The road to “good” problems goes through initial responses to stimulating socio-mathematical situations

Abstract

Despite its almost four-decade history, research remains in the early stages of understanding the phenomenon of mathematical problem posing. In particular, the quality of problems created by beginning posers has been recognized as a persistent challenge. In this conceptual paper, I endorse an approach that identifies posing and solving as co-emergent components of steps learners take in a mathematically problematic situation. I further argue that some of the initial responses to the situation may constitute productive ingredients for creating problems that are personally meaningful and interesting to the learners. Drawing on the literature, I offer two principles through which the process of transitioning from initial responses to fully-fledged problems can be supported: making the didactical contract of the problem-posing activity transparent and immersing learners in socio-mathematical settings that are conducive to “good” problems. The approach is illustrated with fragments from a workshop for in-service teachers. The concluding discussion focuses on how the presented approach addresses some common issues in problem posing research.