The problem of the decreasing number of bluefin was taken up as a teaching material for mathematical modeling, and an educational experiment for junior high school students was conducted. Students were asked to think about the mathematical solution to this problem of the decreasing number of bluefin, utilizing the data on the number of bluefin and the catch of bluefin in the past. The proportion model for the first-grade students, the linear function model for the second-grade students, and the recurring formula calculation model for the third-grade students were used in this educational experiment. This is meant to be a mathematical modeling activity that will develop people who can lead the way in our society. The students’ perception of mathematics changed for the better as a result of this educational experiment. Students who answered that mathematics is useful for solving real-life problems accounted for 91% of the 1st-graders, 89% of the 2nd-graders, and 84% of the 3rd-graders. Students who thought this teaching material was interesting accounted for 85% of the 1st-graders, 76% of the 2nd-graders, and 79% of the 3rd-graders.

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The purpose of our research is to develop scales for teachers' and students' affect to mathematics in arithmetic education and to find out relationships between teacher's and student's affect to mathematics.To develop scales for assessing teachers' and students' affect to mathematics, we carried out two examinations which were intended for 137 teachers and 332 6th grade students in elementary schools. According to results of the exploratory factor analysis for two tests, values of Cronbach's α coefficients of reliability were good in the loaded factors . Moreover, Goodness of Fit Index(GFI), Adjusted Goodness of Fit Index(AGFI), and Root Mean Square Error of Approximation(RMSEA) were good in validity of items of factors loaded by confirmatory factor analysis. Therefore we could develop scales for assessing teachers' and students' affect to mathematics through analyses and inqiries of results of two tests. We also clarified relationships between teachers' and students' affect to mathematics by comparing the more common ones of items of teachers' and students' affect to mathematics.

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Computer algebra system provides not only algebraic calculation but also synchronization of the expression, the graph, and the numerical value. On the other hand, the expression style in the mathematics study is assumed for big relations to exist in the composition of mathematical knowledge. It is pointed out that the conversion of the expression style is important. It was clarified that study using the function of synchronization influenced the ability of the conversion of expression style.

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These days, we expect several senior high schools to train many top-ranking students and we expect several universities to train many top-ranking high school teachers. So, in this paper I will talk my own experiences before 1946, concerning the above problems.

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I had learned a good teaching method of mathematics from Mr. Yokochi for four years and a half during the period of the second girl’s high school, i.e., Yamashiro high school of Kyoto prefecture. His teaching had covered from daily issues to applied and expected problems of mathematics. His investigation method, starting from a small problem and resulting in solution of more magnified and complicated problems, had contributed so much to my study of radiation shielding. My class of measurement of radiation of surroundings has started at elementary school in Japan for the first time, with a word of school principal, ‘are school children able to measure radiations of surroundings? ‘. The principal was found to be an avid reader of Yokochi’s articles of infantile education.

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In Yamashiro Senior High School, just after the Second World War, Professor Yokochi taught us fundamentals of mathematics broadly including abstract ones, beyond the authorized textbooks. These were absolutely effective not only for my study at Kyoto University but also for my invention and development of new products after the graduation.

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