Proof-based teaching as a basis for understanding why

David Reid (1) , Estela Vallejo Vargas

1 University of Bremen

The importance of proofs as a way to gain understanding has been observed many times. In this paper we show the result of two different experiences with division of natural numbers. The first comes from children in grade 3 who have learned about division and divisibility through what we call proof-based teaching (PBT), and the second comes from students who just finished their school studies and intend to become preservice primary teachers. Our main aim is to point out how different school experiences might lead to different (divergent) ways of gaining insight into the relationship between the divisor and the remainder. We particularly focus on describing some elements we identified in the third graders' instruction that might have allowed them to articulate their own understandings.

Keywords: Arithmetic; elementary school mathematics; number concepts; proof

Domains: Mathematics [math]; Humanities and Social Sciences

David Reid, Estela Vallejo Vargas. Proof-based teaching as a basis for understanding why. CERME 10, Feb 2017, Dublin, Ireland. ⟨hal-01865651⟩