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.
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.
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.
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.
In order to further enhance problem-solving statistical education in
elementary and secondary education, it is indispensable to further cultivate each
student's statistical literacy. Thinking that it was essential for students to deal
with real world data and concepts of uncertainty, and believing that repeated
experience in this form of analysis was necessary, we let students tackle
problem-based learning in the field of inferential statistics. As a result, we found
some points worthy of attention during the teaching of actual lessons as well as
some issues which came to light from the reports submitted by students. This
paper is a practical report in regard to these matters.