14. Rethinking mathematics education

I am now concluding my fiftieth year as a professional mathematics educator. That benchmark provides an opportunity to reflect on the emergence of ideas and understandings over the past five decades, and the persistence of challenges that the field continues to face. To quote from the opening page of A Tale of Two Cities, “it was the best of times, it was the worst of times, it was the age of wisdom, it was the age of foolishness, it was the epoch of belief, it was the epoch of incredulity, it was the season of light, it was the season of darkness, it was the spring of hope, it was the winter of despair.” On the one hand, our intellectual advances have been extraordinary. We understand thinking, teaching, and learning in ways that transcend previous understandings. In this chapter, we take a chronological tour through such discoveries—the nature of problem solving, of teaching, of powerful learning environments. On the other hand, both social progress and institutional progress have been hard to come by. Schools and classrooms reflect the structural and racial ills of American society; mathematics instruction, while potentially meaningful and useful in people’s lives, has little to do with the kinds of sense-making it could support. If anything, school mathematics’ distance from meaningful issues in people’s lives serves to reify current structures rather than to problematize and challenge them. The chapter concludes with a proposal to address this state of affairs.