Context: Mathematical problem solving is considered important in learning and teaching mathematics. In a recent study, Proulx and Maheux presented mathematical problem solving as a continuous dialectical process of small problem posing and solving instances in which the problem is continuously transformed, which they call problematizing. This problematizing conceptualization questions many current assumptions about students’ problem solving, for example, the use of heuristics and strategies. Problem: We address two aspects of this conceptualization: (a) how does problematizing evolve over time, and (b) how do the students’ problematizations interact? Method: In this study, we apply and further develop Proulx and Maheux’s enactivist perspective on problem solving. We answer our questions by applying micro-analysis to the mathematical problematizing of a group of students and, using Ingold’s pathways and meshwork as our framework, illustrate the lived practice of a group of students engaged in mathematical problem solving. Results: Our analysis illustrates how mathematical problematizing can be viewed as a complex, enmeshed and wayfaring journey, rather than a step-by-step process: in this enactive journey, smaller problems co-emerge from students’ interactions with one another and their environment. Implications: This research moves the focus on students’ mathematical problem solving to their actions, rather than strategies or direct links from problems to solutions, and provides a way to investigate, observe and value the lived practice of students’ mathematical problem solving. Constructivist content: Our work further strengthens the understanding of mathematical activities from an enactivist perspective where mathematical knowledge emerges from interaction between individual and environment.

Key words: Problem solving, problematizing, journey, heuristics, emergent, enactive, movement, rhythm, traces, artefacts.

Abstract: We briefly discuss how far we take metaphors for learning or doing mathematics while challenging the descriptive-prescriptive paradigm in favor of a larger view of research and language (use) emphasizing the evocative and provocative texture of our work and Ingold’s writing. In so doing, we also bring forth an ethical dimension to research writing, which may help situate what we did not present, discuss and suggest in the target article: missing fragments, students’ backgrounds, teachers’ potential roles and direct implications or recommendations, for example. Finally, we also offer a reflection on how our study contributes to research through both its similarities to and distinctions from other conceptualisations. Jean-François Maheux & Robyn Gandell