The Effects of a Combined Mathematics Content/Methods Course Involving Learning Cycles on Preservice Elementary Teachers' Beliefs about the Nature, Teaching and Learning of Mathematics

Abstract

The purpose of this study was to determine whether a one-semester combined mathematics content/methods course based on Simon's (1994) Learning Cycle framework for the mathematical preparation of preservice elementary teachers was more effective at aligning preservice teachers' beliefs with the philosophy of the Standards documents (NCTM, 1989, 1991, 1995, 2000) and other reform literature than another content/methods course. While the six-cycled Learning Cycles framework has been used in separate content and methods courses (Simon, 1995), it has not been used in a combined content/methods setting. The preservice teachers enrolled in two sections of the course Teaching Math to Children: N-6 were involved in the study with one section investigating the topics measurement, geometry and fractions using the Learning Cycles framework while the other section used a different framework to investigate number concepts and place value; addition and subtraction strategies; multiplication and division strategies; geometry and spatial sense; ratio, proportion, percent, similarity and scale; and probability, counting techniques and statistics. Beliefs about the nature, teaching and learning of mathematics were measured both quantitatively and qualitatively. All participants' beliefs were assessed quantitatively at the beginning and the end of the course using a beliefs instrument with three subscales that measured beliefs about the nature, teaching and learning of mathematics. Five preservice teachers from the Learning Cycles course served as case studies and provided qualitative data through interviews and journal prompts. Analyses of Covariance were calculated for course of enrollment and each of the three beliefs subscales. For beliefs about the nature of mathematics, there was a significant difference between the adjusted post-test scores of the Learning Cycles group and the comparison group favoring the Learning Cycles group. Similar results were found regarding beliefs about the teaching of mathematics. While significant differences were found between the groups with regards to beliefs about the learning of mathematics, the scores on the corresponding subscale changed only slightly. Qualitative analyses confirmed the findings regarding the beliefs about the nature and teaching of mathematics. Differences were also found in the preservice teachers' beliefs about learning mathematics. The case study participants attributed certain characteristics of the course with their changing beliefs. These results indicate that the Learning Cycles course was somewhat successful at aligning preservice teachers' beliefs with those of the reform movement.