Date on Master's Thesis/Doctoral Dissertation

12-2018

Document Type

Doctoral Dissertation

Degree Name

Ph. D.

Department

Middle and Secondary Education

Degree Program

Curriculum and Instruction, PhD

Committee Chair

Peters, Susan

Committee Co-Chair (if applicable)

Adelson, Jill

Committee Member

Bay-Williams, Jennifer

Committee Member

McGatha, Maggie

Author's Keywords

teacher knowledge; algebra; mathematics education; KAT; MKT

Abstract

For the past few decades, researchers in mathematics education have been exploring the concept of pedagogical content knowledge (PCK)—or knowledge related to teaching content—and applying it to various areas of mathematics, such as algebra. Research related to teacher knowledge of algebra is critical because researchers (e.g., Hill, Rowan, & Ball, 2005) have found correlations between some types of teacher knowledge and student achievement in mathematics; students from around the world are outperforming U.S. students on international assessments of mathematics, including algebra (Organization for Economic Cooperation and Development, 2014, 2016); and algebra plays an integral role in the K-12 mathematics curriculum in the U.S. (National Council of Teachers of Mathematics, 2000). Given this background, the purpose of this study was to explore the knowledge of algebra for teaching (KAT) by investigating the following research questions: What is the factor structure underlying mathematics teachers’ KAT, as measured by an established instrument? Are KAT constructs measured similarly in preservice and inservice teachers? And if so, are there latent mean differences in the KAT of these two groups? These research questions were addressed using multiple-group confirmatory factor analysis—a form of structural equation modeling—to analyze survey data (n = 1,248) gathered by KAT researchers at Michigan State University. These researchers designed an instrument to measure three types of algebra knowledge, based on their conceptual framework of KAT: knowledge of school algebra; knowledge of advanced mathematics; and mathematics-for-teaching knowledge, which is similar to PCK (Reckase, McCrory, Floden, Ferrini-Mundy, & Senk, 2015). The analyses suggested that KAT may be a unidimensional construct because a one-factor KAT model fit the data better than a two- or three-factor model. Additionally, the analyses suggested that KAT was measured similarly in preservice and inservice teachers, and that preservice teachers had slightly higher KAT than inservice teachers. Following the results, there is a discussion of connections between the findings and the research literature and implications of the findings, such as providing more CK- and PCK-focused professional development opportunities for algebra teachers. The researcher concludes with some recommendations for future research and closing remarks.

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