In this study, we developed programs for teaching statistical probability to the third grade in elementary school. A purpose of this study is to improve recognition of probability among children; another is to evaluate the effect of the lessons. The paradigm for these teaching programs emerged out of Okabe’s 2006 curriculum, based on the standard Van Hiele theory. The concrete educational objectives of the programs are for students to enumerate elementary events, and compare probabilities. As a result of the educational practices, it is clear that: (a) In the pre-test, the third-graders were at a stage to judge subjectively (the zeroth standard), that is, they enumerated elementary events and compared the probabilities; (b) However, in the post-test, they developed to the next stage, and judged the result of the experiment as premise (the first standard).

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The purpose of this research is to improve the didactical methods of the basic mathematical education in regard to functional analysis at Japanese junior high schools. Particularly, this research shall support the way to teach the understanding of a function and its meaning along the present curriculum. In order to develop these methods, a study was conducted examining the school type called “Gymnasium”. As an example, a school in Bavaria, Germany, was studied. This paper analyzes and considers the results of this study, regarding the present knowledge of the bavarian students and their motivation to learn.

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The purpose of this paper is to develop the scale for aesthetic appreciation of students in mathematics education. For that purpose we carried out the test, which was designed for 325 6th grade students in 5 Kobe municipal elementary schools. According to the result of an exploratory factor analysis for the test, we found 4 factors. Values of Cronbach's α coefficients of reliability were good in items of respective factors and the loaded factors. Moreover, we investigated content validity, criterion-related validity, and construct validity. For content validity, Goodness of Fit Index(GFI), Adjusted Goodness of Fit Index (AGFI), Comparative Fit Index(CFI), and Root Mean Square Error of Approximation(RMSEA) were good in validity of items of factors loaded by confirmatory factor analysis. And the value of correlation coefficient for predictive validity in criterion-related validity was good. Also values of correlation coefficient for convergent validity and discriminant validity in construct validity were good. Therefore we could develop the scale for aesthetic appreciation of students in mathematics education through analyses and inquiries of the result of the test.

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The two books of “The elementary school education plan” is kept in the Konen-ji temple in Higashi-ku, Sakai-shi.In Japanese education system period, their author is Matsuno Seinyo who was a teacher in a Kasyu Kanata Elementary School (present Sakai municipal Kanaoka Elementary School) From them, we understand a state in an elementary school in those days.And, about education system and arithmetic education of the early period of Meiji era, we can inspect the content from the situation of one district. In this paper, I clarify the educational situation and the reality of the arithmetic education of our country in the those days And moreover we discribes the educational situation and arithmetic education in Sakai prefecture, in particular, the arithmetic text book called “Sanjyutsusyo” which is edited by the Sakai prefecture normal school conversantly.

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The purpose of this study is to show concretely the fact that educational policy in Sakai prefecture were reflected in primary school in the period of Gakusei (the Education System Order) mainly on arithmetic education. As the preparations, we detailed the polices of our country and the Sakai prefecture to shift to Western mathematics, in our previous note. In this paper, we further analyze the two books “Syogaku Kyohou (Teaching plan of Elementary School)” which is written by Seinyo Matsuno. As a result, we make it clear that Syogaku Kyosoku (elementary school teaching rules) in Sakai prefecture and the contents of an arithmetic textbook were reflected in elementary schools in Sakai prefecture.

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In the elementary school teaching guide for the Japanese course of study, the units on population density and speed are indicated as examples of derived units in mathematics. However, derived units other than area or volume are not taught in elementary school lessons. The study investigated this with the aim of obtaining suggestions on instruction methods concerning “size per unit quantity” and “speed,” based on the units. Primary school teachers participated in this study and their understanding of the derived units was examined. Three solutions to each problem for (the number in a group) × (the number of groups) ＝ (the total number) that were presented to the participants, who were asked to write down the unit of each value in the solution. At the same time, the participants’ profiles were asked. Results showed that the participants understood the derived units of speed, such as “km/h” regardless of their years of experience as a teacher, and their math or science ability. However, their understanding about the unit of the quantity calculated by multiplication or division for two types of quantities without the derived units of speed was not enough.

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Being based on the viewpoint of the language development, we will discuss where the sense of values judging “usefulness” comes from. We will find some similarity in the developments of the languages of Europe and Japan. From that viewpoint we will analyze how the Japanese introduced the letter from China in ancient time and changed it from hieroglyph to phonotype. In a society or in a human race the language is categorized to three groups, home language, social language and writing language. Referring the historical developments of a number of societies, it is seen that the coincidence of those three is necessary for the innovation. The goal is to see the role of Mathematics and Mathematical education in the Japanese society in relation with the globalization.

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This study was performed to test the next matter, the possibility of treating the intensive quantity as the extension quantity, and the necessity of dividing the instruction grade of “size per unit quantity” and “speed” in the intensive quantity. Fourth, fifth, and sixth grade students participated in this study. They had not received formal instruction on speed. They were asked to solve problems using three terms of proportion about speed and price per unit, and to answer subjective difficulties about these problems. As a result, the following five points were clarified: (a) there was no significant difference in the scores of fifth graders, and sixth graders on any of the problems; (b) the fourth graders’ scores on the problem were significantly lower than the scores of other grades; (c) the scores on the first and third terms of proportion were lower than the scores on the second term of proportion in the fourth grade; (d) in the fifth and sixth grades, there was no significant difference in the subjective difficulty of the speed problem; and (e) regardless of the problems, every grade found the first and third terms of proportion difficult. These results suggest that it is possible to treat the intensive quantity as the extension quantity, and to teach “speed” like “price per unit” or “density” in instruction on multiplication or division; this would require instruction in division to be associated with instruction on multiplication.

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Introduction of “mathematical exploration (tentative name)” is being considered in the next the government course guidelines. Also, not only solving a given problem but also developing readiness to realize the virtue of mathematics and positively think about is also an important problem from a point view of mathematics education. Therefore, based on inventory theory applying probability, we developed games that can be considered mathematically. We provide opportunities to realize the usefulness of application of probability by playing our games. Here we mention the background of a plan, an outline and practical results for the class dealing with the games.

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