13th International Congress on Mathematical Education Hamburg, 24-31 July 2016 1 - 1 SETTING ASIDE: HOW TEACHERS CAN SUPPORT STUDENTS TO BUILD ON PRIOR KNOWLEDGE Amanda Allan Tina Rapke Lyndon Martin York University York University York University How can understanding grow when students encounter ideas that are inconsistent with their prior knowledge? We draw upon the Pirie-Kieren Theory’s construct of folding back (Pirie & Kieren, 1994) and elaborate on it to describe how, when building on existing understandings for a mathematical concept, teachers may need to encourage students to ‘set aside’ specific, context- limited ideas in order to build a more generalizable understanding. Folding back offers a way to characterise how learners can build understanding through returning to and ‘thickening’ existing knowledge for a concept. We theorize ‘setting aside’ as a specific instance of thickening, and suggest that it can be seen as a process of reconstructing and reorganizing of context-dependent knowings. To locate, develop, and illustrate ‘setting aside’ within teaching, we draw on three data sets from different levels, all involving teachers who had experience with the Pirie-Kieren construct of folding back. We propose that ‘setting aside’ is a cognitive act that can be deliberately encouraged by teachers and, as such, is of interest to both mathematics educators and those who train them. INTRODUCTION The NCTM ‘Learning Principle’ (NCTM, 2000) states that “students must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge” (p. 20). However, a review of the literature indicates a lack of examples of what this might look like in classrooms, and which characteristics might describe this process. There is little documentation of the small nuances that are observed when teachers support students to build on prior knowledge and experience. To encourage teachers to implement the NCTM learning principle, it is imperative that we empirically study classroom data and develop defining features to describe and identify the process of how teachers encourage students to build on prior knowledge. To aid in this endeavor, we introduce the notion of ‘setting aside,’ which we ground in the Pirie- Keiren Theory’s construct of folding back (Pirie & Kieren, 1994). We propose that teachers can support students to build thicker understanding by guiding students to consider how new situations might require them to question their prior understandings, ultimately ‘setting aside’ some ideas that are context-limited, and building on other ideas that are more generalizable and have potential in the students’ current situation/mathematical problem. Here, we draw upon three data sets with the common element that they all involved classroom teachers who had experience (through professional development or graduate work) with the theoretical notion of folding back. When these teachers drew on elements of folding back, rather than simply reminding students of prior knowings, we observed cases of teachers exploring what would be problematic about these knowings in a new context. We encountered teachers guiding students to consider how new