PROCEEDINGS OF THE 16TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 2)
2013
Denver, Colorado
Pre-Service Secondary Teachers’ Meanings for Fractions and Division
Page: 2-56
In this study, seventeen math education majors completed a test on fractions and quotient. From this group, one above-average calculus student was selected to participate in a six-lesson teaching experiment. The major question investigated was “what constrains and affords the development of the productive meanings for division and fractions articulated by Thompson and Saldanha (2003)?” The student’s thinking was described using Steffe and Olive’s (2010) models of fractional knowledge. The report focuses on the student’s part-whole meaning for fractions and her difficulty assimilating instruction on partitive meanings for quotient. Her part-whole meaning for fractions led to the resilient belief that any partition of a length of size m must result in m, unit size pieces. It was non-trivial to develop the basic meanings underlying the concept of rate of change, even with a future math teacher who passed calculus.