Report of U.S.-Japan Cross-National Research on Students' Problem Solving Behaviors.

In 1986 the United States (U.S.)-Japan Seminar on Mathematical Problem Solving convened to compare the state of problem solving in the classroom and in research in the two countries. The data and results given in this paper are the results of research conducted in the United States in response to the 1986 seminar. The U.S. and Japanese research groups decided to collect problem solving data at the 4th, 6th, 8th, and 11th grade school levels. Problems were collected from a pool of problems submitted by both the United States and Japan. U.S. subjects were from at least two 4th-, 6th-, 8th-, and 11th-grade classes from large rural, small urban, and large urban schools in areas around Carbondale and Champaign/Urbana, Illinois; Pittsburgh, Pennsylvania; Gainesville, Florida; and Athens, Georgia. In addition to the problems, student questionnaires collected data on students' attitudes towards problem solving, their comparison of the problems to textbook problems, and their reactions to the problems. A teacher questionnaire collected information about the schools, teachers' views of their classes, their reactions to the problems, and their perceptions of how students worked on problems. These questionnaires are included in the appendix. Five research reports include the results for each of five problems developed for varying grade levels, as follows: (1) the "Marble Arrangement Problem" for grade 4 (researched by E. Silver, S. Leung, and J. Cai); (2) the "Matchsticks Problem" for U.S. students in grades 4 and 6 (M. Hart and K. Travers); (3) the "Marble Pattern Problem" for U.S. students in grades 6, 8, and 11 (K. Fouche and M. Kantowski); (4) the "Arithmogons Problems" for U.S. students in grades 8 and 11 (J. Becker and A. Owens); and (5) the "Areas of Squares Problem" for U.S. students in grade 11 (J. Wilson). (Contains 39 references, as well as references with chapters.) (MDH)