Elementary Preservice Teachers' Transitional Conceptions of Partitive Division with Proper-Fraction Divisors. Issue 4 (2nd October 2017) - Hohensee, Charles; Jansen, Amanda
ABSTRACT: An understanding of partitive division is foundational for numerous other mathematics topics, including unit rate, slope, and probability. However, research has shown that learners tend to have a limited understanding of partitive division when the divisor is a proper fraction. To extend research on conceptions of partitive division in this study, we used Moschkovich's (1999) transitional conceptions perspective to examine how conceptions of partitive division evolve. This article reports on preservice teachers' (PSTs) conceptions of partitive division with proper-fraction divisors before and after they explored partitive division in a mathematics content course for elementary teachers ( N = 17). Our analysis of pre- and post-interviews revealed an initial transitional conception and two levels of refinement of their conceptions. Furthermore, we identified two perturbations that PSTs experienced during refinement of their conceptions. By identifying ordered levels of refinement and associated perturbations, this exploratory study extends the transitional conceptions perspective. Furthermore, this study adds new insights into the conceptual complexities that the partitive model for division of fractions presents to PSTs (and to learners in general) and suggests new hypotheses about ways that conceptions of partitive division undergo refinement.