Sakuragaoka Municipal Elementary School, Setagaya Ward, Tokyo, Japan

Abstract: This study aims to develop an innovative instructional design model that integrates problem-solving and problem-posing approaches in elementary mathematics education, and to verify its effects through practical application at a public elementary school in Tokyo. Drawing on seven years of experience as a classroom mathematics teacher, the researcher recognized the challenge that traditional teacher-centered instruction often fails to foster students' independent thinking and mathematical expression abilities. Building upon Japan's long-standing tradition of structured problem-solving and the increasingly recognized value of problem-posing activities, this study proposes a "dual-cycle" instructional design model that alternates between problem-solving cycles and problem-posing cycles to deepen students' mathematical understanding. The research method employed action research, conducted over a three-month period from April to June 2025 with two fifth-grade classes at Sakuragaoka Municipal Elementary School—one experimental class (32 students) and one control class (31 students)—focusing on the "Area of Plane Figures" unit. The results showed that students in the experimental group demonstrated statistically significant improvements in both mathematical achievement (p<.05) and mathematical thinking and expression skills compared to the control group. Particularly noteworthy was the finding that students' ability to formulate mathematical problems independently increased by 46%, and their ability to explain their solution methods using mathematical language improved by 38%. Qualitative analysis of classroom observations and student work samples revealed that the dual-cycle model effectively stimulated students' curiosity and encouraged them to think more deeply about mathematical relationships. The significance of this study lies in proposing a practical, classroom-ready instructional design model that aligns with the objectives of Japan's new Course of Study, specifically the development of "thinking skills, judgment, and expression skills," while remaining fully implementable by regular classroom teachers without specialized equipment or additional resources.

Keywords: problem-solving, problem-posing, instructional design innovation, elementary mathematics education, classroom teacher, thinking skills, Japanese Course of Study