I will explain the following matters from the standpoint of Cultural History of Mathematics .
1. The short history of the Elements of Euclid in China.
2. Emperor Kangxi's enthusiasm for mathematics and astronomy.
3. Mathematical perspective in Jiao Bingzhen, Nian Xiyao and G.Castiglione.
4. Porcelain of Jingdezhen in the time of Emperor Kangxi and Emperor Yongzheng. And the role of Emperor Kangxi, Nian Xiao and Castiglione in the porcelain of Jingdezhen.
5. How did the porcelain of Meissen reach to the level of that of Jingdezhen. The dolls of Meissen.
Studies and discussion on Mathematical Education, cosponsored by the Mathematical Society of Japan and Japan Society of Mathematical Education, was given from 1952 to 1958.
At first it was where trainers and mathematicians talked and discussed about how to teach students of mathematics and methods of teacher-training. As Japan, under occupation, became independent and made innovations in scientific technology, the contents of the meeting were focused into the following matters because of earnest discussion of participants.
(1) A field of studies for mathematical education was found.
(2) Mathematicians got more interested in mathematical education than ever.
(3) Scholars, practitioners of mathematical education and mathematicians decided to cooperate in order to make their own ways of mathematical education.
(4) An organization of studies for making Mathematics-Education-Study was asked for.
(5)" Studies and discussion on Mathematical Education " developed to be dissolved and it helped to establish " Mathematics Education Society of Japan " independent of other organizations of studies.
:It is known that for the positive integers a, bw hich are coprime to each other an
integer n satisfying n ≥ (a -1) (b -1) can be expressed in the form ax+ by, x, y being non-negative integers. In this paper, we investigate this property in the special cases a= 2, b = 3 and a= 3, b = 4, 5. For the proposition above, G. Polya used a distribution table of numbers. We express these numbers as the products of matrix and vector matrix, and consider some properties by using lattice points in the coordinates plane from the algebraic and geometric viewpoints. We believe that it is important to consider why some numbers can not be expressed as ax+ by from these
viewpoints. We consider the teaching materials relating to the property stated above at the level of high school mathematics. This paper is also a case study of the problem solving.
:In ordinary math classes, it is necessary for the students to combine visual information with acoustic images corresponding to the teacher's oral explanation for constructing a mathematical reasoning flow. Again in traditional math classes, teachers routienly assume that all students already know certain facts that are necessary for
understanding the teacher's explanations in a lesson.If there are some students that don't know these facts, these students cannot understand the teacher's explanation.
These students might be called "under-prepared" for the class. On the other hand, if some students are already familiar with the mathematical reasoning flow, those students are unlikely to learn anything new during the teaching-learning process.
They might be called "over-prepared" for the class.The purpose of the paper is to show the lesson principle of arithmetic and mathematics which uses the thinking activities based on tactile sense information as a base, _and fulfills the following two conditions (1)(2). (l)Both under-and over-prepared students can deduce new facts on the basis of (old)facts they know in their own way;and (2) Each student can construct a new line of reasoning (or flow of reasoning) by combining the results of his /her reasoning with those of other students.
Various solutions may exist in geometric problems. Here, an example of constructing parallel lines is used to show how to draw out various solutions from students and the effectiveness of connecting those to mathematical properties.
The purpose of this study is to examine the acquisition process of method of reproducing solid from photograph and method of freely creating solid, and to clarify the change in the amount of blood in the brain with near-infrared spectroscopy.
The approach employed in this analysis was as follows. We installed the I-channel near-infrared spectroscopy in the right side frontal lobe point of subject's brain, and measured the change in the amount of blood in the brain for the experiment period.
We examined the feature of the amount of the change of oxyHb, deoxyHb, and totalHb, and compared differences in two experiments.
As a result of the experiment, the following were clarified to us. 1) The situation of deoxy Hb in subject's brain was different in two problems. 2) In the reproduction problem of the solid, the feature of changing oxyHb corresponded to the kind of the photograph which the subject selected. It is concluded that whether the subject make
the reproduction of the solid or the creation of the solid is related to the change of the amount of blood in the brain.
In this study, we aim to create systematic contents that pupils can acquire the depth cognition on space. So in this paper, we made a piece of contents ("Notice changes of a plane") for 3rd graders. and we investigated development of their depth cognition through an educational experiment.
The result of our experiment shows the next points. About 90% pupils'cognition was developed, and then about 40% pupils acquired the depth cognition.
Namely, 3rd graders'depth cognition on space was developed by the contents.