Graduation Term

2021

Degree Name

Doctor of Philosophy (PhD)

Department

Department of Mathematics

Committee Chair

Edward Mooney

Abstract

Current recommendations for school mathematics include teaching algebra as a K–12 content stranding beginning in the elementary-school grades. The focus of this study was on preservice elementary mathematics teachers’ knowledge of algebra content in the intended curriculum for K–8 mathematics. In the Common Core State Standards for Mathematics (CCSSM), great emphasis is placed on numerical structure, and the usefulness of number properties in algebraic manipulation. In this study, preservice teachers’ knowledge of structural properties was explored. The purpose of this study was to investigate the knowledge that preservice elementary teachers have about number properties and whether they could apply these properties in meaningful ways. Preservice elementary teachers (PETs) at a community college in the U.S. Mid-Atlantic were sought to participate in this study. Participants were sought from three courses: MT1, MT2, and MT3. The teaching intervention was situated in the MT1 course because part of the course’s learning outcomes included fostering numerical and algebraic reasoning. Participating PETs in MT2 and MT3 received no special instruction on properties of real numbers because that content was supposed to have been taught and learned in the MT1 course. Both the quantitative and qualitative analyses revealed that the participating PETs did not demonstrate strong knowledge of properties. The analyses revealed that there was not an educationally significant difference between MT1 and MT2/MT3 participants’ knowledge of number of properties. The analyses also revealed that the instructional intervention emphasizing properties resulted in modest gains in MT1 PETs’ knowledge of properties but the gains were not educationally significant. The findings revealed the challenges of preparing teachers with well-developed structure sense and strong understanding of properties—knowledge that is essential in helping young learners gain relational understandings of early algebra.

Access Type

Dissertation-Open Access

DOI

https://doi.org/10.30707/ETD2021.20210719070603180440.51

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