Exploring the knowledge of algebra for teaching.

University of Louisville ThinkIR: The University of Louisville's Institutional Repository Electronic Theses and Dissertations 12-2018 Exploring the knowledge of algebra for teaching Jonathan David Watkins University of Louisville Follow this and additional works at: https://ir.library.louisville.edu/etd Part of the Science and Mathematics Education Commons Recommended Citation Watkins, Jonathan David, "Exploring the knowledge of algebra for teaching." (2018) Electronic Theses and Dissertations Paper 3084 https://doi.org/10.18297/etd/3084 This Doctoral Dissertation is brought to you for free and open access by ThinkIR: The University of Louisville's Institutional Repository It has been accepted for inclusion in Electronic Theses and Dissertations by an authorized administrator of ThinkIR: The University of Louisville's Institutional Repository This title appears here courtesy of the author, who has retained all other copyrights For more information, please contact thinkir@louisville.edu EXPLORING THE KNOWLEDGE OF ALGEBRA FOR TEACHING By Jonathan David Watkins B.A., Murray State University, 2003 M.A., University of Louisville, 2011 A Dissertation Submitted to the Faculty of the College of Education and Human Development of the University of Louisville in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Curriculum and Instruction Department of Middle and Secondary Education University of Louisville Louisville, Kentucky December 2018 Copyright 2018 by Jonathan David Watkins All rights reserved EXPLORING THE KNOWLEDGE OF ALGEBRA FOR TEACHING By Jonathan David Watkins B.A., Murray State University, 2003 M.A., University of Louisville, 2011 A Dissertation Approved on November 14, 2018 by the following Dissertation Committee: _ Susan Peters, Dissertation Co-Director _ Jill Adelson, Dissertation Co-Director _ Jennifer Bay-Williams _ Maggie McGatha ii DEDICATION This dissertation is dedicated to my wife Diane Adel Watkins who has been a constant source of love and support throughout my graduate studies & to my parents Dr David and Mrs Peggy Watkins who instilled in me a love of learning and encouraged me to follow my dreams iii ACKNOWLEDGMENTS There are a number of people who deserve special recognition for helping me throughout my doctoral studies and dissertation journey First and foremost, I would like to thank Drs Susan Peters and Jill Adelson for serving as my dissertation co-chairs and for being great teachers, mentors, and friends Sue, I will never forget all that you have done for me Thank you for giving me the opportunity to serve as your first graduate research assistant, allowing me to attend and present at several national conferences with you, providing me guidance throughout my program, and spending countless hours reading and revising my work In short, thank you for believing and investing in me Jill, you have also been such an important mentor in my life Thank you for expanding my knowledge of advanced statistical methods (including SEM and HLM), allowing me to serve as one of your teaching assistants, and providing valuable feedback related to my statistical methods and analyses on my dissertation study and other research projects I look forward to our future collaborations I would also like to thank Drs Jenny Bay-Williams and Maggie McGatha for agreeing to serve on my program and dissertation committees In addition to providing meaningful feedback on my dissertation drafts, Jenny and Maggie have been such an encouragement to me during my doctoral studies Thank you both for your kindness and support iv There are also many other faculty members and friends who have encouraged and supported me throughout this journey These faculty members include Drs Bob Ronau, Bill Bush, Karen Karp, Lateefah Id-Deen, Jeff Valentine, Tom Tretter, Ann Larson, and the late Sam Stringfield Friends include Kathy Cash, Greg Carmichael, Carrye Wilkins, Raymond Roelandt, and my wife, Diane Watkins (I know there are others, so I apologize to those I have neglected to include in this list.) Additionally, I could not have completed this dissertation on the Knowledge of Algebra for Teaching without the assistance of Dr Robert Floden and the KAT research team at Michigan State University Thank you so much for allowing me to explore your data and answering all of my questions along the way Finally, I would like to thank my high-school calculus teacher, Dana Guess, for making mathematics fun and exciting for me Ms Guess, I would not be in mathematics education today if I had not been inspired by your passion for mathematics and desire to help your students succeed Thank you for choosing to become a public-school teacher and for making a difference in the lives of so many students in Henderson County v ABSTRACT EXPLORING THE KNOWLEDGE OF ALGEBRA FOR TEACHING Jonathan David Watkins November 14, 2018 For the past few decades, researchers in mathematics education have been exploring the concept of pedagogical content knowledge (PCK)— or knowledge related to teaching content—and applying it to various areas of mathematics, such as algebra Research related to teacher knowledge of algebra is critical because researchers (e.g., Hill, Rowan, & Ball, 2005) have found correlations between some types of teacher knowledge and student achievement in mathematics; students from around the world are outperforming U.S students on international assessments of mathematics, including algebra (Organization for Economic Cooperation and Development, 2014, 2016); and algebra plays an integral role in the K-12 mathematics curriculum in the U.S (National Council of Teachers of Mathematics, 2000) Given this background, the purpose of this study was to explore the knowledge of algebra for teaching (KAT) by investigating the following research questions: What is the factor structure underlying mathematics teachers’ KAT, as measured by an established instrument? Are KAT constructs measured similarly in preservice and inservice teachers? And if so, are there latent mean differences in the KAT of these two groups? These research questions were addressed using multiple-group confirmatory factor analysis—a form of structural equation modeling—to analyze survey vi data (n = 1,248) gathered by KAT researchers at Michigan State University These researchers designed an instrument to measure three types of algebra knowledge, based on their conceptual framework of KAT: knowledge of school algebra; knowledge of advanced mathematics; and mathematics-for-teaching knowledge, which is similar to PCK (Reckase, McCrory, Floden, Ferrini-Mundy, & Senk, 2015) The analyses suggested that KAT may be a unidimensional construct because a one-factor KAT model fit the data better than a two- or three-factor model Additionally, the analyses suggested that KAT was measured similarly in preservice and inservice teachers, and that preservice teachers had slightly higher KAT than inservice teachers Following the results, there is a discussion of connections between the findings and the research literature and implications of the findings, such as providing more CKand PCK-focused professional development opportunities for algebra teachers The researcher concludes with some recommendations for future research and closing remarks vii ... Mathematical Knowledge for Teaching 55 Knowledge of Algebra for Teaching Framework 60 Knowledge of School Algebra 60 Knowledge of Advanced Mathematics 60 Mathematics -for- Teaching Knowledge. .. ABSTRACT EXPLORING THE KNOWLEDGE OF ALGEBRA FOR TEACHING Jonathan David Watkins November 14, 2018 For the past few decades, researchers in mathematics education have been exploring the concept of pedagogical... of Education and Human Development of the University of Louisville in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Curriculum and Instruction Department of