to develop a high school science and mathematics
curriculum for gifted students. Every year twenty-six high schools are selected to take part in the project for a
period of three years. In this article, we will explain what the Super Science High school project is as well as
categorize the new curricular activities involved.

     Key words: Curriculum, Motivation, gifted students, Creative Process,


BACKGROUND
These days everything changes so fast that things learnt in school often become outdated
in a very short time. In Japan, despite a policy over the last 50 years of a standardized
education for all, in the last 10 years, we have seen a widening gap in achievement
between top-level and low-level. Many students complained that they did not like
mathematics or science. As the result, the Ministry of Education, Cultural, Sports, Science
and Technology (MEXT) set the guidelines for mathematics education at the below
average level in an attempt to reduce the burden for students. However, many university
professors complain that the achievement level of students in mathematics classes is
decreasing, ever to the level where they cannot compute basic calculations such as
fractions (Okabe, T. and others, 1999). On the other hand, rapid development in the
science and technology make it essential to produce creative students with a high-level
ability in science and mathematics. Therefore, MEXT recognized the need to promote
comprehensive research and development in order to accomplish the highest creative
achievements in worldwide comparisons by nurturing the merits of science, technology,
and scientific research, and by seeking harmony and balance between science and
technology on the one hand and scientific research on the other (Japan's Science and
Technology Policy, 2001). The formulation of the "Science and Technology Basic Plan" at
the end of March 2001, MEXT set in place a plan to develop students based on the
creativity of science and technology, including started developing curriculum for gifted
students in science and mathematics. Then, the Super Science High School (SSH) project
started in 2002.


THE SUPER SCIENCE HIGH SCHOOL PROJECT
The purpose of this project is to develop a curriculum in mathematics, physics, biology,
chemistry, and earth science for gifted and mature students. The three-year project was
inaugurated in 2002 and each high school participate for 3 years. MEXT selects 26 high
schools every year. Seventy-seven schools applied for the project in the first year. The
budget for the project was 727,000,000 yen (about 6,000,000 dollars) for 26 schools in
2002, and 1,186,000,000yen (about 9,000,000 dollars) for 52 schools in 2003. Selected
high schools are expected to develop curricula based on science and mathematics in
cooperation with universities or research institutes. Specialists in each field and
researchers in education for each subject make up the research group that will examine
and analyze their activities and curricula.
       th
The 10 International Congress on Mathematical Education, July 4-11, 2004, Copenhagen, Denmark
                   TSG4: Activities and Programs for Gifted Students


RESULTS
We referred to reports from the SSH and the data from the websites of these high schools
to categorize the curricular topics and their activities.

(1) Lectures by university professors to introduce new areas in mathematics
All schools planned lectures by university professors. In scientific topics (physics, biology,
chemistry, and earth science), there were many lectures by people from companies, but
few lectures on mathematical topics. Nineteen mathematical topics were lectured by
eleven high schools. They were beyond the government guidelines mathematics, such as,
“Fractal science and the Logalism,” “A Polyhedron and Geometry,” “The Forefront of
Modern Mathematics: Chaos Theory.” These topics matured students about new areas in
mathematics. In two high schools, students investigated the lecture topic before the lecture
and continued to study it after it. For example, Benoit Mandelbrot gave a lecture on fractals
at a high school attached to the Education Department of Kyoto University. This is a very
new topic in high school curricula. To prepare for listening to the lecture, students studied
affine geometry, sequences, logalism, and such beforehand. After the lecture, they
investigated fractals on the computer and reported what they learned.
Students in Nagaoka High School in Niigata prefecture took lectures “Chaos Theory” to
introduce modern mathematics by the Professor Kawamura. Results of a questionnaire
showed 43% of students were practically able to take an image what chaos theory is and
55% of students were interested in the lecture. Forty-eight percent of students became
motivated to learn mathematics as a result of the lectures.
    .
(2) Constructing New Curricula that Combine Mathematics With Other Subjects.
Six schools tried to combine mathematics with other subjects. For example, Honjyo High
School which is attached to Waseda University, constructed a curriculum that combines
mathematics with physics and chemistry. At first, students learn what a vector is, the
reason why you need a vector, and calculation of vectors in their mathematics class. Then,
they learn about projection from a slanting direction, relative speed, and the composition of
powers in their physics class. As table 1 shows students take the mathematics class and
physics class in turn, and the classes are called “corroboration classes.”
Students in Daiichi Girls High School in Miyagi prefecture took a lecture “The Roles of
Mathematics in Economics”. In their impression of the lecture, some students wrote that
they understood from the lecture the importance of mathematics even for students who are
not majoring in science, engineering or mathematics and other students were interested
the relation between mathematics and the economy
Students in Chiba High School took lectures entitled “Fractal Science”. The goal of these
lectures was to connect mathematics to physics and biology. After the lectures students
visited a university laboratory and observed by microscope fractals in the pattern of
bacterial development and crystallization. It was written in students’ visiting reports that
they understood fractals more clearly after visiting the laboratory.
        th
 The 10 International Congress on Mathematical Education, July 4-11, 2004, Copenhagen, Denmark
                       TSG4: Activities and Programs for Gifted Students




                                Table 1. Corroboration Classes
      grade class               Mathematics class                 class                Physics class
      1st     1st    What is a vector?                             2nd    A projection from slant direction
      grade          Why do you need a vector?                            Relative speed
                     Calculation of vectors.                              Composition of power
              3rd    Inner products                                 4th   Power
                     What you can see with inner products                 Moment of force
              5th    Vector space                                   6th   Calculation of physical power by
                     Linear Independence and Linear                       Composition of trigonometric functions
                     Dependence                                           and Decomposition of them
                     Dimension
              7th    Transformation of a vector                     8th   Rotations of coordinate axis
                     Linear mapping                                       Problems of slope
      2nd     1st    What is differential calculus？                2nd    Description of moment by differentiation
      grade          The basic rules of differentiation and               Position of drop speed power, Speed,
                     proof of them                                        acceleration and the relation of power
              3rd    Differentiations of trigonometric function     4th   The motion of a pendulum
                                                                          A circular movement
                                                                          The relation of speed, acceleration and
                                                                          power
              5th    Differentiations of exponential functions      6th   Expression and graph for the speed with
                     and logarithmic functions                            air resistance
                                                                          Power for the speed with air resistance
              7th    Application of differentiations                8th   The maximum speed of a pendulum
                     and graphs                                           The relation between energy and power
                     Taylor expansions and approximation
                                     Math                                                Chemistry
      2nd     9th    Why do you need differential equations        10th   Method of 14C-age calibration Differential
      grade                                                               equations, Altamira’s pictures

              11th   The group theory                              12th   The group theory and an organic
                                                                          compound




(3) Trial of New Curricula and New topics for High School Mathematics
Five schools held lectures about fractals by university professors. They held extra classes
to understand the topic, and some of the classes used computers.
Other schools tried new materials such as “the structure of ciphers,” “learning mathematics
and science in English,” “statistics.”. In Japan, text books which are used in school are
usually published by MEXT. In this project, six schools produced their own text book.
Some of them changed the order of teaching. Some of them added new topics connected
with other subjects like modeling, more advanced materials like epsilon-delta logic or
introduction of symbolic logic.


(4)   Using Technology
Five schools conducted classes with technology. Three of them used Mathematica, and
two of them used a programming language. In the high school attached to the Education
Department of Kyoto University, students made a program to draw Sierpinski triangles and
explored the characteristics of these triangles. Two of them planned to use a graphical
calculator. At Kaiho High School in Okinawa, students used the calculator to explore the
foci of quadratic curves and the functions of sounds. A software for learning functions,
Grapes, produced by a high school teacher, Katsuhisa Tomoda, and offered in his
       th
 The 10 International Congress on Mathematical Education, July 4-11, 2004, Copenhagen, Denmark
                   TSG4: Activities and Programs for Gifted Students
website as a freeware (http://okumedia.cc.osaka-kyoiku.ac.jp/~tomodak/grapes/volume.
html) is widely used in high schools.


(5)   Increasing Mathematics Classes and Enhancing the Topics in Standards.
Most of the SSH schools increased mathematic classes by two or three per week and
went beyond government guidelines by teaching more advanced and challenging material.
In other subjects, they tried to make scientific experiments beyond the government
guideline material. Some of them made experiments at the university laboratory.
Experiments in other subjects motivated students in learning mathematics. Increasing
mathematics classes must be effective for all science. One student comments, "it was too
difficult to understand the university professor’s lecture in a physic class, without basic
mathematics knowledge. So, I should study mathematics more" in his report.


CONCLUSION
New trials of mathematics classes lead to motivating students to learn mathematics more
effectively. Moreover experiences in other subjects also motivated then to learn
mathematics. In this research, systematization of these trails in the SSH for a curriculum
for gifted students is left.


ACKNOWLEDGEMENTS
We deeply appreciate the twenty-six SSH 2001 schools and for allowing us to view their
reports and for cooperating with our research. This research is supported by the science
research fund of MEXT 14022101.


REFERENCE
[1] Japan's Science and Technology Policy (2003) http://www.mext.go.jp/english/org/
    science/07a.htm
[2] Okabe, T., Tose, N. and Nishimura, K. (1999), University students who are not able
    to calculate fractions, Toyo Keizai Shinpou


ABOUT THE AUTHOR
Kyoko Kakihana
Department of Computer Science
Tokyo Kasei Gakuin Tsukuba Women’s University
3-1 Azuma Tsukuba
Ibaraki 305-0031
JAPAN
Cell phone: +81 29 858 6292
Е-mail: kakihana@cs.kasei.ac.jp

Suteo Kimura, PhD
University of Meijyo
JAPAN