Date of Award

2020

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Graduate Group

Education

First Advisor

Janine T. Remillard

Abstract

The Common Core State Standards for Mathematics (CCSSM) set ambitious goals for conceptual understanding through the content standards and developing mathematical habits of mind through the performance standards. Textbooks often serve as a mediator between standards and classroom instruction, as they expand a few short statements into a year of lessons, tasks, and educative supports that teachers use as a primary resource for both making sense of the standards and bringing them to life with students. Because of this critical role, understanding how curriculum developers have interpreted standards contextually and enacted those interpretations through developing textbook structures and content. I explore the concept of alignment between standards and textbooks and argue that many approaches to evaluating alignment are not sufficiently nuanced. Instead, I advocate for an approach that attends to both the holistic intentions and the details of the standards. My intention is to shift alignment conversations from asking if or how much a textbook is aligned to asking how and in what ways it is aligned.

I analyzed how the CCSSM content and practice standards were interpreted and enacted in multiplication lessons across eight curriculum programs for grades 3-5. In each analysis, I addressed both structural features of the standards and structural features of the textbooks that seemed to support or inhibit full enactment of the standards. I identified several structural features of standards that seemed to impact both the depth and frequency at which they were addressed across the curriculum programs. Addressing textbooks, I found that the content standards have largely been successful in designating the topics covered and increasing conceptual understanding, which is an important achievement for mathematics education in the United States. However, I also found that only four of the eight programs meaningfully addressed the practice standards and more rigorous application of the content standards due to several structural features of lesson design. Based on these findings and additional research, I identify three instructional models that have emerged in textbooks in response to the CCSSM.

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