Since the publication of Brown and Walter’s book, “The Art of Problem Posing,” significant progress has been made in mathematical problem-posing (MPP) research. Their well-known “what if not?” (WIN) strategy has been widely adopted in mathematics education. In this chapter, we examined the impact of Brown and Walter’s work on MPP research, specifically focusing on how teachers and students engage in teaching and learning mathematics through problem posing (PP). We found that their WIN strategy directly influenced studies that explicitly employed it to help posers systematically explore alternatives to the given attributes. It also indirectly influenced studies that adopted the underlying principles of the WIN strategy. Moreover, since the introduction of the WIN strategy, studies that incorporate reflective practices into the PP process appear especially promising. These studies offered participants opportunities to evaluate and reflect on their own PP, which, in turn, enhanced their PP competence and deepened their understanding of mathematical concepts. Lastly, we identified studies that positioned teachers as problem posers alongside their students, underscoring the importance of experiencing PP from both perspectives to design more meaningful PP experiences. Suggestions for future research directions are offered at the end of the chapter.

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Teaching Mathematics Through Problem Posing: Contributions of Brown and Walter’s Book “The Art of Problem Posing” in Problem-Posing Research

  • Jaepil Han,
  • Jinfa Cai

摘要

Since the publication of Brown and Walter’s book, “The Art of Problem Posing,” significant progress has been made in mathematical problem-posing (MPP) research. Their well-known “what if not?” (WIN) strategy has been widely adopted in mathematics education. In this chapter, we examined the impact of Brown and Walter’s work on MPP research, specifically focusing on how teachers and students engage in teaching and learning mathematics through problem posing (PP). We found that their WIN strategy directly influenced studies that explicitly employed it to help posers systematically explore alternatives to the given attributes. It also indirectly influenced studies that adopted the underlying principles of the WIN strategy. Moreover, since the introduction of the WIN strategy, studies that incorporate reflective practices into the PP process appear especially promising. These studies offered participants opportunities to evaluate and reflect on their own PP, which, in turn, enhanced their PP competence and deepened their understanding of mathematical concepts. Lastly, we identified studies that positioned teachers as problem posers alongside their students, underscoring the importance of experiencing PP from both perspectives to design more meaningful PP experiences. Suggestions for future research directions are offered at the end of the chapter.