Japan Journal of Mathematics Education and Related Fields

Valuable viewpoints of mathematics which school teachers should learn from Archimedes and Fourier

Haruo Ishigaki

2009 Volume 50 Issue 1-2 Pages 1-4
Published: 2009
Released on J-STAGE: April 21, 2020

DOIhttps://doi.org/10.34323/mesj.50.1-2_1

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Recently, it seems that people like to know the solution soon, but in the classroom it is rather important to understand how to reach the solution. In this respect, school teachers of mathematics should have their own attitude to mathematics as a meaningful part of science, and it is also worthy for students of teacher's college to follow the theories established by excellent mathematicians in the far past. In this paper we pay attention to the great achievements due to Archimedes and Fourier. The former established a thought method, which is a basis of modern sciences, in the time of the Greek, and the latter contributed greatly in the 18th century to the development of the modern mathematics. In this paper we recommend for teachers and students of mathematics to learn a lot of things from Archimedes and Fourier, since they were standard bearers of scientific ideas in the respective periods.

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Change in the number of individuals of Japanese crane and a logistic curve

From interdisciplinary colaborative education with a theme of "Environment"

Yoshio Umeno

2009 Volume 50 Issue 1-2 Pages 5-13
Published: 2009
Released on J-STAGE: April 21, 2020

DOIhttps://doi.org/10.34323/mesj.50.1-2_5

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In our college, some subjects teach it by the theme of enviornment at the same time, which we say "Interdisciplinary Colaborative Education". In the class of mathematics, we analyzed the change in the number of individuals of the Japanese crane by the difference equation, and we confirmed that the change applied to the logistic curve. Moreover, we illustrated that the logistic curve appeared in the various scenes, and we developed it into chaos phenomena. A lot of students were surprised that mathematics was effective for such a natural world, in the following questionnaires. In this paper, we shall consider the mathematics knowledge needed in this teaching material, and the meaning of taking up such real data in the class.

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Proposal of educational mathematical origami model with edutainment

Folding/wrapping model of frat circular membranes by modified Archimedean spiral configurations

Sugiyama Fumiko, Taketosi Nojima

2009 Volume 50 Issue 1-2 Pages 15-25
Published: 2009
Released on J-STAGE: April 21, 2020

DOIhttps://doi.org/10.34323/mesj.50.1-2_15

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The purpose of this paper is to present generalized models of compact folding/wrapping method of flat circular membranes around a central hub using modified Archimedean spiral configurations. By using the formulated simple angle relations between fold-lines, various kinds of wrapping models are shown to be easily designed. The present models are expected not only to design a fundamental modeling of sail wrapping of solar-sail spacecraft but also to be used for instructional materials with edutainment.

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A study on development of a systematic curriculum of probability in elementary school education (I)

Masafumi Kumode, Nobuki Watanabe

2009 Volume 50 Issue 1-2 Pages 27-39
Published: 2009
Released on J-STAGE: April 21, 2020

DOIhttps://doi.org/10.34323/mesj.50.1-2_27

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In the present-day, it is generally important to teach the probability. However, it is said that both quantity and quantity are not enough for teaching the probability in Japan. Especially, the probability is hardly taught in elementary schools. So the purpose of this study is to make the curriculum of teaching the probability in elementary schools. In this paper, we researched cognition about the probability to 1st, 2nd and 3rd graders who have not been taught the probability. From the result of the research, the possibility of teaching the probability from the first grade in elementary schools was shown.

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Theory of real numbers

Teaching programm and practice

Hiroshi Koike, Mayumi Tomobe, Nobuyuki Kenmochi

2009 Volume 50 Issue 1-2 Pages 41-54
Published: 2009
Released on J-STAGE: April 21, 2020

DOIhttps://doi.org/10.34323/mesj.50.1-2_41

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There arc two methods to extend the set of rational numbers to the one of real numbers. One of them is due to Dedekind and another due to Cantor. Their ideas are respectively based on the concept of "cut" and on the one of "fundamental sequence". Both are complete theories on the real numbers which give theoretical definitions of fundamental properties of real numbers, such as the continuity (or completeness). But, unfortunately it seems not easy for students of high schools to understand their theories without studing the general set theory (and the mathematical logic). Nevertheless it would be expected at least for all students belonging to any courses of sciences to study this subject as a part of liberal arts. For this purpose we need to compose a continuous program on the study of "numbers" without theoretical gaps throughout junior high school, high school and universitiy. In this paper, we try to evolve the theory on the extension of numbers, especially the extension from the set of rational numbers to the one of real numbers based on interminate deeimals and report a lesson practiced in a high school.

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Lecturing mathematical education

1+1=2, arrangement of leaves

Ikuo Tayama

2009 Volume 50 Issue 1-2 Pages 55-67
Published: 2009
Released on J-STAGE: April 21, 2020

DOIhttps://doi.org/10.34323/mesj.50.1-2_55

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We introduce our lecture on mathematical education in universities. First, we describe the purpose of our class, our attention while teaching, the contents and the outline of our class. Next, we explain our lecture on the natural numbers and the Fibonacci sequence, precisely. Since it is troublesome to start with Peano's axioms, we pick up 11 formulas from the natural numbers and consider them as the new axioms. While we are making the new axioms, we come across the question why one plus one is equal to two and have some answer to it. As for the Fibonacci sequence, we discuss about how to solve pa_n+2+qa_n+1+ra_n = 0 and describe our study on the arrangement of leaves. We define the condition of the ideal arrangement of leaves and show that 137.5 degrees, which is the angle derived by the Fibonacci sequence, satisfies the condition.

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Errata in Vol.49, No.3·4

2009 Volume 50 Issue 1-2 Pages 69
Published: 2009
Released on J-STAGE: April 21, 2020

DOIhttps://doi.org/10.34323/mesj.50.1-2_69

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