A Case Study of the Mathematical Learning of Two Teachers Acquiring Mathematical Knowledge for Teaching

Authors

David R. Hartman, University of Nebraska-LincolnFollow

Date of this Version

12-1-2010

Comments

A DISSERTATION Presented to the Faculty of The Graduate College at the University of Nebraska In Partial Fulfillment of Requirements For the Degree of Doctor of Philosophy, Major: Educational Studies, Under the Supervision of Professor Ruth M. Heaton. Lincoln, Nebraska: December, 2010
Copyright 2010 David R. Hartman

Abstract

This study offers an analysis of the learning of practicing teachers as they acquire a deeper knowledge of mathematics. While some professional developers have shifted part of their focus to helping practicing teachers acquire a deeper knowledge of mathematics (e.g., Stein & Silver, 1996), the results from studies often describe what translates from the professional development experience into classroom practice and measureable gains in student achievement (e.g., Desimone et al., 2002). Studies showing improvements in pedagogy and student learning are important. However, studying what teachers are learning and how they learn is important in developing understanding of the content and process of teachers’ learning.

This case study describes the mathematical learning of two middle level mathematics teachers while participating in a National Science Foundation-funded math professional development institute based on recommendations of the Conference Board of the Mathematical Sciences (CBMS) (2001). The overarching question guiding this research is: How do teachers deepen their understanding of the mathematics content they teach? The analysis is guided, in part, by mathematical habits of mind (e.g., Cuoco et al., 1996); or ways teachers engage in mathematical practices to strengthen their understanding of mathematical content and communication to others.

Data collected from two teachers to study their learning include: teachers’ written coursework and reflections, observations of teachers’ work and interactions solving problems, and interviews and classroom observations. Qualitative data analysis (Stake, 1995) indicates three findings. First, both teachers embrace collaboration as a tool to learn mathematics. Second, the teachers’ habits of mathematical learning become evident in practices they deploy while learning mathematics. Both teachers utilize making connections, using representations, and testing cases to learn mathematics. Simultaneously, the teachers’ learning looks different from each other: one displays a persistent nature in solving problems while the other consistently looks for ways to link mathematical learning to teaching. Furthermore, Both teachers’ written work indicates a deepening understanding of mathematical ideas (CBMS, 2001) and a growing ability to communicate mathematics to others.