Networking two theoretical frames of variation in a problem-solving-based mathematics instruction task design

Abstract Research on mathematical problem-solving has provided valuable insights, but has faced criticism for its limited impact on real classroom practices. This paper identifies two key issues contributing to this disconnect: (1) debate over whether problem-solving is intended as a tool or a goal of mathematics instruction and (2) teachers' pedagogical challenges in teaching mathematics through problem-solving. We discuss how two theories of variation are networked to underpin the problem-solving-based mathematics instruction task design for tackling these issues. The analysis of data, which includes sequence of tasks designed by a study group, video-recorded lesson observations, audio-recorded post-lesson meetings, and student written solutions to tasks, suggests that the coordination between these two theories of variation, combined with a classroom design study approach, can provide a valuable perspective for designing and implementing effective problem-solving-based mathematics instruction.