A Study of Japanese and Australian Students’ Mathematical Values in Problem-Solving

This study focused on only two of the mathematical values proposed by (Bishop, A. J. (1988). Mathematical enculturation: A cultural perspective on mathematics education. Kluwer Academic Publishers.), namely “control and progress”, and provided suggestions on problem-solving practices in mathematics education that can convey these values in a balanced manner based on cultural similarities and differences. To this end, a questionnaire was designed for students studying the same Japanese mathematics curriculum in Japan and Australia. They were presented with a problem-solving situation involving two variables and three solutions with different ideas and were asked to select the most mathematically important idea. This qualitative research results indicated that weekday mathematics education content may strongly influence students’ values. The importance of focusing on the idea (the mechanism of the relationship between two variables) was demonstrated. In addition, solving only one required problem at a time was insufficient to convey progress values in problem-solving. The importance of taking time in practice to examine the merits of the idea, which could be integrated with other as-yet unaddressed problems, was demonstrated.