Folding back, thickening and mathematical met-befores

• Explores the place of prior knowledge in the building of connected mathematical understandings.
• Considers the place of problematic met-befores and how these might be overcome.
• Elaborates folding back as a pedagogical tool.

The study reported here explores how teachers can encourage students to build mathematical understandings that are connected to their prior experiences and knowledge. We illustrate this through considering data extracts taken from the classroom of one high school teacher, as he works with a Grade 12 class on the concept of vectors in three-dimensional space. Drawing on elements of the Pirie-Kieren theory for the dynamical growth of mathematical understanding we consider how the deliberate and purposeful teaching action of encouraging folding back can offer a way for students to engage with problematic mathematical met-befores and so promote understandings that are both more general in nature and conceptually connected.