The Relationship Between Calibration, Mindset, Mathematics Anxiety and Achievement in Pre

340 Pages·2017·2.8 MB·English

by  Brian Arthur Christopher

University of Northern Colorado
Scholarship & Creative Works @ Digital UNC
Dissertations Student Research
8-2018
The Relationship Between Calibration, Mindset,
Mathematics Anxiety and Achievement in Pre-
Service Elementary Teachers
Brian Arthur Christopher
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Christopher, Brian Arthur, "The Relationship Between Calibration, Mindset, Mathematics Anxiety and Achievement in Pre-Service
Elementary Teachers" (2018).Dissertations. 499.
https://digscholarship.unco.edu/dissertations/499
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© 2018
BRIAN ARTHUR CHRISTOPHER
ALL RIGHTS RESERVED
UNIVERSITY OF NORTHERN COLORADO
Greeley, Colorado
The Graduate School

THE RELATIONSHIP BETWEEN CALIBRATION,
MINDSET, MATHEMATICS ANXIETY AND
ACHIEVEMENT IN PRE-SERVICE
ELEMENTARY TEACHERS

A Dissertation Submitted in Partial Fulfillment
of the Requirements for the Degree of
Doctor of Philosophy

Brian Arthur Christopher

College of Natural and Health Sciences
School of Mathematical Sciences
Educational Mathematics

August 2018
This Dissertation by: Brian Arthur Christopher

Entitled: The Relationship Between Calibration, Mindset, Mathematics Anxiety
and Achievement in Pre-Service Elementary Teachers

has been approved as meeting the requirements for the Degree of Doctor of
Philosophy in College of Natural and Health Sciences in School of Mathematical
Sciences, Program of Educational Mathematics

Accepted by the Doctoral Committee

Gulden Karakok, Ph.D., Research Advisor

Hortensia Soto-Johnson, Ph.D., Committee Member

Anton Dzhamay, Ph.D., Committee Member

James Kole, Ph.D., Faculty Representative

Date of Dissertation Defense

Accepted by the Graduate School

Linda L. Black, Ed.D.
Associate Provost and Dean
Graduate School and International Admissions
ABSTRACT

Christopher, Brian. The Relationship Between Calibration, Mindset, Mathematics
Anxiety and Achievement in Pre-service Elementary Teachers. Published Doctor
of Philosophy, University of Northern Colorado, 2018.

According to most recent studies in mathematics education, mathematics anxiety
is highly prevalent in students’ learning, and in fact has significant negative relationship
with mathematics achievement. Thus, as educators we need to understand the factors that
explain the relationship between mathematics anxiety and achievement to find any
insights for increasing mathematics achievement. This dissertation explored this
particular issue through constructs, calibration and mindset, and their relationship with
mathematics anxiety and achievement of pre-service elementary teachers. The
dissertation has three manuscripts with the first two manuscripts focusing on the
relationship between calibration, mathematics anxiety and achievement, and the third
manuscript focusing on mindset and its relationship with the other three constructs.
To examine these constructs in the first study, the 129 participants took
mathematics anxiety and demographics surveys before their first and last exam, while
they filled out self-efficacy surveys before each of their exam. For the second study, the
142 participants took mathematics anxiety and demographics surveys at the beginning
and end of the semester. Additionally, self-efficacy and self-evaluation surveys were
given right before and one class day or two after each exam. For the third study, the
same procedure as the second study was followed with 321 participants, except a mindset
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survey was given with the mathematics anxiety and demographic surveys. Copies of the
exams were collected after they were graded by the instructors for all three studies.
Results of the studies revealed that calibration, mindset, and mathematics anxiety
affected mathematics performance as supported by the literature where in these
dissertation studies the pre-service elementary teachers have served as the population.
Additionally, these four constructs are related to each other. Based on the metacognition
theoretical framework and literature, the relationship seems to be that mindset may
influence mathematics anxiety, calibration, and mathematics achievement while
mathematics anxiety may influence calibration and mathematics achievement.
Teachers might play an important influence on the relationship between the four
constructs within the pre-service elementary teachers’ mathematics content courses.
Given that different teachers have different styles regarding the teacher- and/or student-
centered approach to teaching, of communication with the students, and of giving
feedback to the students on presentations, assignments and assessments, this indicates
that instructors of pre-service elementary teachers needs to be careful in their instruction
methods in order to promote growth mindset, lower mathematics anxiety, and better
calibration. This work also extends the methods of measuring and calculating calibration
through the use of point values when measuring self-efficacy and self-evaluation instead
of confidence measurements and working with open-ended questions on exams instead of
multiple choice problems. Additionally, this research has implications for policy for
mathematics content courses for pre-service elementary teacher population. One such
implication is metacognitive habits of mind are not only important for understanding and
learning mathematics but are also important for students to be life-long learners of
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mathematics as well as teachers of it by providing students with skills necessary for them
to continually develop their thinking and understanding of the world.
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TABLE OF CONTENTS

CHAPTER

I. INTRODUCTION ……………………………………………………. 1
Statement of the Problem
Purpose and Research Questions
Literature Review
Outline of Dissertation
Significance of the Research

II. CONNECTING PRE-SERVICE ELEMENTARY TEACHERS’ 72
CALIBRATION, MATHEMATICS ANXIETY AND
ACHIEVEMENT: A LINEAR MIXED MODEL ANALYSIS ……..
Introduction
Literature Review
Method
Results
Discussion

III. THE RELATIONSHIP BETWEEN CALIBRATION, 113
MATHEMATICS ANXIETY AND ACHIEVEMENT OF
OFF-TRACK PRE-SERVICE ELEMENTARY TEACHERS ...……..
Introduction
Literature Review
Method
Results
Discussion

IV. PRE-SERVICE ELEMENTARY TEACHERS’ MINDSET AND 165
ITS RELATIONSHIP WITH CALIBRATION, MATHEMATICS
ANXIETY AND ACHIEVEMENT …………………………………..
Introduction
Literature Review
Method
Results
Discussion

V. DISCUSSION …………………….………………………………….. 223
Summary of the Studies
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Summary and Discussion of Findings
Implications
Limitations
Future Research

REFERENCES …………………………………………………………………… 251

APPENDIX
A. Institutional Review Board Approval for First Study ……………………. 280
B. Informed Consent Letter for First Study ………………...……………….. 282
C. Mathematics Anxiety Survey for First Study ………………….………..... 285
D. Example of Mathematics Exam …………………………………………... 288
E. Self-Efficacy Survey for First Study ……………………………………... 297
F. Institutional Review Board Approval for Second and Third Study ……… 302
G. Informed Consent Form for Second and Third Study ……………………. 304
H. Demographics Survey for Second and Third Study ……………………… 307
I. Mathematics Anxiety Survey for Second and Third Study ………………. 310
J. Self-Efficacy Survey Example for Second and Third Study ……………... 312
K. Self-Evaluation Survey Example for Second and Third Study …………... 320
L. Mindset Survey …………………………………………………………… 328

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LIST OF TABLES
2.1 Majors and Concentration Areas of the Participants …...……………. 86
2.2 Descriptive Summary of Calibration, Mathematics Anxiety and 93
Exam Performance ………………...…………………………………
2.3 Correlations Among Possible Continuous Fixed Effects and 95
Dependent …..………………………………………………………...
2.4 Type III Tests of Fixed Effects for Model 1 and Model 2 ..…………. 96
2.5 Linear Mixed Model Parameter Estimates for Model 1 and Model 2 .. 97
2.6 Type III Tests of Fixed Effects for Final Model …………………….. 99
2.7 Linear Mixed Model Parameter Estimates for Final Model …………. 99
2.8 Least Square Means of Exam Scores for Teacher …….……………... 101
3.1 Grade Level by Course ...…………………………………………….. 128
3.2 Majors and Concentration Areas of the Participants ………………… 129
3.3 Descriptive Summary of Calibration, Mathematics Anxiety and 137
Exam Performance ……………………………………..…………….
3.4 Correlations of the End-of-the-Semester Prediction Calibration, 143
Mathematics Anxiety and Exam ……………………………………..
3.5 Parameter Estimates for Final Multiple Linear Regression Model ….. 150
4.1 Grade Level by Course ...…………………………………………….. 178
4.2 Majors and Concentration Areas of the Participants ………………… 180
4.3 Descriptive Summary of Mindset, Calibration, Mathematics Anxiety 188
and Exam Performance ……………………………………………….
4.4 Correlations of the End-of-the-Semester Mathematical Mindset, 200
Prediction Calibration, Mathematics Anxiety and Exam Performance.
4.5 Parameter Estimates for Final Multiple Linear Regression Model ….. 207

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