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From mathematics learner to mathematics teacher : preservice teachers’ growth of understanding of teaching and learning mathematics Borgen, Katharine Louise

Abstract

This study was designed to determine whether using the Pirie-Kieren Dynamical Theory for the Growth of Mathematical Understanding as a model enhanced the growth of preservice teachers’ understanding of teaching and learning mathematics. The study also investigated the efficacy of using the theory as a framework with which to analyze that growth. The study charts the growth of understanding of four preservice, secondary, mathematics teachers during the integrated portion of their teacher education program during which they were introduced to the Pirie-Kieren theory and encouraged to consider it during their reflections on their learning. This portion of the program concentrated on mathematics teaching and learning and was designed to help them develop an understanding and practice of teaching and learning which reflects the present-day conceptions of mathematics and mathematics education as dynamic processes. The Pirie-Kieren Dynamical theory was modeled for the preservice teachers because of its alignment with these views. Video data on the four preservice teachers was collected during the integrated portion of their teacher education program and during their practicum experience. Analysis of this data resulted in a portrait of each of the four individuals. These portraits were then used as the data for the analysis of developing understanding of teaching and learning mathematics. The definitions of the terms used in the Pirie-Kieren theory to describe the different levels of understanding of mathematics were modified, retaining the integrity of the original, to determine whether the theory could be used as an analytic tool to discuss the growth of understanding of teaching and learning mathematics. A modified model that reflected these definitions was also developed. The analysis indicated that the modified definitions provided an effective structure for discussing the growth of understanding of teaching and learning mathematics, both for the preservice teachers and the researcher. It also indicated that, as with the learning of mathematics, the developing understanding of the activity of teaching and of what it means to learn mathematics is an individual experience and is based on one’s own background, or one’s own Primitive Knowing. This development is a dynamic process which involves Folding Back to previously held Images to examine them in light of newly acquired concepts.

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