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This task structure both engages students in serious, grade-level appropriate mathematical work and allows the teacher to do the intentional and purposeful work of building a collaborative classroom culture. We highlight possibilities for adapting this task structure to teach different mathematics content across grade levels 3–5.

We consider how prospective elementary teachers think about multiple mathematical knowledge bases as they consider adapting existing mathematics curriculum materials to meet the needs of culturally, linguistically, and socioeconomically diverse students. Multiple mathematical knowledge bases include both children’s mathematical thinking and the cultural-, home-, and community-based funds of knowledge that children inevitably bring into the classroom. We explored how prospective elementary teachers attended to multiple mathematical knowledge bases as they used a lesson analysis tool, the Curriculum Spaces Table, to evaluate existing curriculum materials and identify spaces for adapting these curriculum materials to more efficiently meet the needs of all students. Our analysis examined 47 written reflections on the analysis of and adaptations for a Grade 3 lesson. Findings showed that prospective teachers paid considerable attention to children’s mathematical thinking and gave some attention to funds of knowledge, but they considered these knowledge bases largely in isolation of each other. Attention to integrating children’s mathematical thinking with funds of knowledge was rare. Nonetheless, prospective teachers overwhelmingly found the Curriculum Spaces Table useful for analyzing an existing lesson and identifying spaces for adaptations to more effectively build on children’s mathematical knowledge bases. Thus, we argue that a lesson analysis tool that draws attention to multiple mathematical knowledge bases offers a promising start for prospective elementary teachers’ development of pedagogical practices that integrate children’s mathematical thinking with diverse cultural-, home-, and community-based funds of knowledge.

The quality of mathematics problems has been a concern to mathematics educators. There are many frameworks to support teachers’ posing problems to students, however, these frameworks have tended to focus primarily on their cognitive demand (e.g., Smith & Stein, 1998 ). Rarely are mathematics problems considered in relation to their social and participation dimensions, namely whether or not they are designed to support students’ collaborative problem solving ( Featherstone et al., 2011 ; Horn, 2012 ; Lotan, 2003 ). In this article the authors explore secondary prospective teachers’ (PTs) analysis and adaptations of mathematics problems after they are introduced to frameworks that foreground collaboration and equity in the teaching and learning of mathematics. Implications are offered to future teachers of mathematics and mathematics education researchers.