Mathematical Knowledge for Teaching, Teacher Practices, and Student Learning within Urban Learning Contexts Open Access

Abstract

Abstract
Mathematical Knowledge for Teaching, Teacher Practices, and Student Learning within
Urban Learning Contexts
By Rubye K. Sullivan

This study explored how the staffing of the classroom with a teacher in possession
of mathematical knowledge for teaching (MKT) or a teacher implementing standards-
based, reform-oriented (SB - RO) teaching practices might relate to classroom and
school-level aggregates of student race, class status, and prior learning in mathematics.
In addition, I examined whether mathematical knowledge for teaching and the use of
standards-based, reform-oriented teaching practices relate to student learning in
mathematics. A correlational analysis along with a multi-level regression analysis,
specifically hierarchical linear modeling, were employed. The teacher level variables are
teacher knowledge (MKT) and teaching practices in mathematics (SB-RO). Student level data consisted of two administrations of the state's criterion-reference test (CRT). Students' grade two and
grade three mathematics scale scores were included along with the student contextual
variables, race and class status. The sample consisted of 531 grade three students nested
in the classrooms of 35 grade three teachers in 17 elementary schools, approximately two
teachers per school, from a large urban district in the southeastern United States. Results
indicated that although mathematical knowledge for teaching and the use of standards-
based, reform oriented practices are positively correlated (r (33) =.30, p < .01), neither
exhibited statistically significant contributions to the prediction of student learning in
mathematics. Additionally, the possession of MKT and the use of SB-RO practices were
not related to the proportion of African American students, the proportion of students
eligible for free or reduced lunch, or the prior learning in mathematics at the class or
school level. The teachers studied, however, possessed lower levels of MKT than the
average elementary teacher in the nation.

Mathematical Knowledge for Teaching, Teacher Practices, and Student Learning within
Urban Learning Contexts
By
Rubye K. Sullivan
B.S., Boston University, 1994
M.Ed., Emory University, 1997
Advisor: Professor Robert J. Jensen, Ed.D.
A Dissertation submitted to the Faculty of the
James T. Laney School of Graduate Studies Division of Emory University
in partial fulfillment of the requirements for the degree of
Doctor of Philosophy
In Educational Studies
2010

Table of Contents

Table of Contents

Chapter One: The Problem ………………………………………………………………....1

Statement of the Problem …................................................2

Rationale …………………………………………………………………………...........5

Conceptual Framework ……………………………………………………….........8

Purpose ……………………………………………………………………………...........8

Research Questions ……………………………………………………………….......9

Question One ……………………………………………………...…….................9

Question Two ……………………………………………………………..................9

Chapter Two: Literature Review…………………………………………………...……....11

Presage: Teacher Knowledge Proxy Measures ………………………………11

Presage: Direct Assessment of Teacher Knowledge ………………………14

Presage: The Evolution of Mathematical Knowledge for Teaching …15

Process: Standards-Based Teaching Practices ………………………………18

Context: Student Race/Ethnicity and Class Status ……………….……..20

Product: Student Learning ……………………………………………………….......24

Chapter Three: Methodology …………………………………………………………….......27

Participants and Setting ……………………………………………………….......…27

Measures ………………………………………………………………...……….............27

Presage Variable: Mathematical Knowledge for Teaching …………..…27

Process Variable: Teaching Practices ……………………………..............29

Context Variables: Student Race/Ethnicity and Class Status ……...31

Product Variable: Student Learning ………………………………..…........…32

Data Collection and Analysis …………………....l.…………………………………34

Question One ………………………..................……………………………………35

Question Two ……………………..................………………………………………36

Limitations ………………………………………………..............………………………37

Chapter Four: Results ……………………….........………………………………………...…40

Question One …………………………………….............………………………………43

Question Two …………………………………………………….............………………44

Chapter Five: Discussion ……………………………………………………………..........….48

Question One ……………………………………………………………………..............50

Question Two ……………………………………………………………………..............51

Implications …………………………………………………………………….................53

Conclusion …………………………………………………………………….................…55

References ……………………………………………………………………………..........…57

Figures and Tables …………………………………………………………………….......…75

Appendices ………………………………………………………………………………..........87

Appendix A: Mathematical Knowledge for Teaching, Released Items ..87

Appendix B: Teaching Practices Instrument ……………………………………...90

Appendix C: School District Study Approval Letter ……………………………92

Appendix D: Informed Consent Form ………………………………………...........93

About this Dissertation

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• Permission granted by the author to include this thesis or dissertation in this repository. All rights reserved by the author. Please contact the author for information regarding the reproduction and use of this thesis or dissertation.

School	Laney Graduate School
Department	Educational Studies
Degree	PhD
Submission	Dissertation
Language	English
Research Field	Education, General Education, Mathematics
Keyword	Teacher Effectiveness Mathematics Education
Committee Chair / Thesis Advisor	Jensen, Robert J, Emory University
Committee Members	Engelhard, George, Emory University Cheong, Yuk Fai, Emory University

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