An Exploratory Study of Japanese and American Students' Problem-solving Behaviors

这项合作努力是1986年7月在美日数学问题解决研讨会上发起的讨论的直接结果。在那次会议上，确定和讨论了未来合作研究的几个方向，并对开展与数学情境建模和非常规数学问题解决有关的跨文化合作研究表示了一致的热情和支持。该项目由来自美国的五名研究人员和来自日本的至少五名研究人员共同努力，研究日本和美国学生解决非常规问题的教学和学习。在合作的这个初始阶段，具体的工作重点将是非常规的、“开放式”的数学问题。拟议的工作将直接与Nobuhiko Nohda教授和他的同事在日本研究和使用的“开放方法”教学方法有关。这种教学方法（Nohda, 1983,1986,1987）侧重于通过使用开放式数学问题使学生参与数学探究。通过他们对问题的个人研究，通过课堂上对各种方法和解决方案的讨论，通常在整个课堂期间或更长时间内，学生们培养了对所涉及数学的深度和复杂性的欣赏，以及对分析和解决问题的各种策略的欣赏。这种方法已经在日本的一些学校进行了实验。

This collaborative effort is a direct result of discussions initiated at the U.S.-Japan Seminar on Mathematical Problem Solving in July 1986. At that conference, several directions for future collaborative research were identified and discussed, and there was unanimous enthusiasm and support for undertaking cross-cultural collaborative research related to the modeling of mathematical situations and the solution of nonroutine mathematical problems. The project represents a collaborative effort by five researchers from United States, and at least five researchers from Japan to study the teaching and learning of nonroutine problems solving by Japanese and American students. The specific focus of the work in this initial phase of the collaboration will be nonroutine, "open-ended" mathematics problems. The proposed work would relate directly to the "open approach" teaching methodology studied and used by Prof. Nobuhiko Nohda and his colleagues in Japan. This teaching methodology (Nohda, 1983, 1986, 1987) focuses on engaging students in mathematical inquiry through the use of an open-ended mathematics problem. Though their individual work on the problem and through class discussion of various approaches and solutions, often during an entire class period or longer, students develop an appreciation for the depth and complexity of the mathematics involved as well as an appreciation of the various strategies available for its analysis and solution. This approach has been used experimentally in some schools in Japan.