著者

杉野本 勇気

出版者

全国数学教育学会

雑誌

数学教育学研究 : 全国数学教育学会誌 (ISSN:13412620)

巻号頁・発行日

vol.17, no.1, pp.53-59, 2011

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Recently, the lesson plan from a constructivist perspective is central problem of mathematics education. Therefore teachers must have belief from constructivist perspective in mathematical teaching. In this paper I consider the impact of mathematics teacher's view of mathematics on practice. View of mathematics as conception of mathematics has been brought to light by Dossey (1992). Teachers need to take Aristotle's, and Fallibilist's views of mathematics. We can assume the hypothetical teaching trajectory for the way to consider the impact of mathematics teacher's view of mathematics on practice. It is formed the basis for Simon's hypothetical learning trajectory, and thought of the hypotheses about the teacher's prediction as to the path by which learning might proceed. The hypothetical teaching trajectory is also made up of three components: teacher's supposition about the learning goal, the learning activities, and the learning process. In this paper, while considering the factor of mathematics teacher's view of mathematics on practice, I constructed a framework of teacher's belief System based on the View of Mathematics for the hypotheses of these components.

著者

岩崎 秀樹 杉野本 勇気 大滝 孝治 岩知道 秀樹

出版者

全国数学教育学会

雑誌

数学教育学研究 : 全国数学教育学会誌 (ISSN:13412620)

巻号頁・発行日

vol.23, no.2, pp.1-13, 2017-07-31 (Released:2019-09-09)

参考文献数

36

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This paper simply aims at development of teaching materials on mathematical proof based upon the theory of substantial learning environment proposed by Wittmann.  We think proof attitude and proving skills will become a core for new literacy in future days after modern times.  Mathematics education has to play a big role to realize it. So far mathematics education research, however, paid much attention to the entrance of school mathematics, i.e. arithmetic teaching in Japan.  She missed the exit of school mathematics, especially high school mathematics.  In other words the issue has not been problematized academically on secondary mathematics throughout six years although almost all of students go up to senior high school after graduation of compulsory junior level.  Oncoming mathematics education research, therefore, should focus on the exit of school mathematics from the various angles as well as the entrance.   On the other hand, senior high school mathematics still seems to be a cluster of teaching materials or collection of new instructional resources.  They are not always examined and surveyed carefully and academically.  They need to be scrutinized another angle besides mathematics because mathematics in senior high school stands at the exit of whole school mathematics.  That is to say institutional angle, cultural angle, and societal angle are inevitable.  Many students more than half launch out society with relevant citizenship after graduation of senior high school.  Moreover they must engage in lifelong learning and highly advanced information society whether they like it or not.   In this paper, “Sylvester’s  partition theorem” is chosen as a throughout proof teaching material.  She will be prepared and considered in terms of substantial learning environments as an authentic teaching material first.  She will be analyzed by means of the core of mathematics education as a scientific discipline proposed by Wittmann second.  As consequences, some methodological techniques for developing instructional materials are identified.  The techniques imply not only developmental methods in mathematics education research, but also new direction of training-system for mathematics teachers in educational practice.