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.
