Date on Master's Thesis/Doctoral Dissertation

8-2025

Document Type

Doctoral Dissertation

Degree Name

Ph. D.

Department

Elementary, Middle & Secondary Teacher Education

Degree Program

Curriculum and Instruction, PhD

Committee Chair

McFadden, Justin

Committee Member

Bay-Williams, Jennifer

Committee Member

Tretter, Thomas

Committee Member

Immekus, Jason C.

Author's Keywords

Mathematical thinking; textbook analysis; mathematics curriculum; cognitive demand; instructional materials; mathematics education

Abstract

Mathematical thinking is essential not only for students’ academic achievement but also for their ability to compete in a global workforce (Schoenfeld, 1992; Mullis & Martin, 2017). However, students in the United States continue to lag behind their international peers on assessments that measure mathematical thinking (Mullis et al., 2020; van Davier et al., 2024). These gaps emerge as early as elementary school, where the foundation for future academic success is established (Aunola et al., 2004; Locuniak & Jordan, 2008). Given the importance of mathematical thinking and the persistent disparities in student performance, this study examined how mathematical thinking is developed in fourth-grade mathematics textbooks, focusing specifically on Opportunities for Mathematical Thinking (OMT). The study was guided by four research questions: (1) To what extent are different types of OMT represented in fourth-grade textbooks? (2) How is OMT represented across mathematical content domains? (3) How is OMT represented across different lesson components? (4) How does OMT vary within and between textbooks? A content analysis approach was used to address these questions, incorporating both qualitative coding and statistical analysis, including chi-square and z-tests of proportions (Krippendorff, 2004; Drisko & Maschi, 2016). A total of 3,800 items were coded from two widely used fourth-grade curricula—Illustrative Mathematics (IM) and Zearn. Each item was categorized into one of three OMT types (Knowing, Applying, or Reasoning) and analyzed across two content domains (Number & Operations in Base Ten [NBT] and Number & Operations–Fractions [NF]) and three lesson locations (Practice, Teacher Moves, and Closing). The study yielded three key findings. First, it offers an operationalized definition of OMT grounded in cognitive complexity. Second, the two curricula varied in how they structured OMT: IM distributed items more evenly, while Zearn emphasized lower level Knowing items. Third, the analysis revealed that OMT is shaped by both instructional design and content standards. The final chapter discusses these findings in relation to relevant literature, presents implications, and provides recommendations for future research.

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