Impact of Student-Centered Learning in Mathematics

122 Pages·2015·3.98 MB·English

IMPACT OF STUDENT-CENTERED LEARNING IN MATHEMATICS

By

Brittany L. Garner

A thesis submitted to the faculty of
Wittenberg University
In partial fulfillment of the requirements for the degree of

MASTER OF ARTS

Education Department

Wittenberg University

July 2015
W I T T E N B E R G U N I V E R S I T Y

GRADUATE STUDIES IN EDUCATION

MASTER OF ARTS IN EDUCATION COMMITTEE APPROVAL

of a thesis submitted by

Brittany L. Garner

Each member of the following Thesis Committee has read and has found this thesis to be
satisfactory.

Date Chair: Dr. Regina Post

Date Dr. Kathryn Calabrese

Date Dr. Amy McGuffey
W I T T E N B E R G U N I V E R S I T Y

F I N A L R E A D I N G A P P R O V A L

I have read the thesis of Brittany L. Garner in its final form and have found that
(1) its format, citations, and bibliographic style are consistent and acceptable; (2) its
illustrative materials including figures, tables, and charts are in place; and (3) the final
manuscript is satisfactory to the candidate’s thesis committee and is ready for submission
to Wittenberg University.

_________________ ______________________________________
Date Dr. Regina Post
Chair: Thesis Committee

Approved for the Education Department

_________________________________________
Roberta A. Linder
Director of Graduate Studies
Wittenberg University
Honor Statement
Master of Arts in Education

“I affirm that my work upholds the highest standards of honesty and academic integrity at
Wittenberg, and that I have neither given nor received any unauthorized assistance.”

Name of Candidate: Brittany L. Garner

Signature Date

Director of Graduate Studies: Roberta A. Linder

Signature Date
TABLE OF CONTENTS
Abstract …………………………………………………………………………………viii
List of Tables ………………………………………………………..………………….. ix
Acknowledgements ………………………………………………………...……...……. .x
Chapter One: Introduction ……………………….…………………………….…………1
The Statement of the Problem …………………………………………………….5
Research Questions ……………………………………………………………….7
Significance of the Study …………………………………………………………7
Limitations ………………………………………………………………………..8
Definition of Terms ……………………………………………………………….8
Conclusion. ……………………………………………………………………….9
Chapter Two: Literature Review …………..……………………………………………10
Theoretical Framework …………………………………………………………10
Effective Teaching Strategies in Mathematics ………………………………….13
Effective Mathematics Tasks ……………………………………………………16
Student-centered Mathematics Curriculum ……………………………………..21
Summary ………………………………………………...………………………24
Chapter Three: Methodology ……………….……………………..…………………….26
Research Design …………………….………………………………………..….27
Data Collection …………………………………………………….……..……..34
Timeline and Relevance of Data Collection Instruments ……….………...….....38
Data Analysis ………………………………………………………..…..………39
Summary ………………………………………………………….…..…..……..42
Chapter Four: Findings ………………………………………….………..…..…………43
Pre-Assessment and Post-Assessment Results …………….……….….………..43
Pre-Survey and Post-Survey Results ………………………….………..……….47
Student Journals with Samples of Student Communication …………...………..48
Teacher Notes …………………………………………………….……..………49
Student Interviews …………………………………………………………...….55
Summary …………………………………………………………...……………58
Chapter Five: Discussions ……………………………………………………………….60
Discussion of Findings and Conclusions ……………………………………….61
Discussion of Research Questions …………………………….………………..68
Reflections ……………………………………………………………………...69
Summary …………………………………………………………….………….71
Appendix A: Pre-Assessment ……………………………………….…………………. 73
Appendix B: Post-Assessment ……………………………………………..……..……. 78
Appendix C: Attitudes Towards Mathematics Survey …………………………...……. 83
Appendix D: Journal Prompt ……………………………………………………...…… 89
Appendix E: Relationship Between Data-Collection Instruments and
Research Questions ………………………………………………………. 92
vi
Appendix F: Ability to Problem Solve and Communicate Rubrics…………………..... 94
Appendix G: Examples of Student Work on Journal Entries …………………………...97
Appendix H: Informed Consent ……………………………………….…...…………..103
Appendix I: Institutional Review Board Approval ………………..………….………..106
References …………………………………………….……………………….…….....108

vii
Abstract
Mathematics students in the United States appear to be underachieving when compared to
other comparable countries as evident by global studies. Despite research that has linked
student inadequacies to their lack of true understanding of mathematical concepts, many
teachers continue to teach students through procedural, lecture-based methods. This
mixed methods experimental study examined the impact of a student-centered learning
environment on middle school students’ as evident by their ability to problem solve and
communicate thinking on various summative assessments in mathematics. Additionally,
the students’ perceptions of this type of learning was evaluated. It was found that the
student-centered learning methods led to an increase in student understanding as evident
through various assessment measures. Also, it was made clear that students enjoyed
these problem-based tasks and appreciated the collaboration made available through this
method of learning. This study affirmed that a student-centered environment is beneficial
to student learning in mathematics and leads to an increase in students’ ability to problem
solve and communicate their thinking.
viii
List of Tables
Table 3.1: Instructional Task Alignment to Common Core State Standards ……..……. 33
Table 3.2: Student Interview Questions………………………………...………………. 37
Table 3.3: Data Collection Timeline………………………………….………………… 38
Table 3.4: Pre-/Post- Assessment Question Types ……………………………………...39
Table 4.1: Overall Mean Pre- and Post-Assessment Results………….………………....44
Table 4.2: Mean Pre- and Post-Assessment Results: Procedural Tasks…………………45

Table 4.3: Mean Pre- and Post-Assessment Results: High-Problem Solving Tasks…….46
Table 4.4: Mean Pre- and Post-Assessment Results: Ability to Communicate
Mathematical Thinking …..…………………………………….….…..……..46
Table 4.5: Pre-Questionnaire and Post-Questionnaire Results…….…….…..……….…47
Table 4.6: Journal Mean Rubric Scores …………………………….…..….….…....…...49
Table 4.7: Theme One: Ability to Understand Student Thinking……………………..…50
Table 4.8: Theme Two: Students’ Understanding of In-class Learning…………………51
Table 4.9: Theme Three: Students’ Perceptions of Student-centered Learning…………52
.
Table 4.10: Theme Four: Student Engagement ………………………………….….…..53
Table 4.11: Theme Five: Students’ Ability to Solve Procedural Problems ……….…….54
Table 4.12: Question One Theme: Students’ Perception on Learning Mathematics ……55
Table 4.13: Question Two Theme: Student Perceptions on Homework………………...56
Table 4.14: Question Three Theme: Students’ Perceptions on In-class Tasks………….57
Table 4.15: Question Four Theme: Students’ Reaction to Student-centered Instruction .58

ix
Acknowledgements
In full gratitude I would like to provide due credit to all of the individuals who
provided support and guidance in the completion of this thesis. Without these
individuals, I would not have been able to fulfill my lifetime goal of pursuing a higher
education degree.
First, I must give unending thanks to my thesis chair, Dr. Regina Post, who not
only provided frequent feedback and encouragement, but employed some of the same
constructivist learning methods mentioned in this thesis so that I, too, grew in my ability
to conduct and analyze action research.
Second, I would like to thank my committee members Dr. Kathryn Calabrese and
Dr. Amy McGuffey. Their advice on my research design provided valuable direction in
my methodology. Furthermore, I appreciate their willingness to read my thesis and give
supportive feedback.
Finally, I give thanks to my family and friends for their support during this thesis
process. Without their love and understanding, I would not have been able to fulfill my
master’s program requirements.

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