In this article, firstly I outline the function of a representation and the conditions of a diagram. Secondly, I review studies on the effects of using diagrammatic representation on problem solving and instruction in representing a problematic problem situation with a diagram. Lastly, I propose the conditions of effective diagrammatic representation to solve text-based questions about 'speed'. Thirteen diagrammatic functions have been pointed out, and three conditions of an effective diagrammatic representation to solve problems have been indicated. There are very few studies on the effects of diagrammatic representation on problem solving and the effects of instruction in representing the problem situation with a diagram. In addition, the subjects of these studies were non-representative. The conditions of an effective diagrammatic representation to solve text-based questions about 'speed' are as follows: The drawing should detail that the motion towards overtaking or collision is about to start, the provisional overtaking or collision points and the fact that the distance or volume changes in proportion to time.

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This study aims at clarifying the process by which 7th grade students develop their empirical conceptions into theoretical ones. In particular, this paper explores how they develop their geometric conceptions by analyzing two kinds of classroom teaching practices concerning geometric construction. In the first classroom teaching practice study, it is suggested that students can interactionally develop their geometric concept of a kite as well as their way of constructing it. Initially, students conceived a kite as its shape and its collection of properties. They then began to use it as a tool for their geometric constructions, and gradually started to understand the relationship between the procedure of construction and the properties of the geometric figure. Finally, they could not only use the tool explicitly and mentally, but also become aware of the relationships between the properties of the kite itself. That is, their conception of the geometric figure sustained their construction activity and at the same time the activity promoted their understanding of the properties of the geometric figure. However, although we also intended in our teaching plan that students could eventually prove their construction procedure, they were unable to do so. As a result of this, we observed classroom lessons at the university-attached school and analyzed some factors for students to succeed in finding this proof. The results and implications for teaching about geometric construction are as follows. Firstly, students naturally use geometric figures as their cognitive tools in construction. Therefore we think that in the classroom lessons teachers should encourage students to become conscious of and reflect on their own cognitive activities. Secondly, in order to succeed in justifying the construction procedure, students need to not only differentiate it from the product, but also to use this procedure as a condition of proof. Thirdly, if we admit the existence of empirical proof, students have the potential to find some proof and justify it by activating their own image schema.

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The aim in this paper is to systematize the theories of history teaching based on social history through typing social history materials for use in secondary schools in the U.S. with the ultimate aim of affecting change in the content of history education. After analysis, I could classify them into two basic types, namely the Topical Approach Types and the Chronological Approach Types. Moreover, the former could be classified into the following three subgroups: teaching social history from the viewpoint of the social activities of ordinary people; teaching social history from the viewpoint of expanding social life space; and teaching social history including the contents of both social activities and social life space. The latter type could also be classified into three subgroups: teaching national political history based on a social history approach; teaching comprehensive national history based on a social history approach; and teaching comprehensive world-cultural zone history based on a social history approach. Thus far, theories of history teaching based on social history have gradually developed from the Topical Approach to the Chronological Approach, but no unified paradigm has emerged.

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This study focuses on clarifying the fundamental principles of history lesson planning based on Social Constructivist theory. By analyzing the American High School History Curriculum "History Alive!", this study was able to isolate three elements to be defined as follows: (1) Interpreting historical meaning through materials (historical materials) and experience. (2) Improvement of knowledge through the cooperative examination of historical interpretation. (3) Improvement of historical understanding by the application and reconstruction of prior knowledge. By applying these basic fundamentals, it is suggested that students can improve their historical understanding, broadening their point of view as a by-product of their expanding history-related semantic network.

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The aim of this research is to investigate the relationship between logical thinking ability and learning mathematics. The purpose of this paper is to make clear the characteristics of university students' logical thinking ability. As a result of the analysis, the following were discovered. 1) The scores of the students who are majoring in mathematics are significantly higher than those of students who are not. 2) The scores of the third grade students who are majoring in mathematics are significantly higher than those of the first grade students majoring in mathematics. This isn't the same case among students who aren't majoring in mathematics. As a result, I came to the assumption that students can enhance their logical thinking ability by learning mathematics at university.

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As a method of teaching when utilizing the history of mathematics for mathematics education, I proposed the 'history-preceding method' and the 'skill preceding method', and investigated the difference between the two methods in the effects produced by introducing the history of mathematics into the study of calculus. The 'history-preceding method' utilizes the history of mathematics from the beginning of the study of calculus and puts emphasis on the process of developing mathematical thinking. On the other hand, the 'skill-preceding method' teaches how to solve problems first, and then utilizes the history of mathematics in order to lead students to better understanding. The result was that the 'history-preceding method' is effective only in the emotional domain of recognizing the merit of mathematical thinking, while the 'skill-preceding method' is effective not only in the emotional domain but also as regards the awareness of knowledge and skill.

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For a general studies course, the core focus of which was "clothing" as presented in elementary school home economics, we developed classes designed to foster the practical ability and desire to look at world clothing, and to stimulate interest in children's clothing. We previously reported on the overall class structure and learning process. In this report, we will present an analysis and evaluation of the course focusing on how the class was received by the children, as determined by questionnaires and descriptions from the children before and after the course. Finding include: 1. 95% of the children reported the class was "fun." 2. In classes that incorporated primary topics, 60% of the children reported that they contributed to a topic. 3. The children participated most enthusiastically in the secondary activity presented in the form, "Let's make clothes from a single piece of cloth" 4. After the course, a higher percentage of children reported interest in foreign countries and the link between clothes and the world. Attitudes toward clothing changed. 5. We discovered that a single topic in general studies can multiply and lead into many related topics. Thus, we obtained results beyond our objectives. From the above, we confirmed that our class materials, class content, and teaching method were positively accepted by the children, and we achieved satisfactory results in terms of the learning objectives.

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