The Effects of a Mathematics Course on Candidates’ Beliefs About Learning and Teaching Mathematics

Abstract

This qualitative case study examined a cohort of prospective teachers who completed a university mathematics course during which they were given the opportunity to relearn geometry conceptually and gain experience teaching using contemporary approaches. The course embedded mathematics content using the context of (a) problem solving in university-based seminar classes and (b) a concurrent Grade 7 and 8 teaching placement. Questionnaires, administered at the beginning and end of the semester, and individual interviews were used to obtain data about the prospective teachers’ beliefs about the nature of mathematics and its teaching, and about their pedagogical content knowledge. The pre-course profile was that of a group who held comparable views about mathematics teaching as passive, learning as procedural, and mathematics itself as instrumental. The post-course profile, however, was of a radically different group who once again claimed to hold comparable beliefs about reform-based teaching methods, conceptual learning, and a dynamic view of the utility of mathematics. There are five findings from this study with import for preservice mathematics teacher education. First, learning best occurs within a community. Second, an inquiry-based approach to mathematics provides a rich learning opportunity for students. Third, the instructor, who must have expertise in both mathematics and mathematics pedagogy, must embody reform-based teaching practice. Fourth, to enhance their competence and confidence, teacher candidates must have opportunities to emulate the instructor in a safe environment. Fifth, reflecting critically about course experiences is an essential part of learning for prospective educators.