RUME 26
2024
Omaha, Nebraska
Guided Reinvention of the Definitions of Reducibles and Irreducibles
Page: 310
Informed by Realistic Mathematics Education, we designed a hypothetical learning trajectory on graduate students’ guided reinvention of reducible and irreducible elements in unique factor- ization domains. We created experientially real tasks for use in a teaching experiment, in which students used algebra tiles as an emergent model of factoring integers and quadratics in ℤ[#]. In students’ mathematical activity, this became a model for abstracting the shared structure of (ir)reducible elements in ℤ and ℤ[#], which students used as they formally defined (ir)reducibles.