When it’s on zero, the lines become parallel: Preservice elementary teachers’ diagrammatic encounters with division by zero

摘要: Abstract We investigated preservice elementary teachers’ diagrammatic encounters with division by zero. Pairs of teachers explored a transformable diagram where the locations points on x and y axes could be continuously varied. Quotients were defined in as intersection line y-axis. For zero divisors, quotient was parallel to y-axis, there no point intersection. report our analysis two episodes transformability spurred In each episode, pairs used repeated movements explore conditions under which would become Our shows how these movement-based material experiments gave rise different conceptions discuss diagrams create new contexts for exploring arithmetic concepts.