This paper reports a study of preservice teachers who investigated their own teaching during a field-based component of a mathematics education methods course. The course was designed to engage the preservice teachers in both mathematical and pedagogical inquiry. Analysis of video recordings of course discussions, audiotaped interviews with preservice teachers, audiotaped discussions of instructor's planning meetings, and copies of the instructor's and preservice teachers' journals identified two critical incidents that depict students' resistance to the course directions. Analysis of these critical incidents suggests that prospective teachers' interactions with their students can become the mirror through which we can investigate their interactions with us, as teacher educators, and with our course activities. In this way we might reframe the problem of resistance to one of listening—listening to the students, to each other, and to ourselves.

Place-based education has traditionally had a limited focus on mathematics, and critical mathematics education often lacks explicit attention to place and space. We explore integrating theories of place, spatial justice, and critical mathematics education. To begin, we consider various frameworks of place—including Indigenous, urban, and critical perspectives—to situate a discussion on how place acts as a shaping force on social relations like race, gender, and sexuality, and, conversely, how social relations shape place. We include mathematics as a category of social relations in that guiding framework. We next summarize and build on various notions of place and spatial justice, toward their integration with critical mathematics education. In so doing, we present teaching mathematics for spatial justice, or using mathematics 1) to identify power relations in and through place and 2) to transform the world by re-imagining and remaking place. We sidestep a false urban-rural divide and instead, illustrate the potential of teaching mathematics for spatial justice using rich examples organized around four thematic categories: geographies of opportunity, mapping, human mobility, and land relations and obligations.