Date of Award
Doctor of Philosophy (PhD)
Department of Mathematics
Craig J. Cullen
The Common Core content standards and standards for mathematical practice (SMP) have introduced an unprecedented opportunity in U.S. history to consider the implications of a national scale standards reform effort that provides teachers the individualistic opportunity to select instructional practices aimed at achieving the standards. The content standards and SMP specifically lay out what students should be able to do by the end of each grade but do not describe how teachers should support students through instructional practices in order to achieve these goals (CCSSI, “Myths About Implementation,” para. 1). Seemingly in contradiction to the Common Core State Standards Initiative’s proclamation that instructional practices should be left to individuals and schools, Cobb and Jackson (2011) asserted that large-scale mathematics reform efforts are likely to be successful if “a detailed vision of high-quality mathematics instruction specifies concrete instructional practices that have the potential to lead to the attainment of learning goals” (p. 13). In the absence of a national-scale vision of high-quality mathematics instruction to accompany the Common Core Standards for Mathematics (CCSSM), the purpose of this study was to describe how teachers reasoned about specifying instructional practices aimed at addressing the goals of the CCSSM.
Four case study teachers were selected from an initial interview as to categorically represent the visions for mathematics instruction (V4MI) described by 10 secondary mathematics teachers from one mathematics department in one high school located in the Midwestern region of the United States within an urban city. The four case study teachers participated in a pre-lesson and post-lesson interview surrounding a lesson of their choice. In the initial, pre-lesson, and post-lesson interview, teachers reasoned about ideal, planned, and instructional practices. Using the method of constant comparative analysis, I found emerging themes in teachers’ reasoning and described them as categories of reasoning about instructional practices. Themes emerged among the four case study teachers in the following forms of reasoning: prior knowledge, building conceptual knowledge, external sources of influence, establishing classroom culture, cultivating general learner qualities, and cultivating mathematics learner practices. During which interviews these categories of reasoning emerged (i.e., initial, pre-lesson, post-lesson interviews), the type of language case study teachers used when discussing each category of reasoning (i.e., teacher-centered or student-centered), the alignment or misalignment of the category of reasoning with teachers’ V4MIs, and teachers explicit reasoning about V4MIs and CCSSM are explored. Findings suggest that teachers and those leading large-scale Common Core mathematics reform (e.g., administration, state-level lawmakers) should explore the external sources of influence that teachers adhere to when specifying instructional practices. Furthermore, teachers should be provided opportunities to build explicit connections between their V4MIs, instructional practices, and the goals of the CCSSM.
Clarkson, Kelsey A., "Visions for Mathematics Instruction, Instructional Practices, and Common Core: Individuality in Large-Scale Reform" (2020). Theses and Dissertations. 1209.