The main purposes of the seminar were to examine the present status of school mathematics problem solving; to explore classroom practice and what is known about research; to compare the situations appearing in textbook word problems; and to make plans for cross-cultural research in both countries. A paper from each country was presented during the eight sessions. The session topics were: (1) "The Present States of Problem Solving in the U.S. and Japan"; (2) "Classroom Practice of Problem Solving"; (3) "Comparison of Achievement"; (4) "Comparison of Situations Appearing in Word Problems"; (5) "Typical Word Problem Solving"; (6) "Pattern Finding"; (7) "Non-Routine Problem Solving"; and (8) "Mathematical Modelling." The closing session was an open discussion on the formulation of the seminar and joint cross-cultural research and the formation of a joint study group. A discussion of the findings and proposals is given, and an appendix includes examples of problems in mathematics for the entrance examinations to national and private universities in Japan. (YP)