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Toward the problem-centered classroom: trends in mathematical problem solving in Japan

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Abstract

In this paper, I summarize the influence of mathematical problem solving on mathematics education in Japan. During the 1980–1990s, many studies had been conducted under the title of problem solving, and, therefore, even until now, the curriculum, textbook, evaluation and teaching have been changing. Considering these, it is possible to identify several influences. They include that mathematical problem solving helped to (1) enable the deepening and widening of our knowledge of the students’ processes of thinking and learning mathematics, (2) stimulate our efforts to develop materials and effective ways of organizing lessons with problem solving, and (3) provide a powerful means of assessing students’ thinking and attitude. Before 1980, we had a history of both research and practice, based on the importance of mathematical thinking. This culture of mathematical thinking in Japanese mathematics education is the foundation of these influences.

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Notes

  1. Although problem solving was not in the goal statement, it was mentioned in the instruction manual of the current Course of Study.

  2. As described in “Development of teaching materials and effective lesson organization with problem solving”, in Japan we have the tradition of practice-based research by schoolteachers. Their active involvement in such research activities seems to realize a closer relationship between research and practice. However, Sakitani interviewed five school teachers and pointed out concretely the need of research findings that are useful enough for their teaching practice.

  3. Mathematics as an optional course in the ninth grade was adopted in the Course of Study revised in 1989. In accordance with the students’ characteristics, it was intended that various learning activities should be designed and dealt with while implementing lessons in the course.

  4. “Problem situation learning” was introduced in the Course of Study revised in 1989 at the lower secondary school level. The purpose of “problem situation learning” is to stimulate the students’ spontaneous learning and to foster their views and ways of thinking mathematically by setting up appropriate problem situations by, e.g., integrating the learning content in different areas, relating mathematics to the events in everyday and social life, and by emphasizing activities such as concrete manipulation, observation, or experimentation. Problem situation learning was intended to make more room for cultivating motivation and attitude than the acquisition and consolidation of knowledge and skills. It was planned to be included in the eighth and ninth grades, in a total teaching plan with an appropriate allocation and implementation. In the Course of Study revised in 1998, both problem situation learning and mathematics as the optional course were extended to all grades at the lower secondary school level.

  5. In Japan, we do not have standardized examinations at the national level. Therefore, these four standards have not been developed for the purpose of preparing examination items. Instead, they were developed as a way of writing school reports to parents, etc. At the same time, in the assessment conducted by the Ministry of Education mentioned earlier in this section, the standards have been used. Overall, these educational policies have an influence on classroom practice.

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  1. Department of Education, Utsunomiya University, 350 Mine-machi, Utsunomiya, Tochigi, 321-8505, Japan

    Keiko Hino

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Hino, K. Toward the problem-centered classroom: trends in mathematical problem solving in Japan. ZDM Mathematics Education 39, 503–514 (2007). https://doi.org/10.1007/s11858-007-0052-1

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