Abstract
Mathematics education community in Japan has continuously and extensively developed 'mathematical thinking' as an educational value. In this paper, the historical review was conducted on mathematical thinking in terms of its evaluation and educational method, textbook change, and research on treatment of diversified mathematical thinking. This approach can provide methodologically an important perspective to grasp, clarify and make relative the values in mathematics education in different times of each culture. Values here mean those attitudes which lay at the back of the intention, judgment, and selection of teaching-learning activity exhibited by primary teachers. As a result of this research, it is learnt that the theme in mathematics education research does reflect values held by the primary mathematics teachers. They, in turn, have held central ideas and value utilizing children's diversified mathematical thinking, letting them subjectively and extensively construct mathematical ideas in the lesson. The major characteristics of Japanese Mathematics education is the open-ended approach, which has been developed as an evaluation and educational method of mathematical thinking. This is available as translated version of 'The Open-Ended Approach: A New Proposal for Teaching Mathematics' (The original version (Shimada) is in Japanese published in 1977).
Highlights
The Teaching Gap: Best Ideas from the World’s (Stigler & Hiebert, 1999) called in earnest for attention to be paid to the lesson study and Mathematics education in Japan, where the lesson study has been developed
The two mentioned initiatives start to raise fundamental questions over what introducing the Mathematics education in a particular country such as Japan means, what is first of all the Mathematics education in Japan like, and what has been valued in Japanese Mathematics education by many people who have been involved in it
The symposium confirmed that the whole clothe of mathematics education in Japan has developed coherently with mathematical thinking being as it were its warp and social and historical needs as its weft (Baba, 2006)
Summary
Atsumi Ueda , Takuya Baba, Taketo Matsuura ematics education to the international community, and one of the typical ones is EARCOME 5 To enable students to understand basic concepts and principles about numbers and quantities, and geometrical figures, and let them develop more advanced mathematical thinking and how to treat it. Speaking, the mathematical idea as philosophical stance in national textbook Jinjo-shogakusanjutsu used since 1935 preceded the mention of mathematical thinking (Ueda, 2006) In this sense, there was a continuing aspiration of Japanese mathematics education community despite of temporal mutation during the WWII. The central ideas had an intention to integrate algebra and geometry in mathematics as one subject and to extract mathematical methods and activities common to both of them They are not exactly the same as mathematical thinking, which has become an objective of primary mathematics education, but it certainly had an influence on its introduction. As we have seen so far, Katagiri and Nakajima have been the most famous researchers that contributed to analytical research on mathematical thinking in Japan
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