How do we know?: an epistemological journey in the day-to-day, moment-to-moment of researching, teaching and learning in mathematics education




Maheux, Jean-Francois

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In this dissertation, I offer an epistemological journey in the day-to-day, moment-to-moment of mathematics education. Drawing on enaction and cultural historical activity theory, I examine various episodes from research involving children in second and third grade doing geometry with their regular teacher and a research team using tools from the tradition of interaction and conversation analysis. My interest is to go beyond interpreting teachers’ and students’ mathematical activity to explore the question of “How do we know” in mathematics education, including a reflection upon the researcher’s own actions. I want to better understand how the actions of researchers, teachers and students intertwine to co-produce mathematics education in its actual form and, from that angle, articulate some of the aspects by which mathematics education becomes a (more) meaningful undertaking for all of us. In total, I present five studies from a travel journal (first written as book chapters or journal articles) that came to fruition from this journey. The first one looks at how geometrical knowings came into being in a second grade classroom, and articulates the interdependence of abstract, concrete, cultural and bodily mathematical knowings. The second takes a more critical look at the analysis of classroom episodes from video data to produce such “knowledge” about students’ knowing. The third study examines student-teacher communication. It articulates the irreducible, dynamical nature of mathematical knowing through communicative activity that is always knowing-with another and therefore constitutes an ethical relation. The forth study takes yet another look at the role of researchers and that of knowledge production to appreciate how, in collecting data, research can create learning opportunities for both teachers and their students. The final study returns to the first one, and presents a more elaborated understanding of what it means to know geometrically from the students’ perspective. Rethinking knowing through relationality with oneself, others, and the material world, it concludes with a reflection on the ethical responsibility that comes with knowing mathematically. As a whole, the dissertation presents itself like a single (textual) utterance, a “turn taking” in our ongoing conversations about researching, teaching and learning in the field of mathematics education. Running through the studies themselves and the reflections surrounding them, metaphors (such as that of a journey across a landscape of theories, methods, and concrete observations in the day-to-day, moment-to-moment of mathematics education) invite the reader to “walk the walk” of thinking differently about “how we know.” In the last chapter, I call upon the reader to join the conversation by questioning, taking up and accepting, or even rejecting what has been done, hence acknowledging it in/as present, so that the dialogue is furthered.



mathematics, education, research, teaching, learning, epistemology, theory, method