The secret life of mathematical problems through the lens of research-practice partnerships

In this plenary talk, I address two longstanding challenges for mathematical problem solving as a teaching and learning practice for all: (1) the many potential (and divergent) roles of a teacher in problem-solving instruction; (2) the vast diversity in intentions, goals, and meanings of tasks intended to be problems in different classrooms. In relation to the first challenge, I develop a metaphor of a problem as a living (discursive) creature whose “live” depends on who and how attends to it. This metaphor posits teachers as “revivers” of problems in their classes. In relation to the second challenge, I show how mathematical tasks are transformed in a chain of intended, planned, enacted, and experienced activity, and argue for research-practice partnerships as a useful perspective for making problem-solving instruction feasible.