Learning to teach mathematics for understanding
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The purpose of the study was to explore and describe how a preservice elementary teacher, Mary, learned to teach mathematics for understanding. I was interested in the influence of her prior experiences and the formal teacher education program on the development of her conception of teaching mathematics for understanding. I was also interested in the relationship between her conception and her instructional practice. This study was conducted over a period of 3 years and followed Mary through her experiences as a preservice elementary teacher and a beginning teacher. Data were collected in the form of interviews, course assignments, survey instruments, lesson observations, and post-lesson reflections. Data were analyzed within the interpretive paradigm, utilizing methods of content analysis (Merriam, 1998) and phenomenology (Miles & Huberman, 1994). Mary began the teacher education program expecting to be taught how to efficiently and successfully help students memorize the content of the mathematics curriculum. This expectation mirrored her experiences learning mathematics in school. With her prior experiences serving as filters, Mary developed a well-defined conception of teaching mathematics for understanding, which embraced ideas from the writings of Piaget, Bruner, Ausubel, and Vygotsky. Her new ways of thinking about teaching mathematics for understanding reflected her beliefs about mathematics, teaching, and learning. Mary’s classroom practice was analyzed using Hiebert and Carpenter’s (1992) notions of the most effective instruction for promoting mathematical understanding. Mary’s approach to instruction embodied both top-down and bottom-up approaches. In most cases, however, the top-down approach was her principal instructional strategy. The top-down approach that she used closely paralleled Ausubel’s (1968) meaningful reception learning. Her classroom practice reflected, to a large extent, her ideals about teaching mathematics for understanding. The constraints of insufficient instruction time, the exigencies of standardized testing, and the restrictions of a prescribed curriculum were mitigating factors that she identified as having limited her attempts to teach in ways that conformed with her ideals.