Japan Journal of Mathematics Education and Related Fields
Online ISSN : 2434-8899
Print ISSN : 1349-7332
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Showing 1-5 articles out of 5 articles from the selected issue
• Topological Lessons in upper secondary school with essential definitions of vertexes, edges, and faces
Masafumi KANEKO, Maki NAGAO, Takashi MATSUOKA, Kazutaka MATSUZAKI
2018 Volume 59 Issue 3-4 Pages 1-15
Published: 2018
Released: April 15, 2020
JOURNALS OPEN ACCESS
This paper proposes a definition of vertexes, edges, and faces (VEF) suitable for high school students, modifying its essential definition in topology. The paper describes difficulties in finding a proper definition of VEF, and the detailed process of revising the definition. In our previous lesson on Euler’s formula for polyhedron in a high school, students were confused to count the number of VEF of a torus. This confusion came from the fact that they were seized with the meaning of VEF in school mathematics. We tried to define VEF as terms in everyday use, which represent essential meanings in topology.
• Masato KAWASAKI, Tomoya Hukuma
2018 Volume 59 Issue 3-4 Pages 17-25
Published: 2018
Released: April 15, 2020
JOURNALS OPEN ACCESS
In teaching intensive quantity, it is important to properly understand the meaning of numerical values as quantity. Understanding the meaning of the quantity also requires understanding its unit. However, arithmetic education discusses extensive quantity such as length and weight, but not intensive quantity, operations between units, and expression in units. This study was conducted in January 2017, with the aim of obtaining suggestions on teaching intensive quantity. Fourth (n=131), fifth (n=122), and sixth (n=130) graders participated in this study. Their understanding of meaning and unit of quantity was examined using investigation problem regarding second term of three kinds of intensive quantity. Participants were asked to solve three problems about intensive quantity. Results showed that although the success rate was high, some participants solved the problems without grasping the meaning of the numerical value.
Takashi HIROSE, Katsuhisa HASEGAWA, Noboru SAITO, Satomi NISHIZAWA
2018 Volume 59 Issue 3-4 Pages 27-39
Published: 2018
Released: April 15, 2020
JOURNALS OPEN ACCESS
The purpose of this paper is to clarify the relations among students' aesthetic appreciation, conceputual knowledge, and procedural knowledge for the figure area. Judging from analyses and considerations of the results of the test, we found the following. (1)All students got the high scores in aesthetic appreciation of figures regardless of fluctuation of the scores in conceputual knowledge and procedural knowledge of figures. Therefore the students have some aesthetic appreciation of figures or other.(2)There was no correlation between sum total scores of the acqirement of knowledge of figures and sum total scores of aesthetic appreciation of figures in 4th grade students and 5th grade students. To students, originally, formation of concepts of figures, aesthetic appreciation of figures, and the acqirement of knowledge of figures are influential and compensatory one another. Therefore we found it necessary to connect aesthetic appreciation of figures with the acqirement of knowledge of figures and improve students' formation of concepts of figures.
• Takashi HIROSE, Katsuhisa HASEGAWA, Noboru SAITO, Satomi NISHIZAWA
2018 Volume 59 Issue 3-4 Pages 41-52
Published: 2018
Released: April 15, 2020
JOURNALS OPEN ACCESS
The purpose of this paper is to propose teaching methods which bring aesthetic appreciation and knowledge for 5th grade students in the figure domain together and try to form their concepts of figures and to clarify learning effects. Judging from analyses and considerations of the pretest, lesson practices, the test of figures, and the posttest, we found the following. (1) According to the pretest of aesthetic appreciation, there was no difference between the experimental group and the control group. (2)As results of respective learning reflection, it was meaningful for 5th grade students to take individual guidance, description of students' opinions, getting students' ideas of the group activities, and drawing figures in shape very seriously. (3)By comparing respective results of the pretest and the posttest of the experimental group and the control group, for students' aesthetic appreciation, lesson practices of the experimental group were effective, lesson practices of the control group weren't effective.(4) According to comparison of results of the posttest between the experimental group and the control group, lesson practices of the experimental group were more effective than the control group. (5)By comparing results of the figure test of the experimental group and the control group, it was effective to attach great importance to individual guidance, description of students' opinions, getting students' ideas of the group activities, and drawing figures. (6)For correlation between results of aesthetic appreciation and results of the test of figures, the experimental group was correlative and the control group wasn't correlative. Therefore it was effective to bring aesthetic appreciation and knowledge for 5th grade students in the figure domain together and try to form their concepts of figures.