RUME 26
2024
Omaha, Nebraska
Reinventing the Definition of Unique Factorization Domains
Page: 853
In this study, we conducted a teaching experiment to test hypothetical learning trajectories of reinventing the definition of the unique factorization domain. Six graduate mathematics students who are preservice and in-service teachers were given experientially real tasks of examining factorizations of integers and quadratics using algebra tiles. The experiment showed that their intuitive and informal reasonings about the reducibility and unique factorization were leveraged to formalize two defining axioms of the unique factorization domain by the emergent model of algebra tiles and by the pedagogical moves of the teacher-researcher who led the sessions.