Examining the Specialized Math Content Knowledge of Elementary Teachers in the Age of the Common Core
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University of Massachusetts Amherst ScholarWorks@UMass Amherst Doctoral Dissertations Dissertations and Theses July 2020 Examining the Specialized Math Content Knowledge of Elementary Teachers in the Age of the Common Core Stephanie Purington University of Massachusetts Amherst Follow this and additional works at: https://scholarworks.umass.edu/dissertations_2 Part of the Elementary Education and Teaching Commons Recommended Citation Purington, Stephanie, "Examining the Specialized Math Content Knowledge of Elementary Teachers in the Age of the Common Core" (2020). Doctoral Dissertations. 1917. https://doi.org/10.7275/17206750 https://scholarworks.umass.edu/dissertations_2/1917 This Open Access Dissertation is brought to you for free and open access by the Dissertations and Theses at ScholarWorks@UMass Amherst. It has been accepted for inclusion in Doctoral Dissertations by an authorized administrator of ScholarWorks@UMass Amherst. For more information, please contact [email protected]. University of Massachusetts Amherst ScholarWorks@UMass Amherst Doctoral Dissertations Dissertations and Theses Examining the Specialized Math Content Knowledge of Elementary Teachers in the Age of the Common Core Stephanie Purington Follow this and additional works at: https://scholarworks.umass.edu/dissertations_2 Part of the Elementary Education and Teaching Commons Examining the Specialized Math Content Knowledge of Elementary Teachers in the Age of the Common Core A Dissertation Presented by STEPHANIE B. PURINGTON Submitted to the Graduate School of the University of Massachusetts Amherst in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY May 2020 College of Education Teacher Education and Curriculum Studies © Copyright by Stephanie B. Purington 2020 All Rights Reserved Examining the Specialized Math Content Knowledge of Elementary Teachers in the Age of the Common Core A Dissertation Presented by STEPHANIE B. PURINGTON Approved as to style and content by: ____________________________________ Darrell Earnest, Chair ____________________________________ Elizabeth McEneaney, Member ____________________________________ Michael Hayes, Member __________________________________ Jennifer Randall Associate Dean of Academic Affairs College of Education ACKNOWLEDGMENTS I am very grateful to those who helped me along this journey. Dr. Darrell Earnest guided me through the dissertation process with kindness, while always nudging me to better paths. He also invited me to a graduate student support group that was a lifeline during my years at UMass Amherst. My husband coined the term “group hug” for those regular meetings, as I always came back refreshed and feeling better about life. Dr. Betsy McEneaney was my touchstone through my whole PhD experience, guiding me in my academics, comps research, and allowing me to work on her research. Mike Hayes, whose amazing teaching improves the math identity of so many UMass Amherst students, helped me gain access to a research site and agreed to act as the outside member of my committee. Dr. Martina Nieswandt adopted me when my advisors went on sabbaticals, coached me through research and writing, and introduced me to the iCons program. My fellow students provided immeasurable support, and without them this journey would have been much lonelier. Alicia Gonzalez has been my rock throughout these five years, always willing to listen and to keep me accountable. Chris McGrail and Ally Hunter have rounded out my amazing “squad,” and reminded me to always keep moving “more up, more forward.” Bona Kang had been a great writing buddy and has offered comfort and perspective. Special thanks to my cohort of one, Ryan Ambuter, who arranged writing groups and encouraged a brisk pace. Kristin Tyler and Mike Hanna deserve extra thanks for the many questions they answered, forms they processed, rooms they booked, and freak-outs they calmed. iv This dissertation would have been impossible to complete without the wonderful teachers who agreed to be participants. That they were willing to give of their time so close to the end of the school year was a true gift. Last, but certainly not least, I want to thank my family, Dave, Katy, and Elizabeth, for supporting me and believing in me throughout this process. This work was supported in part by a Graduate School Dissertation Research Grant from the University of Massachusetts Amherst. v ABSTRACT EXAMINING THE SPECIALIZED MATH CONTENT KNOWLEDGE OF ELEMENTARY TEACHERS IN THE AGE OF THE COMMON CORE MAY 2020 STEPHANIE B. PURINGTON, S.B., MASSACHUSETTS INSTITUTE OF TECHNOLOGY M.Ed., UNIVERSITY OF HARTFORD Ph.D., UNIVERSITY OF MASSACHUSETTS AMHERST Directed by: Professor Darrell Earnest Mathematical standards for students have increased with the development of the Common Core State Standards for Mathematics and its accompanying high stakes testing. Teachers need strong conceptual knowledge of the mathematics they teach in order to give students the opportunity to learn that math deeply. An earlier study (Ma, 1999) found that US elementary teachers lack the deep knowledge to teach math conceptually. Given the mathematics standards movements of the last two decades, it is plausible that the knowledge base of teachers has changed. Using the framework of Specialized Content Knowledge (SCK), which is the knowledge required to teach math that extends beyond the knowledge to do math, this study examines the current level of SCK held by practicing elementary teachers. It also examines themes in the explanations they give for the four topics: subtraction with regrouping; multi-digit multiplication; division with fractions; and area, perimeter, and proof. This study used a multiple-case study design and an interview protocol with current elementary teachers (N=18). Analysis of teacher interviews indicates that elementary teacher SCK can vary with the topic being addressed, with all but two of the vi participants falling into different SCK levels across the mathematical content areas. This points to the need for assessments that offer topic-level data so we can determine the support individual teachers need. Most of the current teachers studied have strong Specialized Content Knowledge in areas of whole number calculation, such as subtraction with regrouping and multi-digit multiplication. In those topics they are able to create representations and justify the standard algorithms. In the areas of division with fractions and area, perimeter, and proof, however, Specialized Content Knowledge was frequently much lower, and many of the teachers struggled to create representations or explain the mathematics contained in the algorithms. This indicates a need for teacher education and professional development that extends beyond whole number operations and focuses on conceptual understanding of these challenging topics. vii TABLE OF CONTENTS Page ACKNOWLEDGMENTS ................................................................................................ iiv ABSTRACT ....................................................................................................................... vi LIST OF TABLES ............................................................................................................. xi LIST OF FIGURES .......................................................................................................... xii CHAPTER 1. INTRODUCTION ...........................................................................................................1 1.1 Rationale for the Study ......................................................................................4 1.2 Theoretical Framework ......................................................................................6 1.2.1 Pedagogical Content Knowledge ........................................................6 1.2.2 Mathematical Knowledge for Teaching ..............................................7 1.2.2.1 Developing and Measuring MKT ........................................8 1.2.3 Specialized Content Knowledge .......................................................10 1.2.4 Assessing MKT and SCK .................................................................11 1.3 Overview of Chapters ......................................................................................12 2. LITERATURE REVIEW ..............................................................................................14 2.1 Introduction ......................................................................................................14 2.2 Mathematical Knowledge for Teaching and Specialized Content Knowledge .................................................................................................15 2.2.1 Defining and Measuring MKT and SCK ..........................................16 2.2.1.1 SCK Critiques and Boundaries ..........................................18 2.2.2 Mathematical Knowledge for Teaching and Teaching Quality ........19 2.2.3 MKT and Student Learning ..............................................................21 2.2.4 Efforts to Improve MKT and SCK ...................................................24 2.2.5 MKT in Policy Discussions ..............................................................29 2.3 Specialized Content Knowledge in the Four Mathematical Topic Areas ........36 2.3.1 Subtraction with regrouping .............................................................36 2.3.2 Multi-digit Multiplication .................................................................43 2.3.3 Division