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Electronic Theses, Treatises and Dissertations
The Graduate School
2012
The Effects of Emotional Support and
Cognitive Motivational Messages on Math
Anxiety, Self-Efficacy, and Math Problem
Solving
Tami Im
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THE FLORIDA STATE UNIVERSITY
COLLEGE OF EDUCATION
THE EFFECTS OF EMOTIONAL SUPPORT AND COGNITIVE
MOTIVATIONAL MESSAGES ON MATH ANXIETY, SELF-EFFICACY,
AND MATH PROBLEM SOLVING
By
TAMI IM
A Dissertation submitted to the
Department of Educational Psychology and Learning Systems
in partial fulfillment of the
requirements for the degree of
Doctor of Philosophy
Degree awarded:
Summer Semester, 2012
Tami Im defended this dissertation on June, 18th, 2012
The members of the supervisory committee were:
John Keller
Professor Directing Dissertation
Mika Seppala
University Representative
Vanessa Dennen
Committee Member
Fengfeng Ke
Committee Member
The Graduate School has verified and approved the above-named committee members, and
certifies that the dissertation has been approved in accordance with university requirements.
ii
ACKNOWLEDGEMENTS
I am grateful to the many people who supported me throughout my PhD program and
dissertation process. I can’t imagine reaching my current stage without the support those
wonderful individuals.
I would like to thank Dr. John Keller with all of my heart for always helping me to achieve
my goals. He is not only a major advisor to me, but is a wonderful mentor in my life. He has
been there for me as an expert of motivation research, a persistent motivator, and a warm-hearted
supporter. I decided to conduct a dissertation study related to the motivation of students’ because
I was inspired by Dr. Keller’s Learner Motivation course. Since then, he has graciously assisted
me in improving my research ideas, designs and reports. He also listened to my concerns and
worries about study, work, and personal issues and always provided me with suggestions to help
me improve. I would also like to say thank you to Cecilia Keller, who has always cared for me
and worried about my welfare. Whenever I had good news, Dr. Keller and Cecilia were happy
with me, and whenever I had difficult time, they took care of me.
Thank you to Dr. Vanessa Dennen, who is both a great committee member and personal
mentor. I have worked with her since Fall 2009, and she has trusted and provided me with many
opportunities to work on diverse projects. She is a true friend and a wonderful teacher, and
inspired my interests in qualitative research. I enjoy not only working with her, but also having
the chance to share stories about our lives. I would also like to thank the other members of Dr.
Dennen’s family, George and Sylvie, who are wonderful friends to me as well.
Special thanks to my other committee members, Dr. Mika Seppala and Dr. Fengfeng Ke.
Dr. Seppala gave me several research ideas in the area of mathematics. With his insight, I was
able develop a new understanding about nature of mathematical research. Dr. Ke introduced me
to the area of game-based learning research, of which I am now an enthusiast. During work with
Dr. Ke as her research assistant, I gained valuable research experience which has helped me
define my future career goals as a researcher. I look forward to future collaborative research with
each of my committee members after graduation.
I also would like to thank Dr. Robert Reiser and Dr. Tristan Johnson. Dr. Reiser was my
temporary advisor and helped me tremendously during the early stages of my PhD program. I
developed my dissertation topic in his class and he provided me feedback which helped me
improved my idea into a real dissertation topic. I worked with Dr. Johnson when I first came to
the program, and he advised me on how I could become a good online teaching assistant when
everything was new and unfamiliar to me. His advice helped me to succeed in my work.
Special thanks to my Master’s advisor Dr. Innwoo Park and his wife Eunyoung Kim. Dr.
Park is an alumni of our program and inspired me to original come to this program. He always
provided me with useful advice about my research, career, and my personal life. He is a teacher,
researcher, and mentor for someone who always wished to be like him. I would like to thank to
Eunyoung Kim for taking care of me like I was a part of her family. Her prayers and support
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were a huge help to me when I struggled with my efforts. Dr. Park and his family’s support
helped me to keep moving forward at each step of my PhD journey.
Likewise, I would like to thank Dr. E. Shen and my friends who helped me develop my
dissertation module. My dissertation is built upon Dr. Shen’s research, and when I was confused
trying to develop an agent-integrated computer module, Dr. Shen provided me with help and
suggestions. Also, many of my friends were gracious enough to help me pilot-test my module.
Finally, I would like to express special appreciation to my parents for their consistent
support and love. They always believe in me and knew that I could finish this dissertation and
receive my PhD degree even though the most challenging of times. Their belief in me allowed
me to believe in myself. Their love and support have been the best inspiration to me in my
dissertation process. I am more than happy to keep their faith in me and honor them though my
achievements. I will do my best to be a better person, researcher, and instructor for my parents.
I am also thankful to Matthew Earhart for caring about me and supporting me.
I dedicate this dissertation to my lovely family, supportive committee members, and
wonderful friends.
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TABLE OF CONTENTS
LIST OF TABLES ......................................................................................................... VIII
LIST OF FIGURES .......................................................................................................... IX
ABSTRACT ........................................................................................................................ X
CHAPTER ONE INTRODUCTION ................................................................................ 1
CONTEXT OF THE PROBLEM ................................................................................................ 1
PROBLEM STATEMENT ....................................................................................................... 5
RESEARCH QUESTIONS ...................................................................................................... 5
SIGNIFICANCE OF STUDY ................................................................................................... 6
CHAPTER TWO REVIEW OF RELEVANT LITERATURE ..................................... 7
INTRODUCTION .................................................................................................................. 7
MATH ANXIETY .................................................................................................................. 8
Definitions and dimensions of Math Anxiety ............................................................... 8
Researches on Math Anxiety ........................................................................................ 9
Math Anxiety and Coping strategy ............................................................................. 12
EMOTIONAL SUPPORT ...................................................................................................... 13
Definition of Coping strategy ..................................................................................... 13
Emotion-focus coping vs. Problem-focus coping ....................................................... 13
Research related to coping .......................................................................................... 14
COPE .......................................................................................................................... 15
COGNITIVE MOTIVATIONAL MESSAGES ............................................................................ 20
ARCS Model for motivational design ........................................................................ 20
Achievement Motivation & Expectancy-value theory ............................................... 22
Implicit theory............................................................................................................. 23
Research on Incremental ability beliefs ...................................................................... 24
Motivational messages ................................................................................................ 25
PEDAGOGICAL AGENT ...................................................................................................... 28
Benefits of pedagogical agent ..................................................................................... 28
Roles of pedagogical agent ......................................................................................... 29
Research on pedagogical agent ................................................................................... 30
SELF-EFFICACY ................................................................................................................ 33
HYPOTHESES .................................................................................................................... 34
PURPOSE AND PREDICTIONS ............................................................................................. 37
CHAPTER THREE METHOD ....................................................................................... 38
INTRODUCTION ................................................................................................................ 38
PARTICIPANTS .................................................................................................................. 38
RESEARCH DESIGN .......................................................................................................... 39
INDEPENDENT VARIABLES ............................................................................................... 40
Emotional support ....................................................................................................... 40
Cognitive motivational messages ............................................................................... 42
DEPENDENT VARIABLES .................................................................................................. 45
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Math anxiety ............................................................................................................... 45
Self-efficacy ................................................................................................................ 46
Math problem solving ................................................................................................. 46
AGENT DEVELOPMENT ..................................................................................................... 47
MATERIALS ...................................................................................................................... 49
PROCEDURE ..................................................................................................................... 51
Pre-experiment ............................................................................................................ 51
Experiment .................................................................................................................. 51
Post-experiment .......................................................................................................... 52
DATA ANALYSIS .............................................................................................................. 53
CHAPTER FOUR RESULTS ......................................................................................... 54
PRELIMINARY DATA ANALYSIS ....................................................................................... 54
Missing data ................................................................................................................ 54
Pre-test on math problem solving ............................................................................... 55
TEST OF STATISTICAL ASSUMPTIONS ............................................................................... 55
Assumption 1: Independence of observations ............................................................ 55
Assumption 2: Homoscedasticity ............................................................................... 55
Assumption 3: Multi-normality .................................................................................. 56
Assumption 4: Linearity ............................................................................................. 56
Assumption 5: Correlations ........................................................................................ 56
EXAMINATIONS OF THE HYPOTHESES .............................................................................. 57
Descriptive Statistics ................................................................................................... 57
Two-way MANOVA Test .......................................................................................... 58
INDIVIDUAL HYPOTHESIS TEST ........................................................................................ 60
Hypothesis 1................................................................................................................ 60
Descriptive Statistics ................................................................................................... 60
Univariate MANOVA Test ......................................................................................... 61
Follow-up ANOVA Test............................................................................................. 62
Hypothesis 2................................................................................................................ 63
Descriptive Statistics ................................................................................................... 63
Univariate MANOVA Test ......................................................................................... 64
Follow-up ANOVA Test............................................................................................. 65
Hypothesis 3................................................................................................................ 66
MANOVA Test ........................................................................................................... 66
Follow-up ANOVA Test............................................................................................. 66
CHAPTER FIVE DISCUSSIONS ................................................................................... 69
OVERVIEW ....................................................................................................................... 69
OVERALL EFFECTS OF EMOTIONAL SUPPORT .................................................................... 71
Effect of emotional support on Math Anxiety ............................................................ 71
Effect of emotional support on Math problem solving ............................................... 73
OVERALL EFFECTS OF COGNITIVE MOTIVATIONAL MESSAGES .......................................... 74
Effect of cognitive motivational messages on Self-efficacy....................................... 76
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Effects of cognitive motivational messages on math anxiety and math problem
solving............................................................................................................................. 77
MAJOR CONTRIBUTIONS OF THE STUDY........................................................................... 79
LIMITATIONS .................................................................................................................... 81
IMPLICATIONS .................................................................................................................. 82
FUTURE RESEARCH DIRECTIONS ...................................................................................... 83
CONCLUSIONS .................................................................................................................. 84
APPENDIX A PRE-TEST AND POST-TEST ON MATH PROBLEM SOLVING.. 86
APPENDIX B PRE-TEST AND POST-TEST ON MATHEMATICS ANXIETY .... 89
APPENDIX C PRE-TEST AND POST-TEST ON SELF-EFFICACY ....................... 91
APPENDIX D THEORIES OF INTELLIGENCE SCALE ......................................... 93
APPENDIX E STORYBOARD ....................................................................................... 94
APPENDIX F HUMAN SUBJECT COMMITTEE APPROVAL ............................. 134
APPENDIX G INFORMED CONSENT FORM ......................................................... 136
REFERENCES ................................................................................................................ 138
BIOGRAPHICAL SKETCH ......................................................................................... 144
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LIST OF TABLES
Table 2.1: Types of Treatment and Associated Examples Based on the Hembree’s Study
(1990) .................................................................................................................................. 11
Table 2.2: COPE scales ....................................................................................................... 15
Table 2.3: Coping strategies from Zeidner (1998)’s study.................................................. 17
Table 2.4: Examples of COPE categories used in Shen (2009)’s study .............................. 18
Table 2.5: ARCS definitions and related strategies............................................................. 21
Table 2.6: Examples of motivational messages used in Shen (2009)’s study based on
ARCS categories ................................................................................................................. 27
Table 2.7: Desired features of agents: Results from the quantitative study ........................ 31
Table 2.8: Four conditions based on treatment in this study ............................................... 35
Table 3.1: Examples of emotional support in each situation............................................... 41
Table 3.2: Sample of emotional support messages based on four categories ..................... 42
Table 3.3: Sample cognitive motivational messages by each agent .................................... 44
Table 3.4: Math problem solving grading rubric by Shen (2009) ....................................... 47
Table 3.5: Overall module structure of this study ............................................................... 49
Table 3.6: Summary of organization of module of each group ........................................... 52
Table 3.7: Summary of activities and time for each stage of the study............................... 53
Table 4.1: Levene's Test of Equality of Error Variances .................................................... 55
Table 4.2: Box's Test of Equality of Covariance Matrices.................................................. 56
Table 4.3: Correlations among dependent variables .......................................................... 56
Table 4.4: Means and Standard Deviations of Math Anxiety, Self-efficacy, and Math
Problem Solving of Each Group.......................................................................................... 57
Table 4.5: Means and Standard Deviations of three DVs based on two IVs ...................... 58
Table 4.6: Effects of Emotional Support and Cognitive Motivational Messages from
MANOVA ........................................................................................................................... 59
Table 4.7: Means and Standard Deviations: Effects of Emotional Support on Math anxiety,
Self-efficacy, and Math Problem Solving from MANOVA – continued ............................ 61
Table 4.8: MANOVA results: Effects of Emotional Support ............................................. 61
Table 4.9: ANOVA table: Effects of Emotional Support on Math Anxiety ....................... 62
Table 4.10: ANOVA table: Effects of Emotional Support on Self-efficacy ....................... 62
Table 4.11: ANOVA table: Effects of Emotional Support on Math Problem Solving ....... 63
Table 4.12: Means and Standard Deviations: Effects of Cognitive Motivational Messages
on Math anxiety, Self-efficacy, and Math Problem Solving from MANOVA ................... 64
Table 4.13: MANOVA results: Effect of Cognitive Motivational Messages ..................... 64
Table 4.14: ANOVA table: Effects of Cognitive Motivational Messages on Math Anxiety
............................................................................................................................................. 65
Table 4.15: ANOVA table: Effects of Cognitive Motivational Messages on Self-efficacy 65
Table 4.16: ANOVA table: Effects of Cognitive Motivational Messages on Math Problem
Solving................................................................................................................................. 66
Table 4.17: ANOVA table: Interaction Effects of Emotional Support and Cognitive
Motivational Messages on Math Anxiety............................................................................ 67
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LIST OF FIGURES
Figure 2.1: Audience analysis result from a pilot test ......................................................... 22
Figure 2.2: Relation among ability beliefs, expectancy, value, and performance ............... 23
Figure 3.1: Instructor agent, peer agent, scientist agent in this study ................................ 48
Figure 4.1: Interaction Effects of Emotional Support and Cognitive Motivational
Messages on Math Anxiety ................................................................................................. 68
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ABSTRACT
Math problem solving has been regarded as one of the major weaknesses in U.S. students’
math performance for many years (Orabuchi, 1992). One of the main reasons that students do not
perform well in math problem solving may be due to math anxiety. There has been increasing
interest in math education areas on how to reduce math anxiety to enhance students’ math
performance. However, there were few empirical studies which examined the effects of various
interventions towards decreasing math anxiety. Given the lack of empirical studies on how to
reduce students’ math anxiety and to increase math learning, this study examined the effects of
emotional support and cognitive motivational messages on math anxiety, self-efficacy, and math
problem solving. This study built upon the work done by Shen (2009) by modifying elements of
his design and stimulus materials and by introducing a new independent variable: incremental
ability beliefs. Thus, two independent variables – one for decreasing affective math anxiety
(emotional support) and another for alleviating cognitive math anxiety (cognitive motivational
messages) were used in this study. The pedagogical agents were used as a delivering method of a
computer based module in this study, but not an independent variable of this study.
Emotional support messages were designed to alleviate students’ affective dimension of
math anxiety. Emotional support messages were developed based on Shen’s (2009) study, which
was based on the multidimensional coping inventory (COPE) (Carver et al., 1989). In this study,
emotional support messages included four scales related to emotion-focus coping, which are:
positive reinterpretation and growth (RG), focus on and venting of emotions (VE), use of
instrumental social support (IS), and use of emotional support (ES) from COPE (Carver et al.,
1989). Emotional support messages were delivered by an instructor agent and peer agent to the
emotional support group.
Cognitive motivational messages were designed to reduce students’ cognitive dimension
of math anxiety which related to worry of performing well in mathematics. In this study,
cognitive motivational messages specifically contained ability belief change messages to
alleviate the cognitive dimension of math anxiety. Implicit theory separated students’ ability
beliefs into two categories: entity belief and incremental belief (Dweck, 1999). Incremental
ability belief messages were provided to the cognitive motivational messages treatment group
x
primarily by a scientist agent in a computer-based module with video clips and short messages
which emphasize the students’ abilities were not fixed and could be improved through effort.
The initial idea for cognitive motivational messages came from an article “You can grow your
intelligence: New research shows the brain can be developed like a muscle” which was used in
previous experimental study (Blackwell et al., 2007). Thus, cognitive motivational messages
were developed by the researcher based on Blackwell et al (2007)’s study and then were
reviewed by an expert in motivational design.
Eighty-eight GED students enrolled in GED math classes at a community college in
Florida were distributed to four groups (emotional support only, cognitive motivational messages
only, emotional support and cognitive motivational messages, and a control group) and asked to
individually study a computer-based module about vocabulary, concepts, and formulas related to
the Pythagorean Theorem for 45 to 60 minutes. Two different math anxiety questionnaires
[Mathematics Anxiety Questionnaire (MAQ) (Wigfield & Meece, 1988) and Mathematics
Anxiety Scale (MAS) (Fennema & Sherman, 1976)] were used in a pre-test and post-test. Selfefficacy questionnaires were modified to be aligned with the context of this study focusing on
math problem solving using Kim’s (2004) questionnaire. The math problem solving items were
developed based on Shen (2009)’s items.
MANOVA results indicate emotional support significantly affect the combined DV of
math anxiety, self-efficacy, and math problem solving. A follow-up ANOVA revealed that
emotional support had a significant effect on math anxiety and math problem solving. The
emotional support group reported significantly lower math anxiety than the no emotional support
group. Also, the emotional support group scored significantly higher in the post-test of math
problem solving than the no emotional support group. MANOVA revealed a primary effect of
cognitive motivational messages on the combined DV of math anxiety, self-efficacy, and math
problem solving. A follow-up ANOVA revealed that cognitive motivational messages had a
significant effect on self-efficacy. The cognitive motivational messages group reported
significantly higher self-efficacy than the no cognitive motivational messages group. MANOVA
revealed an interaction effect of emotional support and cognitive motivational messages on the
combined DV of math anxiety, self-efficacy, and math problem solving. A follow-up ANOVA
xi
revealed that there was an interaction effect of emotional support and cognitive motivational
messages on math anxiety.
This study shows possibilities of adapting coping strategies as a form of emotional support
and use incremental ability beliefs as the content of cognitive motivational messages. Also, the
study found that pedagogical agents could be effective as a form of emotional and motivational
support for students in a computer-based module. Further research studies which examine the
effects of emotional support and cognitive motivational messages with different populations,
subject areas, delivery medium, and long term treatment would be needed to expand the findings
of this study. It is expected that further research based on this study would improve the nature of
treatment and provide more solid evidence to researcher and teachers.
xii
CHAPTER ONE
INTRODUCTION
Context of the problem
For many years, math problem solving has been regarded as one of the major weaknesses
in U.S. students’ math performance (Orabuchi, 1992). In 2003, U.S. performance in math
problem solving was lower than the average performance of most Organization for Economic
Cooperation and Development (OECD) countries listed in the Program for International Student
Assessment (PISA) (Lemke et al., 2004). Math problem solving is different from simple
calculation such as 1+2=3, and is an upper level of math performance which requires analysis
and application skills. Math problem solving is defined by PISA as a situation where a student’s
known attempts or ideas for resolving a problem do not work because of the problem’s novel
features (Dossey, McCrone, & O'Sullivan, 2006). So in this situation, a student should analyze
the problem and simplify it to a workable form which is familiar to the student and thus helps the
student apply his existing mathematical knowledge and skills in solving this problem. In this
study, math problem solving refers to one form of transfer of learning in math, which requires
students to apply their mathematical knowledge and problem–solution skills they have learned in
the class to novel problems in real world context (Fuchs et al., 2008). There are many reasons
why U.S. students are having difficulties in math problem solving. For example, curriculum,
teaching methods, materials, and motivational issues can be possible reasons. In the present
study, one of the possible reasons, math anxiety, was the focus, and two possible solutions such
as emotional support and cognitive motivational messages were investigated to see their effects
on alleviating math anxiety, increasing self-efficacy, and improving math problem solving.
One of the main reasons that students are not good at math problem solving might be due
to math anxiety. Math anxiety is a prevalent phenomenon which is shown from students in all
grade levels through elementary school to higher education (Perry, 2004). Researchers and
teachers have thought that math anxiety was one of main reasons why students did not like math
and wanted to avoid math (Ashcraft, 2002). Math anxiety is defined as feelings of tension and
anxiety that occur when people face to do some manipulation of the numbers and to solve math
problems in various situations such as school setting and daily life (Richardson & Suinn, 1972).
1
In other words, math anxiety refers negative feelings toward math and worries on doing well in
math tasks. Several studies found that math anxiety was negatively related to math performance
(e.g., Cates & Rhymer, 2003).
Math anxiety consists of two dimensions, one is affective dimension and another is
cognitive dimension (Choi & Clark; Ho et al., 2000; Wigfield & Meece, 1988). Affective math
anxiety refers to feeling of nervousness, tension and fear on math. Cognitive math anxiety refers
to negative expectancy of doing well in math. A correlation study found affective math anxiety
correlated more strongly and negatively to elementary and middle school students’ math ability
perceptions and math performance than cognitive math anxiety (Wigfield & Meece, 1988).
Hembree (1990) conducted a meta-analysis using math anxiety related studies and found that a
cognitive behavioral intervention which aimed to alleviate emotionality as well as worry on math
had stronger effect on decreasing math anxiety than use of emotionality decreasing intervention
only. From this result, it is expected that mixed use of behavioral (focusing on affective math
anxiety) and cognitive treatment (focusing on cognitive math anxiety) would have stronger effect
on decreasing math anxiety in this study. Thus, two independent variables – one for decreasing
affective math anxiety (emotional support) and another for alleviating cognitive math anxiety
(cognitive motivational messages) were used in this study.
One possible solution to alleviate math anxiety can be emotional support. It is expected
that emotional support reduces the affective dimension of math anxiety in this study. When
students get math anxiety in a stressful situation such as failing to solve a math problem, the
most critical challenge for students is that they cannot control their emotional conflict. In this
situation, emotional support might help students overcome affective math anxiety such as
nervousness.
A coping strategy was used as a way of emotional support to decrease math anxiety (Shen,
2009). Coping refers to efforts for managing stress. Different coping strategies were used in
previous studies to control people’s stress in various situations (Carver, Scheier, & Weintraub,
1989; Folkman & Lazarus, 1985). In one of these efforts, a multidimensional coping inventory
(COPE) was developed and validated to measure the various ways that people responded to
stress (Carver et al., 1989). COPE consists of 13 scales which contain both emotion-focused
coping strategies and problem-focused coping strategies. A recent experimental study found
2
positive effects of emotional support as measured by four scales from COPE on decreasing math
anxiety and improving math learning (Shen, 2009).
Another possible solution to reduce math anxiety can be focused on the cognitive
dimension of math anxiety which is related to worries of doing well in math (Ho et al., 2000;
Shen, 2009). As a part of Shen (2009)’s study, he examined the effect of cognitive motivational
messages as a way to alleviate cognitive math anxiety. He conducted a motivational analysis
based on the four motivational components in Keller’s (1987) ARCS model and found that the
major problem of his participants was confidence. Thus, cognitive motivational messages
embedded in the instructor agent were mainly developed for the confidence problems but there
were some for relevance and satisfaction issues. The findings indicated that cognitive
motivational messages had no effect on math anxiety, motivation, and math learning. A possible
reason why he failed to find effects of cognitive motivational messages was likely due to the
overlapped nature of emotional support and cognitive motivational messages.
Thus, in this study, cognitive motivational messages were clearly distinguished from
emotional support by focusing on incremental ability beliefs. There has been a wrong belief
among students that aptitude is more important than effort for succeeding in math (Ashcraft,
2002) and this can result in decrements in performance together with increases in math anxiety.
However, it is possible that if students will have positive belief that they can do well in math by
their effort, their math anxiety will be decreased. In this line of thought, implicit theory of
intelligence can be useful to change students’ belief on success in math.
Implicit theory categorized students’ ability beliefs into two distinctions, one is entity
belief and another is incremental belief (Dweck, 1999). Students who have entity belief think
intelligence is an unchangeable, fixed thing, but students who have incremental belief think
intelligence is a malleable thing which can be cultivated through efforts and learning (Blackwell,
Trzesniewski, & Dweck, 2007; Dweck, 1999; Kennett & Keefer, 2006). Students who have
incremental beliefs tend to try to overcome challenges when they face some problems using
various strategies such as more effort and persistence (Doronh, Stephan, Boiché, & Le Scanff,
2009; Kasimatis, Miller, & Marcussen, 1996). There were empirical evidences that students who
were provided treatment about incremental ability belief performed better than students who did
not get the treatment (Aronson, Fried, & Good, 2002; Good, Aronson, & Inzlicht, 2003).
3
However, there was no attempt to investigate the effect of incremental ability belief on
alleviating math anxiety. Thus, incremental belief is adopted as one independent variable in this
study to alleviate math anxiety, and cognitive strategies in the form of motivational messages
(Visser & Keller, 1990) are applied as a way to affect students’ ability belief.
Motivational messages are one kind of strategy to promote students’ motivation to learn
through messages in forms of letters, mini posters, or e-mails which are designed based on
motivation analysis (Visser & Keller, 1990). There were empirical studies which found that
motivational messages had positive effect on motivation. For example, Kim and Keller (2008)
designed personalized motivational volitional e-mail messages to facilitate motivation for all
components of ARCS model (Keller, 1987) including attention, relevance, confidence,
satisfaction and also volition. The findings indicated that personalized motivational and
volitional e-mail messages had positive effects on confidence compared with non-personalized
motivational and volitional e-mail messages.
Another reason that students are not good at math problem solving might be due to
students’ low self-efficacy (Pajares & Graham, 1999; Pajares & Kranzler, 1995; Pajares & Miller,
1994). Self-efficacy is defined as people’s own judgments on their capabilities to organize and to
perform series of activities which are required to achieve success in certain tasks (Bandura,
1997). Self-efficacy does play an important role in determining how much effort will be
expended and how long it will be sustained for the task (Zimmerman, 2000). In this study, selfefficacy refers to the student’s beliefs that he is capable of expending the necessary effort to
succeed in math problem solving and he can sustain his efforts long enough to achieve success in
math problem solving. Various studies indicated that self-efficacy was strongly related to the
high math problem solving performance in undergraduate students and middle school students
(Pajares & Graham, 1999; Pajares & Kranzler, 1995; Pajares & Miller, 1994). From this line of
thought, self-efficacy was chosen as a dependent variable to find the relationship with math
problem solving.
A pedagogical agent can be suggested as one of the useful strategies for improving
students’ self-efficacy. A pedagogical agent can enhance students’ self-efficacy, because the
pedagogical agent stimulates social interaction on students (Kim, Baylor, & Shen, 2007).
Pedagogical agent’s social interaction effects worked as social persuasion to students, and the
4
social persuasion leads to increase students’ self-efficacy. There were empirical studies which
found positive effects of a pedagogical agent on pre-service teachers’ attitude to learning and
performance, and motivation (Baylor & Kim, 2002; Baylor & Ryu, 2003). Thus, in this study,
pedagogical agents were used as a way to affect students’ self-efficacy and to result in high math
problem solving. Also, it was expected that pedagogical agents would have a positive effect on
decreasing math anxiety.
Overall, there has been increasing interest in math education areas on how to reduce math
anxiety to enhance students’ math performance. However, there were few empirical studies
which examined the effects of various interventions towards decreasing math anxiety. Thus, in
this study, two strategies, emotional support and cognitive motivational messages were
investigated to decrease math anxiety, to increase self-efficacy, and to enhance students’ math
problem solving. Also, pedagogical agents were imbedded as a delivery method for support
messages in a computer based module in this study.
Problem Statement
The purpose of this study is to examine the effects of emotional support (coping strategy)
and cognitive motivational messages (incremental ability belief) provided by pedagogical agents
(instructor agent, peer agent, scientist agent) on math anxiety, self-efficacy, and math problem
solving.
Research Questions
The main research question of this study pertains to the effects of emotional support and
cognitive motivational messages on math anxiety, self-efficacy, and math problem solving. To
explore this question, the following specific research questions are investigated:
1. What are the effects of emotional support delivered by pedagogical agents on math
anxiety, self-efficacy, and math problem solving?
2. What are the effects of cognitive motivational messages delivered by pedagogical
agents on math anxiety, self-efficacy, and math problem solving?
5
3. What are the interactive effects of emotional support and cognitive motivational
messages delivered by pedagogical agents on math anxiety, self-efficacy, and math
problem solving depend on each other?
Significance of Study
The primary significance of this study is investigating possible ways to alleviate students’
math anxiety, to increase self-efficacy, and to improve math problem solving. Previous studies
found math anxiety was negatively related to math performance. However, there were few
attempts to investigate the effects of possible solutions on alleviating math anxiety. Therefore,
this study examines the integrative effectiveness of emotional support and cognitive motivational
messages on math anxiety, self-efficacy, and math problem solving.
The second significance of this study is providing cognitive motivational messages
focusing on incremental ability beliefs. Even though there were several studies which
investigated the effects of incremental ability beliefs on students’ motivation and learning, there
was lack of empirical studies which implemented motivational messages to deliver incremental
ability beliefs on students’ math anxiety, self-efficacy, and math problem solving. Thus, this
study can provide fundamental evidences how to adopt motivational messages to deliver
incremental ability beliefs.
The third significance of this study is adopting various pedagogical agents in a computer
based module to deliver motivational messages related to coping and ability beliefs change in
order to alleviate math anxiety, to increase self-efficacy, and to improve students’ math problem
solving. There was no attempt to use pedagogical agents as a medium for delivering ability
beliefs change messages. From this study, instructional designers can develop ideas on how to
design pedagogical agents to deliver ability beliefs change messages so as to alleviate math
anxiety, to enhance self-efficacy, and to improve math problem solving.
6
CHAPTER TWO
REVIEW OF RELEVANT LITERATURE
Introduction
Mathematics is a good subject to learn logic systems and problem solving skills.
Mathematics is useful not only for academic reasons but also for enhanced perception of
everyday life. For this reason, mathematics is regarded as a core discipline in all levels of
education, from primary to higher education (Jain & Dowson, 2009).
Among all relevant skill sets, the skill of math problem solving is considered one of the
important in mathematics. Math problem solving is different from simple calculation or
manipulation of numbers. Math problem solving requires students to understand a problem,
analyze it, and apply their math knowledge to solve the problem. Thus, math problem solving is
an advanced level of cognitive mathematical tasks.
There is a prevalent negative tendency toward mathematics in U.S. Some people believe
mathematics is inherently difficult, and some people believe that to succeed in mathematics,
aptitude is important than effort (Geary, 1994). Based on these beliefs, some people regard
mathematics as a relatively unimportant or optional subject in their life (Ashcraft, 2002).
Regardless of the importance of math problem solving, the majority of students in U.S.
have difficulties with this kind of task. There are various reasons why students are weak in math
problem solving skills. Curriculum, teaching style, teachers’ feedback and motivational issues
are examples of the reasons. Aligned to these reasons, Shields (2005) suggested five ways how
teachers can alleviate math anxiety for their students. First, teachers’ enthusiastic and helpful
attitude, including demonstrating the usefulness of math to their students, is important. Also,
teachers need to increase students’ confidence on math and help them focus on logical thinking
instead of memorization. He suggested providing interactive feedback and support for students’
focusing on the learning process rather than finding one correct answer. Second, curricula need
to be changed as a way to facilitate students’ deep understanding on math topics and apply their
knowledge to new problems. The typical abstract math curriculum from middle school tends to
lead students to believe that math success depends more on their innate ability than effort. Third,
7
teachers need to change their pedagogy to emphasize understanding and reasoning. Fourth, rigid
classroom culture needs to be shifted as to facilitate students’ logical thinking and learning. Fifth,
assessment should be aligned with math curriculum and conducted in various ways. Building on
his suggestions, this paper focused on how to increase students’ confidence on math.
Math anxiety has been widely considered as one of the key reasons for students’ weakness
in mathematics. There are several statistical evidences regarding U.S. students’ anxiety in
mathematics. Two thirds of adults in U.S. report fear toward mathematics (Burns, 1998), only 7%
of Americans answered that they had positive experiences in mathematics during their school
years (Jackson & Leffingwell, 1999). Some researchers said that math anxiety might be
exacerbated by an increased pressure on U.S. students after the “No Child Left behind Act”
(Rueter, 2005). In this section, to provide a solid foundation of the study, literature review
related to math anxiety, emotional support, cognitive motivational messages, pedagogical agent
and self-efficacy will be presented.
Math anxiety
Definitions and dimensions of Math Anxiety
For many decades, math anxiety has been regarded as one of the major issues in math
education. There have been various definitions of math anxiety during this period. Math anxiety
is most often defined as feelings of tension and anxiety that occur when people must perform
some manipulation of numbers and to solve math problems in various situations, such as a school
setting and daily life (Richardson & Suinn, 1972). Math anxiety can be defined as the panic,
helplessness, and mental disorganization arising from some people when they need to solve a
math problem (Tobias & Weissbrod, 1980). In other words, math anxiety refers to negative
feelings toward math and worries about performing well in math tasks.
Math anxiety consists of two dimensions, one is the affective dimension and another is the
cognitive dimension (Choi & Clark, 2006; Ho et al., 2000; Wigfield & Meece, 1988). The
affective dimension of math anxiety refers to feeling of nervousness, tension and fear towards
math. The cognitive dimension of math anxiety refers to the negative expectancy of doing well in
math. Wigfield and Meece (1988) conducted research about correlations among two dimensions
of math anxiety and math performance. It showed that the affective domain of math anxiety
8
correlated more strongly and negatively to elementary and middle school students’ math ability
perceptions and math performance than the cognitive domain of math anxiety. In addition, the
cognitive domain of math anxiety more positively related to the value that students’ attached to
math and their actual efforts on math. These results are different from a similar study using test
anxiety.
Morris, Davis, and Hutchings (1981) conceptualized two components of test anxiety,
worry and emotionality. Worry refers to the cognitive component of test anxiety, like cognitive
concerns about oneself, and emotionality refers to affective components such as nervousness.
This study shows the worry scale (cognitive component of test anxiety) related more strongly
and negatively to test performance than emotionality (affective component of text anxiety). One
possible reason why there is difference between the result of cognitive domain of test anxiety
and math anxiety with regards to performance is that the two anxiety scales measured different
aspects of worry. The math anxiety scale focused on students’ worry to perform well in math, but
test anxiety measured their worry on performing badly in testing situations. It meant the
cognitive math anxiety scale may deal with cognitive concerns to motivate the students to try
harder, but the cognitive text anxiety scale may deal with task-irrelevant cognitions which
aroused concerns about failure that decrease performance (Ho et al., 2000; Wigfield & Meece,
1988). In some degrees, students’ cognitive anxiety towards mathematics performance can
produce positive results towards motivating students to make a better effort towards math
learning and consequently enhance math performance in the long term (Wigfield & Meece,
1988).
Researches on Math Anxiety
Researchers and teachers thought that math anxiety was one of the main reasons why
students did not like math and wanted to avoid math (Ashcraft, 2002). Thus, there have been
various studies about math anxiety. Majority of studies found that math anxiety was negatively
related to math performance (e.g., Cates & Rhymer, 2003). A cross national study explored the
relation between dimensions of math anxiety and math achievement in China, Taiwan, and U.S.
The results showed that the affective dimension of math anxiety was significantly associated
with math achievement in a negative direction (Ho et al., 2000). However, the relationship was
not strongly correlated in many cases.
9
Mainstream math anxiety-related studies can be categorized based on the elements they
focused on (Cates & Rhymer, 2003). Previous research focused on finding relationships between
math anxiety and self-efficacy, gender, working memory, and math perceptions. Hembree (1990)
found that girls had higher math anxiety than boys in U.S. Ashcraft (2002) proposed that math
anxiety was related to working memory because anxious students paid attention to worries rather
than task itself. This tendency might affect students’ preconception such as fear and dislike of
math and low confidence with math. From this reason, math anxiety might decrease math
performance by distracting attention from the math task to intrusive concerns (Ashcraft, 2002).
In summation, previous studies related to math anxiety tended to see math anxiety as an
independent variable. However, there was lack of studies using math anxiety as a dependent
variable. Jain and Dowson (2009) constructed a Structural Equation Model for math anxiety,
verifying that math anxiety is a dimension which can be analyzed in a multidimensional selfregulation mediated by self-efficacy model as an outcome. Also, it was found that self-efficacy
and self-regulation were positively correlated to each other, but negatively correlated to math
anxiety (Jain & Dowson, 2009).
With consistent interests in math anxiety, various strategies of how to alleviate math
anxiety have been suggested. Hembree (1990) analyzed 151 studies by meta-analysis and found
four treatment categories as shown table 2.1 which were used in those studies. He found
classroom intervention had no effect on math anxiety and math performance. Systematic
desensitization with anxiety management and conditioned inhibition had strong effects in
alleviating math anxiety and significantly improving math performance. Cognitive restructure of
faulty beliefs and building confidence in math showed moderate effects on eliminating math
anxiety and increasing math performance. When cognitive restructuring was paired together with
systematic desensitization, their effect on math anxiety was increased compared to the systematic
desensitization-only treatment. From the result, it is expected that mixed use of two interventions,
one for alleviating affective math anxiety and another for decreasing cognitive math anxiety,
would have a strong effect on decreasing math anxiety in this study.
He also found a relation between math anxiety and several attitude-related variables. Selfconfidence in math and self-concept in math highly correlated to lower anxiety. Medium
10
correlation was found between math anxiety and attitude toward problem solving. In addition, a
small correlation between math anxiety and attitude toward success in math was found.
Table 2.1: Types of Treatment and Associated Examples Based on the Hembree’s Study (1990)
Treatment Style
Examples
Effects on Math
Effects on Math
Classroom
Intervention
(To alleviate math
anxiety within
whole classes)
Anxiety
Performance
(Mean Effect Size)
(Mean Effect Size)
Curriculum Change
-0.04
0.02
Psychological
-0.10
0.03
Intervention
Behavioral
Systematic
-1.04*
0.60*
Intervention
Desensitization
(To alleviate
‘emotionality’
Relaxation Training
-0.48
0.07
toward math –
affective math
anxiety)
Cognitive
Group counseling
-0.03
-0.07
Intervention
(To relieve worry
Reconstruction
-0.51*
0.32*
about the subject –
cognitive math
anxiety)
Cognitive-1.15*
0.50*
behavioral
Intervention
(To alleviate
emotionality as well
as worry)
*p<.01
*Note: From “The Nature, Effects, and Relief of Mathematics Anxiety”, by Hembree, 1990,
Journal for Research in Mathematics Education, 21(1), 43-44.
Cates and Rhymer (2003) suggested that math anxiety may be related to the level of
learning and not to overall math performance. And they also suggested that the level of anxiety
may become apparent when multiple operations are required. This suggestion is aligned with
11
Ashcraft (2002)’s study. Thus, this study focused on examining the relationship between math
anxiety and math problem solving, and not overall math performance.
Math Anxiety and Coping strategy
There were few studies which investigated the effects of interventions to reduce math
anxiety. Training was suggested to alleviate students’ math anxiety in terms of fear toward math
(Wigfield & Meece, 1988). A study found a positive effect of Computer Assisted Instruction
(CAI) on math anxiety, but not on math achievement in 245 sixth grade students (Mevarech &
Ben-Artzi, 1987). There were three groups in this study: a non-CAI group, a fixed feedback CAI
group, and an adaptive feedback CAI group. CAI was used for solving questions and getting
feedback in a 6th grade math class. Differences between the fixed feedback and adaptive
feedback were the features of feedback and summary reports. Students in the adaptive feedback
group received different feedback based on the nature of the questions. At the end of each
session, students received a summary report. Summary reports for the fixed feedback group
included the specific level of performance on each strand for each individual student. Students in
the adaptive feedback group received a summary report including the numbers of correct
answers on each attempt, excluding the number of incorrect answers, and reinforcement
messages. However, researchers could not find a difference between the fixed feedback and
adaptive feedback on students’ math anxiety and math achievement. It was likely due to the
limited use of adaptive feedback in their study. There was another study which found that writing
a journal about students’ frustration and feelings reduced college students’ anxiety toward a
statistics course (Sgoutas-Emch & Johnson, 1998).
Shen (2009) investigated effects of emotional support and cognitive motivational messages
on math anxiety, motivation, and math learning. He found emotional support focusing on coping
strategies had positive effects in alleviating math anxiety and increasing math learning. However,
given the overall lack of empirical studies on how to reduce students’ math anxiety and to
increase math learning, this study examined the effects of emotional support and cognitive
motivational messages on math anxiety, self-efficacy, and math problem solving. Furthermore,
this study built upon the work done by Shen (2009) by modifying elements of his design and
stimulus materials and by introducing a new independent variable: incremental ability beliefs.
12
Emotional support
One possible solution to alleviate math anxiety can be emotional support. It was expected
that emotional support reduces the affective dimension of math anxiety in this study. When
students get math anxiety in a stressful situation such as failing to solve a math problem, the
most critical challenge for students is the inability to control their emotional conflict. In this
situation, emotional support might help students overcome affective math anxiety, such as
nervousness. In this section, literature related to emotional support specifically focusing on
coping strategies will be reviewed and related studies will be presented.
Definition of Coping strategy
Coping has been shown to have an important role to mediate stressful situations into
adaptable outcomes (Zeidner, 1998). From this line of thought, coping would be expected to
support students’ adaptation to stressful situations like math problem solving. Coping can be
defined as cognitive and behavioral efforts to reduce trouble which arouses between a person and
the environment (Folkman & Lazarus, 1980; Folkman & Lazarus, 1985; Gross, 1999). Coping
refers to efforts for managing stress. Different coping strategies were used to control people’s
stress in various situations (Carver et al., 1989; Folkman & Lazarus, 1985). Effective coping
seems to increase self-belief and one’s own ability to cope with difficulties (Frydenberg, 2004).
In this context, coping strategy was used as a way of emotional support to decrease math anxiety
(Shen, 2009).
Emotion-focus coping vs. Problem-focus coping
Coping strategy was perceived as having two major functions, emotion-focus coping and
problem-focus coping, by some researchers (Carver et al., 1989; Folkman & Lazarus, 1980;
Folkman & Lazarus, 1985). Emotion-focused coping is used for managing emotional distress
aroused from the situation (regulation of stressful emotions). Problem-focused coping is used in
a case of problem-solving or doing something to change the source of stress (Folkman & Lazarus,
1985). Emotion-focus coping aimed to alleviate negative emotional experiences while problemfocus coping aimed at fixing the problem (Gross, 1999). Researchers found people used both
coping strategies based on their specific situations (Folkman & Lazarus, 1985). A study found
the interaction between problem-focus and emotion-focus coping strategies was related to
13
alleviating stress (Sideridis, 2006). Based on these studies, researchers concluded the mixed use
of coping strategies may be more adaptive than the use of a single coping strategy.
Research related to coping
Carver, Scheier, & Weintraub (1989) recommended that in an academic context where
students are confronted exams, it would be beneficial engage in adaptive problem-focused
coping strategies, such as planning, active coping, seeking social support for instrumental
reasons rather than maladaptive coping strategies such as behavioral disengagement, denial,
blame, distraction. Lazarus (1993) summarized the major generalizations from coping research
and commented that when people thought the stressful situation was hard to control, they tended
to use emotion-focus coping strategies and when they thought the situation could be controlled
by themselves they preferred to use problem-focus coping strategies.
A study explored relationships between students’ ability beliefs and coping strategies
(Doronh et al., 2009). Doronh et al. (2009) adopted Dweck (1986)’s implicit theory for
explaining students’ ability beliefs – incremental vs. entity. Incremental ability beliefs may lead
to use of strategies such as increased efforts and preference for challenge to solve problems when
students’ face some difficulties. Also, incremental ability beliefs were found to be negatively
related to worry and the use of strategies for avoiding demonstrations of low ability (Cury, Da
Fonseca, Zahn, & Elliot, 2008). Researchers found incremental ability beliefs positively and
significantly predicted problem-focused coping such as active coping, planning, seeking social
support for instrumental reasons and emotion-focused coping such as seeking social support for
emotional reasons, including the venting of emotions. It showed that incremental ability beliefs
seemed to increase the use of various coping strategies when students had difficulties (Doronh et
al., 2009). As some researchers pointed out, adaptive coping requires a flexible use of diverse
coping strategies including both problem-focus coping and emotion-focus coping (Doronh et al.,
2009). From these findings, it can be assumed that if students increase their incremental ability
beliefs they will be better able to actively manage their challenges by using various coping
strategies. Researchers suggested that during coping process both problem-focus coping and
emotion-focus coping were presented in each interaction (Frydenberg & Ramon Lewis, 2000).
14
COPE
A multidimensional coping inventory (COPE) was developed and validated to measure the
various ways how people respond to stress (Carver et al., 1989). COPE consists of 13 scales
(four items each) which contain both emotion-focused coping strategies and problem-focused
coping strategies as shown table 2.2. From a second order factor analysis, four factors were
found and each factor captured three scales. First factor consisted of active coping, planning, and
suppression of competing activities. Second factor consisted of seeking social support for
instructional reasons, seeking social support in emotional reasons, and focus on and venting of
emotions. Third factor consisted of denial, mental disengagement, and behavioral disengagement.
Fourth factor was composed of acceptance, restraint coping, and positive interpretation & growth
(Carver et al., 1989).
Table 2.2: COPE scales – continued
Active coping:
I take additional action to try to get rid of the
problem.
I concentrate my efforts on doing something
about it.
I do what has to be done, one step at a time.
I take direct action to get around the problem.
Planning:
I try to come up with a strategy about what to
do.
I make a plan of action.
I think hard about what steps to take.
I think about how I might best handle the
problem.
Suppression of competing activities:
I put aside other activities in order to
concentrate on this.
I focus on dealing with this problem, and if
necessary let other things slide a little.
I keep myself from getting distracted by other
thoughts or activities.
I try hard to prevent other things from
interfering with my efforts at dealing with this.
Positive reinterpretation and growth:
I look for something good in what is
happening.
I try to see it in a different light, to make it
seem more positive.
I learn something from the experience.
I try to grow as a person as a result of the
experience.
Acceptance:
I learn to live with it.
I accept that this has happened and that it
can't be changed.
I get used to the idea that it happened.
I accept the reality of the fact that it
happened.
Religious coping:
I seek God's help.
I put my trust in God.
I try to find comfort in my religion.
I pray more than usual.
Focus on and venting of emotions:
I get upset and let my emotions out.
15
Table 2.2: COPE scales – continued
Restraint Coping:
I force myself to wait for the right time to do
something.
I hold off doing anything about it until the
situation permits.
I make sure not to make matters worse by
acting too soon.
I restrain myself from doing anything too
quickly.
Use of instrumental social support:
I ask people who have had similar experiences
what they did.
I try to get advice from someone about what to
do.
I talk to someone to find out more about the
situation.
I talk to someone who could do something
concrete about the problem.
I let my feelings out.
I feel a lot of emotional distress and I find
myself expressing those feelings a lot.
I get upset, and am really aware of it.
Denial:
I refuse to believe that it has happened.
I pretend that it hasn't really happened.
I act as though it hasn't even happened.
I say to myself "this isn't real."
Behavioral disengagement:
I give up the attempt to get what I want.
I just give up trying to reach my goal.
I admit to myself that I can't deal with it,
and quit trying.
I reduce the amount of effort I'm putting
into solving the problem.
Mental disengagement:
I turn to work or other substitute activities to
take my mind off things.
I go to movies or watch TV, to think about it
less.
I daydream about things other than this.
I sleep more than usual.
Use of emotional social support:
I talk to someone about how I feel.
I try to get emotional support from friends or
relatives.
I discuss my feelings with someone.
I get sympathy and understanding from
someone.
*Note: From “Assessing Coping Strategies: A Theoretically Based Approach” by Carver, Sheier,
& Weintraub, 1989, Journal of Personality and Social Psychology, 56(2), 272.
Zeidner (1998) conducted factor analysis using subscales of COPE (Carver et al., 1989)
with 241 college students. Two psychologists selected two items (out of four) for each scale
based on face validity procedures. He categorized three types of coping strategies including
problem-focused coping, emotion-focused coping, and avoidance coping from this analysis as
shown table 2.3.
16
Table 2.3: Coping strategies from Zeidner (1998)’s study
Coping Strategies
Scales
Problem-focused coping
Active coping
Planning
Suppression of competing activities
Emotion-focused coping
Emotional social support
Instrumental social support
Ventilation
Positive reinterpretation
Restraint
Humor
Avoidance coping
Mental disengagement
Behavioral disengagement
Religion
Denial
Alcohol
*Note: From Test anxiety: the state of the art, by Zeidner, 1998, New York: Plenum Press.
Problem-focused coping refers to efforts to manage the problem by removing the stressor
(e.g., studying hard, carefully planning study schedule for preparing for an exam). Emotionfocused coping refers efforts to reduce the emotional stress associated with the stressful situation
(e.g., seeking emotional support from friends, distancing oneself from the evaluative threat).
Avoidance-oriented coping refers to either the use of person-oriented strategies (e.g., seeking out
others) or task-oriented strategies (e.g., engaging in non-relevant tasks such as watching TV) to
avoid the stressful situation (Zeidner, 1998).
Among the three coping strategies, a recent experimental study found positive effects on
emotional support based on the four scales related to emotion-focus coping from COPE in
decreasing math anxiety and improving math performance (Shen, 2009). Shen (2009) selected
positive reinterpretation and growth (RG), focus on and venting of emotions (VE), use of
instrumental social support (IS), and use of emotional support (ES) from COPE (Carver et al.,
1989). Shen also used pedagogical agents and table 2.4 presents four coping strategies that Shen
(2009) used together with example behaviors from the agents to provide each coping strategy to
students.
17
Table 2.4: Examples of COPE categories used in Shen (2009)’s study
COPE categories
Example Behavior from the Agent Providing
Emotional Support
Seeking Social Support for emotional Agent script “… I was also a GED student. I know
Reasons (ES)
you are feeling anxious now. I know what that’s like
(e.g. get sympathy and understanding when I had the same class last year.”
from someone; discuss feelings with
someone)
Positive representation and growth
(When answered the practice question wrong) Agent
(RG)
script: “Do not worry…. It just takes a little time to
(e.g. try to see it from a different light grasp all these concepts. The good news is that you
and make it look positive; it is a
will have another exercise problem to practice. I
learning process from experience)
predict that you will be fine as the learning
progresses.”
Instrumental social support (IS)
Agent script “If you are feeling anxious, the best
(e.g. get advice from someone about
thing is to just focus on the learning task and as you
what to do; talk to someone to find
make progress, it will probably go away.”
out more about the situation; talk to
someone who could do something
concrete about the problem)
Venting of emotions (VE)
Agent script “Take a deep breath and as you exhale,
(e.g. let the emotions out; express the let your feelings go out with it. Then type in the
feelings)
textbox to let me know how you feel now.”
*Note: From “The effects of agent emotional support and cognitive motivational messages on
math anxiety, learning, and motivation”, by Shen, 2009, Dissertation at Florida State
University.
Shen (2009) examined the effects of emotional support and cognitive motivational
messages delivered by pedagogical agents on math anxiety, learning and motivation. The
pedagogical agent is an animated life-like character on a digital screen that provides
contextualized advice, feedback, and information with voice output, gestures, body movements,
and facial expressions which is used to support learning in a computer based learning
environment (Johnson, Rickel, & Lester, 2000; Moreno, Mayer, Spires, & Lester, 2001).
Participants were 109 General Educational Development (GED) students in a math course and
they were randomly assigned to one of four conditions: emotional support-only, cognitive
motivational messages-only, both, and neither. Participants in all conditions worked on a
computer-based learning module individually in a classroom during regular class time. An
instructor pedagogical agent led the learning module and provided both emotional support and
cognitive motivational messages. Also, a peer pedagogical agent was used to provide better
18
emotional support, but not for cognitive motivational messages. The findings indicated that
emotional support focusing on coping strategy had positive effects in decreasing math anxiety
and increasing learning. However, this study failed to find a positive effect of emotional support
on the dependent variable of motivation. The present study contained an emotional support
component that is similar to Shen’s (2009) but changed the cognitive motivational messages
treatment to focus on entity versus incremental ability beliefs.
19
Cognitive motivational messages
Another possible solution to reduce math anxiety can be derived from the focus on the
cognitive dimension of math anxiety related to worry of performing well in mathematics (Ho et
al., 2000; Shen, 2009). In this study, cognitive motivational messages specifically contained
ability beliefs change messages to alleviate the cognitive dimension of math anxiety. Review of
the literature related to motivation, motivational messages and incremental ability beliefs will be
presented in this section.
ARCS Model for motivational design
Motivation is a key element in performance and it refers to what people desire, what
people decide to do, and what people commit to do (Keller, 2010). In other words, motivation
explains what goals people choose to pursue and how much effort people input to pursue the
goals. Motivational design works as a bridge between the motivation studies and the practices for
enhancing people’s motivation. Motivational design has three basic assumptions: it should be
based on a holistic understanding of the situation, it needs to include a diagnosis of the situation,
and, finally, it should employ multiple strategies that are appropriate to solve the problem in their
prescription (Keller, 2010).
Keller (1979) proposed an integrated motivation model based on an extensive literature
review of motivation studies. The ARCS model (Keller, 1979) consists of four categories:
Attention, Relevance, Confidence, and Satisfaction. Table 2.5 presents definitions for each
category and strategies to promote each category of motivation.
20
Table 2.5: ARCS definitions and related strategies
ARCS category
Definition
Attention
Relevance
Confidence
Related strategies
Capturing the interest of
A1. Perceptual arousal
learner/simulating the
A2. Inquiry Arousal
curiosity to learn
A3. Variability
Meeting the personal
R1. Goal Orientation
needs/goals of the learner to
R2. Motive Matching
effect a positive attitude
R3. Familiarity
Helping the learners’
C1. Learning Requirements
beliefs/feel that they will
C2. Success Opportunities
succeed and control their
C3. Personal Control
success
Satisfaction
Reinforcing accomplishment
S1. Natural Consequences
with rewards (internal and
S2. Positive Consequences
external)
S3. Equity
*Note: From Motivational design for learning & performance: The ARCS model approach,
Keller, 2010
Aligned through ARCS model, Keller suggested a systematic approach on the motivational
design process which consisted of 10 steps, including audience analysis (Keller, 2010). Audience
analysis provides a basic understanding of an audience and a guideline on what aspects of the
motivation problem should be highlighted in motivational design. As shown figure 2.1, the
audience’s attention readiness, perceived relevance, confidence felt, and satisfaction potential are
examined through audience analysis using various resources such as an interview with
instructors, direct observation of audience, or analysis of existing materials.
21
Figure 2.1: Audience analysis result from a pilot test
In this study, audience analysis was conducted to find the most significant motivational
problem of participants using an instructor interview and class observation during a pilot test and
found low confidence was determined to be the most critical motivational issue toward math
problem solving in GED students. Keller (2008) derived the first principles of motivation to
learn and e-learning from comprehensive synthesis of the motivation and reviewing available
literature. One of principles is “Motivation to learn is promoted when learners believe they can
succeed in mastering the learning task”. This principle aligned to confidence category of ARCS
model. Following this principle and the audience analysis result, confidence among the four
categories in ARCS model was highlighted in this study, and related theories and studies will be
presented in the next section.
Achievement Motivation & Expectancy-value theory
Expectancy-value theory stemmed from a cognitive perspective on motivation and this
theory regarded people as active and rational decision makers for their motivation (Pintrich &
Schunk, 1996). Eccles et al (1983) proposed a social cognitive expectancy-value model of
achievement motivation. This model focused on the expectations of students and the role of
those expectancies on academic success and perceived valuation of academic tasks. This model
showed achievement behavior would be predicted by expectancy and value. These two
components – expectancy and value –are a part of an individual’s internal cognitive belief
22
system. The expectancy construct refers to a student’s thought on whether he or she is able to
perform the required task. The value construct refers to a student’s thought on why he or she
should perform the task (Eccles, 1983; Visser & Keller, 1990; Wigfield & Eccles, 2000).
Also, value and expectancy were assumed to be influenced by task-specific beliefs such as
the ability beliefs as shown figure 2.2 (Wigfield & Eccles, 2000). The distinction between
expectancy and ability beliefs is expectancy for success focused on the future, but ability beliefs
focused on current ability.
Figure 2.2: Relation among ability beliefs, expectancy, value, and performance
Students’ ability beliefs were emphasized in cognitive theories of achievement motivation
based on this theoretical background (Stipek, 2002). One of most well-known theories is the
implicit theory about intelligence by Dweck & Elliot (1983).
Implicit theory
Implicit theory separated students’ ability beliefs into two categories: entity belief and
incremental belief (Dweck, 1999). Students who have entity belief think intelligence is a fixed,
immutable aspect, but students who have incremental belief believe intelligence is a malleable
construct which can be cultivated through efforts and learning (Blackwell et al., 2007; Dweck,
1999; Kennett & Keefer, 2006). Many studies investigated how students’ ability beliefs
determined the goals they pursued, their reaction to difficulties, and how well they did in school
(Aronson et al., 2002; Dweck, 1999). Students who have incremental belief tend to try to
23
overcome challenges using various strategies such as increased effort and persistence (Doronh et
al., 2009; Kasimatis et al., 1996). Students who have incremental beliefs tend to focus on
remediating their deficiencies after experiencing failure (Nussbaum & Dweck, 2008).
Research on Incremental ability beliefs
There was empirical evidence that students who were provided treatment for incremental
ability belief performed better than students who did not get the treatment (Aronson et al., 2002;
Good et al., 2003). Undergraduate students who were encouraged to have an incremental ability
belief earned a higher GPA than students who did not get the treatment, controlling for SAT
scores (Aronson et al., 2002). Seventh-grade students who got incremental ability belief
messages earned higher standardized reading test scores than students who did not receive the
messages (Good et al., 2003).
A recent longitudinal study determined junior high school students who possessed
incremental ability beliefs were more likely to believe dedicated study and practice effort was
effective and necessary to achieve their academic goals than students who displayed entity
ability belief (Blackwell et al., 2007). Students who demonstrated incremental beliefs do not
equate a failure to a lack of ability. Instead, these students were more likely to consider changes
to their learning strategy methodology. Overall, students who demonstrated incremental beliefs
at the start of junior high school performed better in mathematics than students who had entity
beliefs, controlling for prior achievement (Blackwell et al., 2007).
Blackwell et al (2007) also examined incremental ability beliefs intervention influencing
students’ achievement and motivation based on their longitudinal study results. Ninety-one
seventh grade students participated in an eight-week workshop. Forty-eight students were taught
that intelligence was malleable and could be further developed. Forty-three students in the
control group were presented a lesson about memory function and participated in related
discussions. The intervention was developed based on previous studies (e.g., Aronson et al.,
2002), including an article, activities, and discussions. An article named “You can grow your
intelligence: New research shows the brain can be developed like a muscle” was used for
incremental ability belief intervention group. This article contained interesting analogies which
supported students’ understanding, such as the concept that brains could be developed like
muscles to become stronger with familiar examples such as babies demonstrating a higher degree
24
of intelligence as they learned. Activities and discussions were followed as a part of the
intervention. It was found that incremental ability belief intervention had positive effects on the
students’ ability beliefs change. Also, researchers examined the growth curve of students’ math
grades over the length of the course to see the effects of the intervention on achievement. They
found students who were in the incremental ability beliefs intervention group that had showed a
continuing decline of grades halted the decline after a few months of incremental ability beliefs
intervention and started to increase their grades (Blackwell et al., 2007).
Based on this theoretical and empirical evidence, researchers suggested teachers encourage
students to adopt incremental ability beliefs rather than entity ability beliefs (Brophy, 2010;
Dweck, 1999). Brophy (2010) suggested teachers encourage incremental ability beliefs by
providing feedback which contained messages stimulating appreciation of current
accomplishments and implying that the students’ final goals would be attained. Regarding the
nature of the feedback, more specific feedback which aligned to students’ current task with
appreciation of students’ efforts toward the task was recommended instead of generic evaluative
feedback or praise of students’ abilities (Dweck, 1999).
Even though there were several studies which investigated the effects of incremental
ability beliefs on students’ achievement, there was no attempt to investigate the effect of
incremental ability belief on alleviating math anxiety and enhancing math problem solving. Thus,
an incremental belief message was adapted as one independent variable in this study to alleviate
math anxiety and cognitive strategies in the form of motivational messages (Visser & Keller,
1990) are applied as a way to affect students’ ability belief.
Motivational messages
Motivational messages are one kind of strategy to promote students’ motivation to learn
through messages in forms of letters, mini posters, or e-mails which are designed based on
motivation analysis (Visser & Keller, 1990). There were several empirical studies which found
that motivational messages had a positive effect on motivation. For example, Visser and Keller
(1990) provided motivational messages which were developed based on the four categories of
the ARCS model in the form of feedback after tests and summaries of assignments using cards,
letters, and mini posters. They found that motivational messages had positive effects on students’
attitude and performance.
25
As use of computers and the internet has increased, studies on motivational messages
using e-mail were conducted. Keller, Deimann, & Liu (2005) investigated the effects of
distributed use of motivational e-mail messages following a model of motivation volition on
students’ motivation. It was found this treatment had positive effects on students’ confidence and
achievement. Kim and Keller (2008) designed personalized motivational volitional e-mail
messages to facilitate motivation including all components of the ARCS model (Keller, 1987) attention, relevance, confidence, satisfaction and volition. The findings indicated that
personalized motivational volitional e-mail messages had positive effect on confidence compared
with non-personalized motivational volitional e-mail messages.
In a previous study, Baylor et al (2004) adopted a pedagogical agent which delivered
motivational messages in a computer based module. A pedagogical agent provided motivational
support to one group and not in the case of another group. They found students who worked with
an agent which delivered motivational support had higher self-efficacy and viewed the agent as
more human-like and engaging than the students in the other group. Students in motivational
messages group had higher scores on learning, but this result was not statistically significant.
Verbal suggestion, affiliation, positive feedback, self-efficacy, and emotional support were
included in the motivational messages for the study (Baylor et al., 2004).
As a part of his study, Shen (2009) examined the effect of motivational messages as a way
to alleviate cognitive math anxiety. He conducted a motivational analysis based on Keller’s
analysis frame (Keller, 2010) and found that the major problem of his participants was
confidence. Thus, cognitive motivational messages embedded in the instructor agent were
mainly developed for the confidence issues, but there were also some messages for relevance and
satisfaction issues. Table 2.6 presents examples of the cognitive motivational messages which
were used in Shen (2009)’s study.
26
Table 2.6: Examples of motivational messages used in Shen (2009)’s study based on ARCS
categories
ARCS Motivational
Examples of the cognitive Motivational Messages
Categories
Confidence
“You’ve made it through the first section of the instructional
module. Next, you will practice solving compass direction
problems. Come on, and give it your best effort! You will be
able to solve them by applying the things that you have just
learned. “(C)
“Some people think math is hard. But if you go slow and think
about what I am saying, you will find out you can do this.” (C)
Relevance
“This instructional module will help you to answer similar
problems on the GED math exam.” (R)
Satisfaction
“All right! You are making good progress! You have
accomplished a lot and are almost done!” (S)
“You are now ready for the final problem!. Congratulations on
being persistent in your efforts to master this important math
skill.” (S)
*Note: From “The effects of agent emotional support and cognitive motivational messages on
math anxiety, learning, and motivation”, by Shen, 2009, Dissertation at Florida State University.
The findings from Shen (2009)’s study indicated that the motivational messages had no
effect on math anxiety, motivation, and math learning. Possible reason why he failed to find
effects of motivational messages was likely due to the overlapped nature of emotional support
and cognitive motivational messages. His cognitive motivational messages encompassed
confidence, relevance, and satisfaction issues. It made the cognitive motivational messages more
general than specific, so it might have caused confusion in students with emotional support. Thus,
in this study, cognitive motivational messages were clearly distinguished from emotional support
messages by focusing only incremental ability beliefs.
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Pedagogical agent
Benefits of pedagogical agent
One limitation in computer based modules is the lack of interaction between students and
instructor. Thus, students sometimes feel they are isolated from the instructor and have problems
maintaining their pace in learning. To assist in resolving this issue, a pedagogical agent has been
developed for use in a computer based learning environment (Shen, 2009).
A pedagogical agent is an animated, anamorphic character on a digital screen that provides
contextualized advice, feedback, and information with voice output, gestures, body movements,
and facial expressions (Johnson et al., 2000; Moreno et al., 2001). Pedagogical agents are used in
a computer based learning environment to support learning processes (Johnson et al., 2000). For
example, in mathematics computer based instructional program, a pedagogical agent might have
the features of a white, 35 year old male dressed up as a teacher. Pedagogical agents have been
suggested as one of the useful strategies for improving learners’ self-efficacy in mathematics
(Kim et al., 2007).
A pedagogical agent enhanced students’ self-efficacy, because the pedagogical agent
stimulates social interaction in students (Kim et al., 2007). Students studying with pedagogical
agent felt affiliation with the pedagogical agent due to the pedagogical agent’s humanlike
features in terms of verbal and non-verbal communications. Moreover, the motivational
messages from the pedagogical agent played a role as social persuasion, so students’ selfefficacy was increased. Social persuasion is one of the sources which affect students’ selfefficacy (Bandura, 1997). Social persuasion means some encouragement from parents, teachers,
and peers whom students trust make students more confident in their academic capabilities to
success on tasks (Usher, 2009). Pedagogical agents can perform various roles as parents, teachers,
and peers to students and motivational messages from a pedagogical agent can serve as a social
persuasion to students. As a result, the pedagogical agent’s social interaction effects worked as
social persuasion on students and the social persuasion lead to increased self-efficacy in the
students (Kim et al., 2007).
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Roles of pedagogical agent
Pedagogical agents can be used in three roles: expert (knowledgeable), motivator
(supportive) and mentor (both knowledgeable and supportive). An empirical research compared
the impact of these three roles in information acquisition and self-efficacy (Baylor & Kim, 2005).
The expert agent provided topical information, the motivator agent provided emotional
encouragement and the mentor agent supplied both information and encouragement. The result
confirmed that the mentor agent led to the highest improved information acquisition and selfefficacy in contrast to the results that the expert agent improved only information acquisition and
the motivation agent improved only self-efficacy (Baylor & Kim, 2005). It was also indicated
that use of two agents together – motivator and expert – had greater effects on motivation and
learning than use of the mentor agent alone, based on several research findings (Baylor, 2009). It
is because students can clearly distinguish information delivered by different agents. It suggested
it would be effective to design separate agents based on the distinct messages each agent delivers.
An experimental study found that students working with co-learner agents who exhibited
characteristics of compassion and interest had significantly enhanced feelings of trust, social
support, and increased memory recall (Lee et el., 2007). It demonstrated the positive effects the
caring co-learner agent had on students’ affective part and learning.
Based on these result, each pedagogical agent mainly delivered different kind of messages
in this study. The instructor agent primarily delivered instruction, the peer agent mainly
delivered emotional support messages, and a scientist agent mainly provided cognitive
motivational messages. However, in order to increase ecological validity of emotional support,
the instructor agent also delivered a limited number of emotional support messages in a manner
that would naturally occur while teaching. If only the peer agent provided emotional support to
students, the ecological validity of emotional support might have been lowered. It was expected
that students would have high validity on emotional support provided by the instructor agent.
Thus, the instructor agent mainly provided math instruction and some emotional support
messages. Thus, pedagogical agents in this study provided both cognitive (information) and
motivational (encouragement) feedback to learners using text and voice together. For example,
an instructor agent provided concrete information related to the Pythagorean Theorem and verbal
encouragement message to students to boost confidence on the tasks during the instruction.
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Research on pedagogical agent
The effects of pedagogical agents have been supported by several studies. Learners
studying with a pedagogical agent experienced deeper learning and higher motivation than
learners without an agent (Moreno et al., 2001). The findings related to the effects of pedagogical
agent on mathematics education revealed that there was a positive effect on learners’ attitude
towards learning, performance, interest and motivation when adopting a pedagogical agent in a
computer mediated learning environment (Baylor, 2002; Baylor & Ryu, 2003). There were
empirical studies which found positive effects of pedagogical agent on pre-service teachers’
attitude towards learning, performance, and motivation (Baylor, 2002; Baylor & Ryu, 2003).
Shen (2009) analyzed the trends of agent-related studies and summarized three key issues
on agent studies. First, the voice of agent was explored in many research studies. It was found
that students considered a human voice agent more human-like and engaging than machine voice
agent (Atkinson, Merrill, & Patterson, 2002) and students in human voice agent group performed
better on learning transfer than students in machine voice group (Atkinson, Mayer, & Merrill,
2005). It shows human voice is recommended to enhance learning and interest. Second, roles of
agents have been consistently studied. The mentor agent improved overall learning and
motivation (Baylor & Kim, 2005) and agents acting in the mastery model were more likely to
promote learning, while agents acting in the coping model were more likely to promote learner
interaction, interest, and motivation (Ebbers, 2007). Third, the animation of agents was another
focus of agent-related studies. Lester, Town, & FitzGerald (1999) found that appropriate facial
expression and gestures had positive effects on learning and motivation. Atkinson, Merrill, &
Patterson (2002) also found that agents’ animation quality enhanced learning. These results
suggested that agents’ nonverbal cues were important as well as verbal cues on increasing
students’ motivation and learning.
On the basis of literature analysis, Shen (2009) conducted a qualitative study to figure out
the desirable features of agents from six GED students’ reactions. He separated key desirable
features of agents into three categories: overall manner, facial expression, and voice quality.
Students preferred agents which saw them as individuals, not as a group using “you” and “I”
instead of “he” and “she”. Also, students desired eye contact, smiles, and changing facial
expressions. Regarding the agents’ voice, positive, expressive, and encouraging voices were
30
preferred by students. Table 2.7 summarized the desirable features of agents based on Shen
(2009)’s qualitative study.
Table 2.7: Desired features of agents: Results from the quantitative study
Themes
Desirable Agent Emotional Ability
Agent Overall Manner
See learner as individual, not as a group
Agent Facial Expression
Eye contact, smiles, change facial expression
Agent Voice Quality
Positive, expressive, encouraging
*Note: From “The effects of agent emotional support and cognitive motivational messages on
math anxiety, learning, and motivation”, by Shen, 2009, Dissertation at Florida State University.
Based on the qualitative study results, Shen developed two pedagogical agents for his
experimental study. One was an instructor agent named Dr. Hendricks and another was a peer
agent named Kate. Both agents were developed as African-Americans in consideration of
students’ preference for same ethnicity in agents, following Baylor (2003)’s study. AfricanAmerican students tended to perceive the agent instructors who had the same ethnicity as more
engaging, credible, instructor-like, and able to better facilitate learning (Baylor & Ryu, 2003).
Due to the fact that majority of Shen (2009)’s participants were African-American, he chose to
develop African-American agents.
Dr. Hendricks led the entire course instruction, providing lecture, emotional support and
cognitive motivational messages. Kate was used in the case of emotional support group when
students clicked the “Talk to a buddy” button. Kate provided two kinds of coping messages
(refer to Table 2.4) including emotional social support (ES) and helped students vent their
emotions (VE). Shen (2009) focused on Kate’s role as expressing sympathy and understanding
of students’ anxiety as a peer perspective. The vent emotions (VE) focused on encouraging
learners to type their feelings in a text box in the computer based module (Shen, 2009). He found
students who vented their emotions many times had significantly lower math anxiety than
students who seldom vented their emotions.
Based on Shen (2009)’s findings, venting emotion (VE) messages were provided every
time students feel nervous regardless of whether the students clicked the “Talk to a buddy”
31
button or not. Students’ choice on venting emotion (VE) was excluded in this study to control
difference effects of emotional support between students who choose to vent their emotion and
not vent their emotion with in the same group. There are several differences in the use of
pedagogical agents in this study compared to Shen’s (2009) study.
First, the instructor agent delivered lectures and emotional support, not cognitive
motivational messages. If the instructor agent delivered both emotional support and cognitive
motivational message, there was possibility students would confuse the nature of two different
support systems. To prevent this confusion, the instructor agent did not deliver cognitive
motivational messages in this study.
Second, the peer agent mainly provided emotional support, but also some of the cognitive
motivational messages. Based on previous study, a peer agent can be effectively used as a
motivator (Baylor & Kim, 2005). So, it was deemed appropriate to deliver both emotional
support and cognitive motivational messages through the peer agent. Also, as previously
mentioned, based on Shen (2009)’s finding, students’ choice for venting their emotions (VE) was
excluded this study to prevent the different effects of emotional support within the same group.
Third, a scientist agent was used in this study to enhance the credibility of incremental
ability belief messages. The scientist agent delivered only cognitive motivational messages to
differentiate her role with the instructor agent (Baylor, 2009).
Thus, in this study, pedagogical agents were used as a way to affect students’ self-efficacy
and promote higher math problem solving skills. Also, it was expected that pedagogical agents
would have positive effect on decreasing math anxiety.
32
Self-efficacy
Another reason that students are not good at math problem solving is potentially the
students’ low self-efficacy (Pajares & Graham, 1999; Pajares & Kranzler, 1995; Pajares & Miller,
1994). Self-efficacy is defined as the judgment of people towards their own capabilities to
organize and perform activities which are required to achieve success in specific tasks (Bandura,
1997). Self-efficacy plays a vital role in determining how much effort will need to be expended
to accomplish tasks, and how long effort will need to be sustained to complete the task
(Zimmerman, 2000). In this study, self-efficacy refers to the student’s beliefs that he is capable
of expending the necessary effort to succeed in math problem solving and he can sustain his
efforts long enough to achieve success in math problem solving.
In general, a number of studies related to self-efficacy revealed that there was a positive
relationship between self-efficacy and academic achievement (Pintrich & de Groot, 1990);
(Pintrich & Schunk, 1996). Learners with high self-efficacy tended to perform better than
learners who had low self-efficacy (Pintrich & Schunk, 1996). This general result was also found
in research related to self-efficacy and math problem solving. In the context of math problem
solving, learners with high self-efficacy were more likely to express greater interest and attention
in working through problems to reach adequate solutions, had an optimistic belief on their
success and they had higher performance than low self-efficacy learners in undergraduate
students and middle school students (Pajares, 1996). Various studies indicated that self-efficacy
was strongly related to the math problem solving performance (Pajares & Graham, 1999; Pajares
& Kranzler, 1995; Pajares & Miller, 1994).
Pajares and Miller (1994) reported that self-efficacy to solve mathematics problems was
more predictive of math problem solving performance than other variables, such as gender, race,
educational background, math anxiety, and the perceived usefulness of mathematics. Pajares and
Kranzler (1995) indicated that self-efficacy made a contribution to the prediction of math
problem solving as strong as general mental capability. Hoffman (2009) formed two primary
conclusions from these prior studies about self-efficacy and math problem solving. First, selfefficacy is a powerful individual factor that can minimize other different, individual factors such
as anxiety and interest in math problem solving. Second, self-efficacy affects math problem
33
solving performance beyond existing ability and skills, which confirms the findings of Pajares
and Kranzler (1995).
Given the theoretical and empirical evidence, self-efficacy was chosen as a dependent
variable to determine the relationship with math problem solving.
Hypotheses
This study is designed to investigate elements of the following question:
How do emotional support and cognitive motivational messages delivered via pedagogical
agents affect students’ math anxiety, self-efficacy, and math problem solving? There were two
independent variables: emotional support and cognitive motivational messages. In regard to this
general question, the following questions were investigated:
1. What are the effects of emotional motivational (Emot M) support delivered via
pedagogical agents on math anxiety, self-efficacy, and math problem solving?
2. What are the effects of cognitive motivational (Cog M) messages delivered via
pedagogical agents on math anxiety, self-efficacy, and math problem solving?
3. What are the interactive effects of emotional support and cognitive motivational
messages delivered via pedagogical agents on math anxiety, self-efficacy, and math
problem solving and how do they depend on each other?
In order to answer these questions, this study implemented four methods to investigate
treatment effects on math anxiety, self-efficacy, and math problem solving: 1) emotional support
(Emot M) distributed via pedagogical agents condition, 2) cognitive motivational (Cog M)
messages distributed via pedagogical agents condition, 3) emotional support (Emot M) and
cognitive motivational (Cog M) messages distributed via pedagogical agents condition, and 4)
neither emotional support (Emot M) nor cognitive motivational (Cog M) messages distributed
via pedagogical agents condition. Table 2.8 describes these four conditions based on treatment in
this study.
34
Table 2.8: Four conditions based on treatment in this study
Emotional support (Emot M)
Presence
Cognitive
motivational
messages (Cog M)
Presence
Absence
Emot M + Cog M Group
Emot M Group
Absence
Cog M only Group
Control group
Hypothesis 1: Students who will receive emotional support will have low math anxiety,
high self-efficacy, and better performance on math problem solving. Specifically, it is
hypothesized that students’ math anxiety will be alleviated, self-efficacy will be enhanced, and
math problem solving will be improved among those receiving emotional support, opposed to the
students not receiving such strategies.
Rationale for hypothesis 1: There were several theoretical and empirical studies that
provided evidence which supported the positive effects of emotional support on alleviating math
anxiety and improving math learning. Hembree (1990) found emotional support in terms of
teaching students coping strategies which had positive effects on decreasing math anxiety and
increasing math learning. Emotional support delivered by pedagogical agents focusing on four
categories of coping strategies showed positive effects on alleviating math anxiety and enhancing
math performance (Shen, 2009). Based on this evidence, it is hypothesized that students who will
be provided emotional support will have low math anxiety, high self-efficacy, and better
performance on math problem solving than students not in the case study.
Hypothesis 2: Students who will receive cognitive motivational messages will have low
math anxiety, high self-efficacy, and better performance on math problem solving. Specifically,
it is hypothesized that students’ math anxiety will be alleviated, self-efficacy will be enhanced,
and math problem solving among will be improved those receiving cognitive motivational
messages than the students not receiving such strategies.
Rationale for hypothesis 2: Research related to motivational messages found positive
effects on students’ attitude and confidence (Keller, Deimann, & Liu, 2005; Kim & Keller, 2008;
35
Visser & Keller, 1990). Also, some studies found positive effect of motivational messages on
students’ learning (Keller, Deimann, & Liu, 2005; Visser & Keller, 1990). Baylor et al (2004)
investigated the effects of motivational messages delivered by a pedagogical agent in a computer
based module. They found students who worked with an agent which delivered motivational
support had higher self-efficacy than students who were not in the case study. Based on this
evidence, it is hypothesized that the use of cognitive motivational messages will decrease math
anxiety, enhance self-efficacy, and improve students’ math problem solving.
Hypothesis 3: It is expected that an interaction of emotional support and cognitive
motivational messages will result in statistically significant differences in students’ math anxiety,
self-efficacy, and math problem solving. Specifically, it is hypothesized that the presence of
emotional support and cognitive motivational messages will have the greatest positive influence
on students’ math anxiety, self-efficacy, and math problem solving.
Rationale for hypothesis 3: A recent study explored relationships between students’ ability
beliefs and coping strategies (Doronh et al., 2009). They found incremental ability beliefs
positively and significantly predicted problem-focused coping such as seeking social support for
instrumental reasons and emotion-focused coping such as seeking social support for emotional
reasons and venting emotions. It showed incremental ability beliefs seemed to increase the use of
various coping strategies when students have difficulties (Doronh et al., 2009). Hembree (1990)
also found mixed use of affective intervention and cognitive intervention had greater effects on
alleviating math anxiety than single use of each intervention. Based on previous studies, it is
hypothesized there will be an interaction effect between emotional support and cognitive
motivational messages, so students in the combination treatment group will have less math
anxiety, higher self-efficacy, and better performance on math problem solving.
In summation, it is expected that students in the combination group (emotional support +
cognitive motivational messages) will score higher than students in the emotional support-only
group who will, in turn, score higher than the cognitive motivational messages-only group, who
will score higher than the control group (Emot M+Cog M> Emot M> Cog M> No
EmotM/CogM) in math problem solving.
36
The order of predicted effects between emotional support and cognitive motivational
messages is based on previous studies (Hembree, 1990; Shen, 2009; Wigfield & Meece, 1988).
Hembree (1990) found affective intervention to alleviate emotionality toward math had greater
effect than cognitive intervention to reduce worry toward math. Wigfield and Meece (1988)
found affective math anxiety correlated more strongly and negatively to elementary and middle
school students’ math ability perceptions and math performance than cognitive math anxiety.
Shen (2009) found positive effects of emotional support on alleviating math anxiety and
enhancing math performance but he could not find any effect of cognitive motivational messages
on math anxiety and math performance.
Based on this evidence, it is hypothesized emotional support only treatment will have
greater effects than a cognitive motivational messages-only treatment on math anxiety, selfefficacy, and math problem solving.
Purpose and Predictions
The purpose of this study is to examine the effects of emotional support (coping strategy)
and cognitive motivational messages (incremental ability belief) provided by pedagogical agents
(instructor agent, scientist agent, peer agent) on math anxiety, self-efficacy, and math problem
solving.
Thus, it is expected that students who receive emotional support and incremental belief
messages will have less math anxiety, higher self-efficacy, and perform better in math problem
solving than students who do not receive them.
37
CHAPTER THREE
METHOD
Introduction
This study is designed to explore the effects of emotional support and cognitive
motivational messages delivered by pedagogical agents on math anxiety, self-efficacy, and math
problem solving. In this section, the research methodology will be described in detail including
participant, research design, levels of independent variables, measurement of dependent
variables, treatment materials, and procedure of experiment.
Participants
In this study, participants were 83 General Education Development (GED) students as
confirmed by Shen (2009), because GED students tend to have high math anxiety, low selfefficacy, and low math problem solving skill. GED students are individuals who have not earned
a high school diploma, so they are preparing to take the GED test to receive a high school
equivalency diploma. Math is one of test subjects in GED test, so GED students who are
attending GED math class in a community college in Florida were the participants in this study.
Majority of participants were African-American. Sixty-seven students were African-American, 8
were White/Caucasian, 5 were Asian/Pacific Islander, and 3 were Hispanic/Latino. Forty-eight
students were males and thirty-five students were females. Students’ ages varied 16 to 48 and the
average age was 24.07 years old.
There were three math classes for GED students based on their math ability level. Students
in all three classes were included in the study, but students in each class were randomly assigned
to one of four groups to control the difference of their pre-math problem solving skills.
The sample size was determined based on power analysis result using G-Power 3.0
software, a medium effect size of .15 (Cohen, 1992), alpha level of .05 and a power level of .8.
A total 40 sample size was suggested to get a power of .8, and if the sample size would be
increased to 56, it would be expected to get a power of .95. Thus, to get more power of the result,
at least 20 participants in each group and 83 participants in total were used in this study.
38
Research Design
This study is designed as a 2 x 2 factorial design. There are two independent variables in
this study – one is emotional support and another is cognitive motivational messages. Each
independent variable has two levels – presence and absence, so there are four groups based on
the support provided by the pedagogical agents. Modules in all groups were led by the instructor
agent because he taught lectures and gave feedback on practice questions.
Group Emot M + Cog M (E+C): The participants in this group studied the computer based
module including emotional support and cognitive motivational messages delivered by instructor
agent, peer agent and scientist agent.
Group Cog M (C): The participants in this group studied the computer based module
including cognitive motivational messages delivered by peer agent and scientist agent.
Group Emot M (E): The participants in this group studied the computer based module
including emotional support delivered by instructor agent and peer agent.
Group Control (control group): The participants in this group studied the computer based
module led by instructor agent without any support.
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Independent Variables
There are two independent variables in this study which are represented by the messages to
be delivered by the pedagogical agents. The pedagogical agent is used as a delivering method of
a computer based module in this study, but not an independent variable of this study.
One independent variable is emotional support and the second independent variable is
cognitive motivational messages. Each variable has two levels: presence or absence.
Emotional support
In this study, emotional support focused on coping strategy. Four types of coping
strategies among all 13 scales from the COPE (Carver et al., 1989) were adapted as the
emotional support provided by the pedagogical agents as same as Shen (2009)’s study because
he found positive effects of these strategies on students’ math anxiety and math learning. Four
types of coping strategies are seeking social support for emotional reasons (ES), seeking social
support for instrumental reasons (IS), positive representation and growth (RG), and venting of
emotions (VE) (see Table 2.4).
The operational definition of emotional support is based on Shen (2009)’s study, because
he retrieved four coping strategies aligned to his purpose of study from COPE (Carver et al.,
1989) and he found those coping strategies had positive effects on alleviating math anxiety and
facilitating students’ learning. Thus, emotional support in this study refers to messages
containing coping strategies delivered by the instructor agent and peer agent to help students
overcome their nervousness in math learning and encourage them to keep studying the math
module.
Emotional support was provided to individual students by pedagogical agents (instructor
agent and peer agent) during the computer based module in the proceeding four situations. Shen
(2009) found the first and second situations are necessary based on his qualitative study results.
Examples for emotional support on each situation are presented in table 3.1.
1) At the beginning of the module: Instructor agent presented some emotional support
messages to alleviate students’ nervousness on math, specifically on geometry word problems
because the students did not have significant prior knowledge in this subject.
40
2) After students solved practice questions and their answers are incorrect: There are five
exercise questions in the module. For each question, if students answered incorrectly, the
instructor agent provided emotional support to help students overcome fear caused by failure.
3) After each section is done: The module consists of four sections, including two lecture
sections and two practice sections, and after each section the instructor agent provided some
emotional support messages to the students.
4) When the peer agent becomes available: Once the instructor agent provided some
emotional support to students after each section the peer agent then presented emotional support
as a previous GED student.
Table 3.1: Examples of emotional support in each situation
Situation
Example of emotional support
At the beginning
“If you are feeling nervous, the best thing is to just accept this
feeling. Don’t try to make it go away.
Instead, just focus on the learning task. As you make progress
you won’t feel so nervous.”
After students solved
practice exercise questions
and they answers are
incorrect
“Don’t worry, this is a learning process. You will gain
understanding of the concept by doing the exercise even if you do
not get it right the first time. Stay relaxed and keep on trying.”
After each section is done
“I understand why you feel anxious. Word problems are confusing
at times. But the following practice exercises will help you
understand the concept.”
“I know you are feeling anxious now. I have found math to be
challenging, but I also know that having anxiety is not going to
help your learning. Stay relaxed.”
When peer agent comes up
This procedure is adapted from Shen’s study (2009) since he confirmed some situations
based on the qualitative research to find the appropriate places of emotional support. Also, he
determined the effects of four coping categories on math anxiety and math learning. Sample
emotional support messages based on the four types of coping strategies are presented in table
3.2.
41
Table 3.2: Sample of emotional support messages based on four categories
COPE categories
Example emotional support messages from
agents
Seeking social support for emotional reasons
(ES)
“I know you are feeling anxious now. I have
found math to be challenging, but I also know
that having anxiety is not going to help your
learning. Stay relaxed.”
Seeking social support for instrumental
reasons (IS)
“Compass directions are confusing at times.
Let’s focus on the learning and don’t worry
about the problem too much. You will do
better next time.”
Positive representation and growth (RG)
Venting of emotions (VE)
“Don’t give up. Practice makes perfect!”
“Let your feelings out by typing in the text
box. That might help you feel better. Also, it
will be interesting to compare your feelings
later in the lesson to the way you are feeling
right now.”
Cognitive motivational messages
In this study, cognitive motivational messages were developed to focus on incremental
ability belief. Incremental ability belief messages were provided to the cognitive motivational
messages treatment group mainly by the scientist agent, while the peer agent delivered a small
amount of messages in the computer-based module with a video clip and short messages which
emphasize the students’ abilities were not fixed and could be improved through effort. Thus, in
this study, cognitive motivational messages were clearly distinguished from emotional support
by focusing on incremental ability beliefs. Based on previous studies, the operational definition
of the cognitive motivational messages in this study refers to motivational messages containing
incremental ability belief statements which emphasize the students’ abilities are malleable and
can be grown through effort and exercise.
The initial idea for cognitive motivational messages came from an article “You can grow
your intelligence: New research shows the brain can be developed like a muscle” which was
used in previous experimental study (Blackwell et al., 2007). Ninety-one seventh grade students
were participated in this study for 8 weeks. Students attended an 8-week group workshop which
included the physiology of brain and study skills and forty eight students in the experimental
42
group were taught that intelligence was not fixed and could be developed through effort.
Students in experimental group received incremental ability belief intervention such as article
reading and discussion, while forty-three students in control group had alternative readings, such
as “Memory Reading” and discussions about academic success, memory and the brain. Session 1,
2, 5, and 6 were the same for both groups but Session 3, 4, 7 and 8 were different based on group.
From this study, it was found that incremental ability belief intervention had a positive effect on
the students’ ability beliefs change. They found students who were in the incremental ability
beliefs intervention group that had showed a continuing decline of grades halted the decline after
a few months of incremental ability beliefs intervention and started to increase their grades
(Blackwell et al., 2007). Thus, cognitive motivational messages were developed by the
researcher based on Blackwell et al (2007)’s study and then were reviewed by an expert in
motivational design.
Shen (2009) conducted an experimental study to see the effects of cognitive motivational
messages on students’ math anxiety, motivation, and learning. He used cognitive motivational
messages which mainly focused on confidence but also included relevance and satisfaction
related messages and found no effect on math anxiety, motivation, and learning. There were
some differences in the use of cognitive motivational messages in this study compare to Shen
(2009)’s study.
First difference in using cognitive motivational messages with Shen’s study (2009) was the
addition of a scientist agent in this study to deliver cognitive motivational messages. Compared
to Shen’s study (2009), the cognitive motivational messages in this study contained more
specific messages focusing on incremental ability belief which were related to the confidence
category under Keller’s ARCS model. The scientist agent was adopted to make students feel
credibility towards cognitive motivational messages which were provided by the scientist agent.
At the beginning, the scientist agent showed a YouTube video about expanding neurons in brain
and explained the incremental ability belief theory that if the students made an effort to use their
mental facilities more and more, their math ability may gradually improve. After students solved
practice questions, the scientist agent provided cognitive motivational messages regardless
whether their answer was correct or not. Examples of the cognitive motivational messages which
were delivered by the scientist agent in this study are shown in Table 3.3.
43
The second difference in the cognitive motivational messages in regards to Shen’s study
(2009) is that a peer agent delivered some of cognitive motivational messages in this study.
Social interaction is expected from through use of the peer agent and it is expected to positively
affect the students’ acceptance of incremental ability beliefs (Kim & Baylor, 2004). It was
assumed that students might feel comfortable with cognitive motivational messages delivered by
the peer agent due to similarity of age and experience built into the agent’s design, which
resulted in a greater effect of the cognitive motivational messages increasing student selfefficacy. A sample of the cognitive motivational messages which were delivered by the peer
agent is shown in Table 3.3.
Table 3.3: Sample cognitive motivational messages by each agent
Delivery subject
Example of cognitive motivational messages
Peer agent
“I used to believe that I just did not have the ability to learn math. But,
after I learned how math ability can grow with effort, I changed my
belief. I became convinced that I could succeed if I tried hard.
Once I changed my belief, I did not give up for solving math problems
even though they were really difficult.
Until recently, I was not good at math. However, I am getting better
all the time because I keep studying hard to grow my “math muscles”.
I hope you can also do like me.”
Scientist agent
“The more you use your brain on these math concepts and skills, the
more connections it forms and the more your ability grows!
Isn’t it fascinating to see what is being learned by modern science?”
The third difference in the cognitive motivational messages used in this study compared to
Shen’s study (2009) is that the instructor agent did not deliver cognitive motivational messages
in this study. The instructor agent provided math content instruction and emotional support only.
If the instructor agent had also delivered cognitive motivational messages, there was possibility
that the students might confuse the meaning of the emotional support and cognitive motivational
messages. Also, it was indicated that use of two separate agents together – motivator and expert
– had a greater effect on motivation and learning than use of the mentor agent alone, based on
several research findings (Baylor, 2009). To enhance the effects of the cognitive motivational
44
messages, the scientist agent and the peer agent delivered these messages in this study, while the
instructor agent was excluded.
Dependent Variables
There are three dependent variables in this study. Math anxiety, self-efficacy and math
problem solving were measured to examine the effects of emotional support and cognitive
motivational messages.
Math anxiety
Math anxiety was measured to determine the change of students’ math anxiety before and
after participating in this study using a pre-test and post-test. Math anxiety refers students’
nervousness (affective domain) and worry about performing well (cognitive domain) on math
problems. To avoid students’ recall of the previously administered math anxiety questionnaire in
the pre-test, two different questionnaires was used in the pre-test and post-test. In the pre-test, the
Mathematics Anxiety Questionnaire (MAQ) (Wigfield & Meece, 1988) was used to measure
students’ pre-existing math anxiety before participating in this study (see Appendix B). This is a
questionnaire with 11 Likert-type scale questions ranging from 1 (Not at all) to 7 (Very much).
The Mathematics Anxiety Questionnaire (MAQ) consists of two sub-scales, one is a negative
affective reaction scale (item 1-7) and the other is a cognitive worry scale (item 8-11). The
Cronbach’s alpha for the negative affective reaction subscale is .86 and the cognitive worry scale
is .76, respectively. Students filled out this questionnaire at the beginning of the module learning
sequence.
Mathematics Anxiety Scale (MAS) (Fennema & Sherman, 1976) was used to measure the
students’ math anxiety after participating in this study during the post-test (see Appendix C).
This is a questionnaire with 12 Likert-type scale questions ranging from 1 (Strongly disagree) to
5 (Strongly agree). The Cronbach’s alpha of this scale is .89. Students answered this
questionnaire after they finished learning the module. Less than 5 minutes were required to
finish each math anxiety questionnaire.
45
Self-efficacy
In this study, self-efficacy refers to the student’s beliefs that he is capable of expending the
necessary effort to succeed in math problem solving and he can sustain his efforts long enough to
achieve success in math problem solving. Students’ self-efficacy was measured to examine the
differences among groups based on effects of emotional support and cognitive messages through
pre-test and post-test.
Some researchers have suggested methods to develop a self-efficacy scale (Baylor et al.,
2003; Bandura & Schunk, 1981; Kim & Baylor, 2004; Pajares, 1996). They recommend “How
sure are you …?” types of question to best capture information about self-efficacy. Based on this
recommendation, a scale consists of five items was developed to measure students’ self-efficacy
related toward math problem solving in this study. This is a questionnaire with 5 Likert-type
scale questions ranging from 1 (Strongly disagree) to 5 (Strongly Agree), two items for pre-test
and three items for post-test (see Appendix C). This questionnaire was modified to be aligned to
the context of this study by focusing on math problem solving using Kim (2004)’s questionnaire.
She reported Cronbach’s alpha of her self-efficacy questionnaire as .95. Less than 5 minutes
were required to finish this questionnaire.
Math problem solving
Math problem solving refers students’ ability to analyze a novel problem and apply their
math knowledge to solve the problem. Math problem solving was measured by pre-test and posttest using three different items, but having similar content (see Appendix A). Before learning the
module, students solved one item related to Pythagorean Theorem to measure students’ prior
problem-solving level. After finishing the learning module, students solved another two items
which were related to Pythagorean Theorem. These items measured the level of students’
analysis skills and application skills of their existing mathematical knowledge and skills in a
novel situation. Less than 10 minutes were required to solve the test.
Students were encouraged to write down as much detail as possible about all steps of the
problem-solving process. A grading rubric developed by Shen (2009) was used for the scoring of
each item. Inter-rater reliability was calculated using two coders’ scores and Cohen’s Kappa
was .84 in this study. Table 3.4 presents the rubric categories and scores for math problem
solving.
46
Table 3.4: Math problem solving grading rubric by Shen (2009)
Rubric category
Score
Demonstrate due south, due north, due east, and due west
1 point
Identify the triangle
Identify the right angle in the triangle
Demonstrate the concept of leg squared + leg squared = Hypotenuse squared
1 point
1 point
1 point
Demonstrate the answer in the correct formula
1 point
*Note: From “The effects of agent emotional support and cognitive motivational messages on
math anxiety, learning, and motivation”, by Shen, 2009, Dissertation at Florida State University.
Agent development
Three pedagogical agents, including an instructor agent, peer agent and scientist agent,
were developed using Character Builder. Character Builder is an agent development tool which
allows developing an agent’s whole body, facial expressions, and gestures. It is also easy to
synchronize the recorded human voice with each agent using this tool. Researchers already
developed a module for the 2010 spring semester to exercise developing agents and two
instructional design experts advised the module.
Agents were developed based on Shen (2009)’s qualitative study. He explored six GED
students’ reaction on his module with an instructor agent name as Dr. Hendricks. He excluded all
support messages for the qualitative study and found the situations when students felt anxious
during learning the module. The results showed students felt anxious at the end of lecture and
after solving exercise questions, especially when their answers were incorrect. He also found
which characteristics students desired in agents. Students wanted agents to view them as
individuals, and not as a group. Students also desired eye contact, smiles, and facial expressions
from the agents. Students also preferred positive, expressive, and encouraging voices in agent
(Shen, 2009).
Based on finding from previous studies (Baylor & Ryu, 2003), pedagogical agents were
developed as African-American to facilitate students to feeling similarities with agents. Also, this
study followed Shen (2009)’s findings when developing agents and modules. Agents used the
47
term “you” instead of “he/she”, and made eye contact with students, smiled at students, and used
facial expression when talking. Real human voices were used as the agents’ voices, so three
African-American volunteers who have positive, expressive, and encouraging voice recorded
their voice for each agent in this study.
For instance, both male and female college students expressed a higher degree of
motivation and increased positive perceptions of agents after they had worked with a male agent
rather than a female agent when designing an e-learning class (Baylor & Kim 2006). Researchers
hypothesized that real world gender-related social stereotypes might be consistently applied to
learner-agent relationships based on this outcome. Social stereotype s in gender refer to a
person’s belief that a male individual is more credible on masculine topics, such as science and
sports, while a female individual is more credible on feminine topics, such as fashion and
cosmetics (Moreno, 2002). In an academic setting such as college, many courses contained
masculine topics, for which students tended to prefer a male pedagogical agent because of the
implied social stereotype (Baylor & Kim, 2006; Moreno, 2002). Based on these findings, the
instructor agent was developed as a male agent and the scientist agent and peer agent were
developed as female agents, since the instructor agent taught math content and the scientist agent
and peer agent focused on delivering emotional support and cognitive motivational messages.
Figure 3.1 presents the actual features of three agents – instructor, peer, and scientist agent.
Instructor agent
– Mr. Gibbs
Peer agent
- Trina
Scientist agent
– Dr. Baker
Figure 3.1: Instructor agent, peer agent, scientist agent in this study
48
Materials
Students in all groups worked on a computer based module about the Pythagorean
Theorem in their classroom. The lengths of the modules were varied depending on their group
because of the absence and presence of emotional support and cognitive motivational messages.
The average module length was 45 to 60 minutes.
Each module was designed to teach students about words, concepts and formulas related to
the Pythagorean Theorem, which finally required students to solve novel problems by applying
what they learned from module. There were two parts in this module and each part had one
lecture session and one practice session, totaling four sessions in all. In the first lecture session,
students learned key words and concepts related to compass directions in the Pythagorean
Theorem. After first lecture, students solved practice questions related to the first lecture.
Afterwards, the second lecture session was presented containing concepts and formulas related to
the right triangle and the Pythagorean Theorem. Students then participated in a practice session
related to the second lecture. Based on their group, students either received emotional support or
cognitive motivational messages during the learning phase of the module. Math content was
revised based on Shen (2009)’s content, which was designed by Shen and an additional GED
math instructor for his study. Students worked individually on the module with a headset in the
classroom.
Table 3.5 presents the overall structure of the module regarding the math contents and the
presence (P) or absence (that is, not present - NP) of each independent variable. The storyboard
which shows all the content of the module is in Appendix E.
Table 3.5: Overall module structure of this study - continued
Session
Emotional Cognitive
support
motivational
group
messages group
Emotional support Control
and cognitive
group
motivational
messages group
P
P
Lesson Introduction
P
P
Pre-test
P
P
P
P
Introduce Scientist agent
NP
P
P
NP
49
Table 3.5: Overall module structure of this study - continued
Session
Emotional Cognitive
support
motivational
group
messages group
Emotional support Control
and cognitive
group
motivational
messages group
P
NP
Cognitive motivational
messages
Introduce Unit 1 Presentation
NP
P
P
P
P
P
Cognitive motivational
messages
Unit 1 Presentation
NP
P
P
NP
P
P
P
P
Anxiety self-report question
P
NP
P
NP
Emotional support
P
NP
P
NP
Cognitive motivational
messages
Unit 1 Practice
NP
P
P
NP
P
P
P
P
Cognitive motivational
messages
Emotional support (if students
cannot select the right answer)
Anxiety self-report question
NP
P
P
NP
P
NP
P
NP
P
NP
P
NP
Emotional support
P
NP
P
NP
Cognitive motivational
messages
Introduce Unit 2
NP
P
P
NP
P
P
P
P
Cognitive motivational
messages
Unit 2 Presentation
NP
P
P
NP
P
P
P
P
Emotional support
P
NP
P
NP
Cognitive motivational
messages
Emotional support
NP
P
P
NP
P
NP
P
NP
Anxiety self-report question
P
NP
P
NP
Emotional support
P
NP
P
NP
Cognitive motivational
messages
Unit 2 Practice
NP
P
P
NP
P
P
P
P
50
Table 3.5: Overall module structure of this study - continued
Session
Emotional Cognitive
support
motivational
group
messages group
Emotional support Control
and cognitive
group
motivational
messages group
P
NP
Cognitive motivational
messages
Emotional support (if
students cannot select the
right answer)
Anxiety self-report question
NP
P
P
NP
P
NP
P
NP
P
NP
Emotional support
P
NP
P
NP
Cognitive motivational
messages
Post-test
NP
P
P
NP
P
P
P
P
Thank you message
P
P
P
P
Procedure
The procedure of this study consists of three parts: pre-experiment, experiment, and postexperiment. Descriptions for each part are presented this section.
Pre-experiment
Eighty-eight participants in three math classes were randomly assigned to one of four
groups in this study: emotional support-only group, cognitive motivational messages-only group,
emotional support and cognitive motivational messages group, and a control group. The
researcher had a short orientation about the study before experiment and received approval from
the participants through a consent form. Each group used a different classroom to control the
students’ interaction between different treatment groups.
Experiment
Students filled out demographic survey, math anxiety pre-test, self-efficacy survey, ability
belief survey, and a math problem solving pre-test at the beginning of experiment,. During the
module learning phase, two presentation sessions were delivered and one practice session
followed after each of the presentation sessions. The difference in the modules for each group
51
was the presence or absence of emotional support and cognitive motivational messages. Math
content and practice questions were identical regardless of group. It took 45-60 minutes to finish
the module learning phase depending on the time required to deliver the emotional support and
cognitive motivational messages. Table 3.6 summarizes the content included in the module,
which agents were used, and the length of time it took to finish the module based on group.
Table 3.6: Summary of organization of module of each group
Presentation Practice Emotional Cognitive
support
motivational
messages
Emotional
support only
group
Cognitive
motivational
messages
only group
Emotional
support and
cognitive
motivational
messages
group
Control
group
Use of
Agents
Maximum
Length
(minutes)
P
P
P
NP
Instructor
Peer
50
P
P
NP
P
Instructor
Scientist
50
P
P
P
P
Instructor
Peer
Scientist
60
P
P
NP
NP
Instructor
45
Post-experiment
The post-test was conducted after the experiment to measure the students’ math anxiety,
self-efficacy, ability belief, and math problem solving. It took approximately 15 minutes to finish
all post-test items. Table 3.7 summarizes activities and time for each phase of the study.
52
Table 3.7: Summary of activities and time for each stage of the study
Stage
Activities
Pre-experiment
Experiment
Post-experiment
Introduction to research
Get approval for consent form
Group assignment
Demographic survey
Pre-test – math anxiety, self-efficacy, ability belief,
math problem solving
Study the module
Post-test – math anxiety, self-efficacy, ability belief,
math problem solving
Time (minutes)
15
45-60
15
Data Analysis
Data was analyzed using MANOVA (Multivariate Analysis Of Variance) and ANOVA
(Analysis Of Variance) in this study.
53
CHAPTER FOUR
RESULTS
This study explored the effects of emotional support and cognitive motivational messages
delivered by pedagogical agents on math anxiety, self-efficacy, and math problem solving. There
were three hypotheses in this study based on theoretical and empirical evidences.
Hypothesis 1: Students who will receive emotional support will have low math anxiety,
high self-efficacy, and better performance on math problem solving. Specifically, it is
hypothesized that students’ math anxiety will be alleviated, self-efficacy will be enhanced, and
math problem solving will be improved among those receiving emotional support, opposed to the
students not receiving such strategies.
Hypothesis 2: Students who will receive cognitive motivational messages will have low
math anxiety, high self-efficacy, and better performance on math problem solving. Specifically,
it is hypothesized that students’ math anxiety will be alleviated, self-efficacy will be enhanced,
and math problem solving among will be improved those receiving cognitive motivational
messages than the students not receiving such strategies.
Hypothesis 3: It is expected that an interaction of emotional support and cognitive
motivational messages will result in statistically significant differences in students’ math anxiety,
self-efficacy, and math problem solving. Specifically, it is hypothesized that the presence of
emotional support and cognitive motivational messages will have the greatest positive influence
on students’ math anxiety, self-efficacy, and math problem solving.
Factorial MANOVA and follow-up ANOVA were conducted to test these three
hypotheses. SPSS 19.0 was used for statistical analysis. Preliminary analysis was done to
identify missing data and outliers. And then, the assumptions for MANOVA and ANOVA were
tested.
Preliminary Data Analysis
Missing data
Eighty-eight students participated in this study. Five students did not complete all of
surveys. These five students’ data was excluded from the results.
54
Pre-test on math problem solving
As in Shen’s (2009) study, a one item pre-test was used to make sure that there was no
difference among groups in their prior knowledge of math problem solving with regard to the
Pythagorean Theorem. Total score of the pre-test was 5 point. Mean score of 83 students’ pretest on math problem solving was 1.83 with a standard deviation of 1.86. Mean score of the math
problem solving pre-test was 1.86 for emotional support and cognitive motivational messages
group, 1.86 for emotional support group, 1.62 for cognitive motivational messages group, and
2.00 for control group, respectively. There was no significant group difference in students’ math
problem solving before experiment.
Test of Statistical Assumptions
Assumption 1: Independence of observations
To satisfy this assumption, participants were randomly assigned to one of four groups for
this study. Students required to work on a computer based module individually and no
interaction with other students were allowed during experiment.
Assumption 2: Homoscedasticity
To check the univariate homogeneity of the dependent variables across groups, Levene’s
test was used. Table 4.1 shows that Levene’s test is not significant with p > .05. This means the
assumption of homogeneity of variance was met in this data.
Table 4.1: Levene's Test of Equality of Error Variances
F
df1
Math anxiety
.62
Self-efficacy
1.67
Math problem solving
1.59
df2
3
3
3
Sig.
79
79
79
.61
.18
.20
*p < .05
The Box’s test reveals that equal variances can be assumed with p>.05, so Wilks’ Lambda
will be used as the test statistic in this study.
55
Table 4.2: Box's Test of Equality of Covariance Matrices
Box's M
F
df1
df2
Sig.
17.49
.90
18
21967.87
.57
*p < .05
Assumption 3: Multi-normality
MANOVA is based on an assumption that the observations on all dependent variables
must follow a multivariate normal distribution in each group. Kolmogorov-Smirnov test
indicates that math problem solving violated multi-normality assumption. However, MANOVA
and ANOVA are robust to moderate violation of multi-normality with 20 in the smallest cell
(Mertler & Vannatta, 2001). This study satisfied the condition for at least 20 participants on each
cell, so MANOVA and ANOVA can be used for analysis regardless of the violation of multinormality assumption.
Assumption 4: Linearity
Assumption of linearity was tested by scatter plots, and it shows an elliptical shape. Thus,
the Linearity assumption was met in this study.
Assumption 5: Correlations
In MANOVA, Correlations among dependent variables should be not too high or low.
Table 4.3 shows that correlations among dependent variables are low or moderate, so this
assumption was met in this study.
Table 4.3: Correlations among dependent variables
Math anxiety
Self-efficacy
Math anxiety
Self-efficacy
Math problem
solving
-.47**
-.11
-.47**
.31**
56
Math problem
solving
-.11
.31**
-
Examinations of the Hypotheses
Descriptive Statistics
Table 4.4 presents the descriptive statistics for three dependent variables: math anxiety,
self-efficacy, and math problem solving, based on four different groups: cognitive motivational
messages and emotional support (A), no support (C), emotional support only (E), and cognitive
motivational messages only (I) in this study. Possible range of all three dependent variables in
this study is 0 to 5.
Table 4.4: Means and Standard Deviations of Math Anxiety, Self-efficacy, and Math Problem
Solving of Each Group
GROUP
Mean
Std. Deviation
N
Math Anxiety
A
2.71
.72
21
C
3.50
.68
20
E
2.57
.75
21
I
2.76
.83
21
Total
2.88
.82
83
Self-efficacy
A
C
E
I
Total
3.92
2.58
3.21
3.97
3.43
.77
.74
1.16
.81
1.04
21
20
21
21
83
Math Problem
Solving
A
C
E
I
Total
2.90
1.33
1.64
1.31
1.80
2.14
1.64
1.96
1.87
1.99
21
20
21
21
83
Note. A= Emotional support + Cognitive motivational messages group
C= Control group
E= Emotional support only group
I= Cognitive motivational messages only group
*Maximum possible score for Math Anxiety, Self-efficacy, and Math Problem Solving was 5, respectively.
57
Table 4.5 shows the descriptive statistics for three dependent variables: math anxiety, selfefficacy, and math problem solving, based on presence and absence of two independent variables:
emotional support and cognitive motivational messages.
Table 4.5: Means and Standard Deviations of three DVs based on two IVs
Emotional Support
Absent
Present
N M
SD
N M
SD
Cognitive
Absent Math Anxiety 20 3.50 .68
21 2.57 .75
Motivational
Self-efficacy 20 2.58 .74
21 3.21 1.16
Messages
Math
20 1.33 1.64 21 1.64 1.96
Problem
Solving
Present Math Anxiety 21
Self-efficacy 21
Math
21
Problem
Solving
2.76 .82
3.97 .81
1.31 1.87
21
21
21
2.71 .72
3.92 .77
2.90 2.14
*Maximum possible score for Math Anxiety, Self-efficacy, and Math Problem Solving was 5, respectively.
Two-way MANOVA Test
A two-way MANOVA was conducted to determine the effect of emotional support and
cognitive motivational messages on the three dependent variables of math anxiety, self-efficacy,
and math problem solving. MANOVA results indicate emotional support (Wilks' Lambda = .85,
F (3, 77) = 4.37, p < .05) and cognitive motivational messages (Wilks' Lambda = .73, F (3, 77) =
9.41, p < .05) significantly affect the combined DV of math anxiety, self-efficacy, and math
problem solving. Also, interaction effect (Wilks' Lambda = .87, F (3, 77) = 3.75, p < .05) was
found as shown as table 4.6.
58
Table 4.6: Effects of Emotional Support and Cognitive Motivational Messages from MANOVA
Effect
Value
F
Hypothesis df Error df
Sig.
a
Intercept
Pillai's Trace
.98
1316.53
3.00
77.00
.00
a
Wilks' Lambda
.02
1316.53
3.00
77.00
.00
Hotelling's
51.29
1316.53a
3.00
77.00
.00
Trace
Roy's Largest
51.29
1316.53a
3.00
77.00
.00
Root
Pillai's Trace
Wilks' Lambda
Hotelling's
Trace
Roy's Largest
Root
.15
.85
.17
4.37a
4.37a
4.37a
3.00
3.00
3.00
77.00
77.00
77.00
.01
.01
.01
.17
4.37a
3.00
77.00
.01
Cognitive
Pillai's Trace
Motivational Wilks' Lambda
Messages
Hotelling's
Trace
Roy's Largest
Root
.27
.73
.37
9.41a
9.41a
9.41a
3.00
3.00
3.00
77.00
77.00
77.00
.00
.00
.00
.37
9.41a
3.00
77.00
.00
Emotional
Support*
Cognitive
Motivational
Messages
.13
.87
.15
3.75a
3.75a
3.75a
3.00
3.00
3.00
77.00
77.00
77.00
.01
.01
.01
.15
3.75a
3.00
77.00
.01
Emotional
Support
Pillai's Trace
Wilks' Lambda
Hotelling's
Trace
Roy's Largest
Root
*p < .05
59
Individual Hypothesis Test
Hypothesis 1: Effects of Emotional Supports on Math Anxiety, Self-efficacy, and Math
problem Solving
Students who will receive emotional support will have low math anxiety, high self-efficacy,
and better performance on math problem solving. Specifically, it is hypothesized that students’
math anxiety will be alleviated, self-efficacy will be enhanced, and math problem solving will be
improved among those receiving emotional support, opposed to the students not receiving such
strategies.
Descriptive Statistics
Table 4.7 presents descriptive statistics regarding the effects of emotional support on math
anxiety, self-efficacy, and math problem solving. The mean score for the students in the
emotional support group (M=2.64, SD=.73) was lower than the mean score for the students in
the no emotional support group (M=3.12, SD=.84) on the Math Anxiety Scale. Emotional
support group (M=3.56, SD=1.04) scored higher than no emotional support group (M=3.29,
SD=1.04) on Self-efficacy Survey. Students in the emotional support group (M=2.27, SD=2.12)
scored higher than students in the no emotional support group (M= 1.31, SD=1.74) on math
problem solving tests.
60
Table 4.7: Means and Standard Deviations: Effects of Emotional Support on Math anxiety, Selfefficacy, and Math Problem Solving from MANOVA – continued
Emotional
Support
Mean
Std. Deviation
N
Math Anxiety
Absent
3.12
.84
41
Present
2.64
.73
42
Total
2.88
.82
83
Self-efficacy
Absent
Present
Total
3.29
3.56
3.43
1.04
1.04
1.04
41
42
83
Math Problem
Solving
Absent
Present
Total
1.31
2.27
1.80
1.74
2.12
1.99
41
42
83
*Maximum possible score for Math Anxiety, Self-efficacy, and Math Problem Solving was 5, respectively.
Univariate MANOVA Test
A Univariate MANOVA test was conducted to determine group difference between
emotional support group and no emotional support group in the combined DV of math anxiety,
self-efficacy, and math problem solving. MANOVA result revealed significant differences
between emotional support group and no emotional support group on the dependent variables,
Wilks' Lambda = .86, F (3, 79) = 4.22, p < .05 as shown as table 4.8.
Table 4.8: MANOVA results: Effects of Emotional Support
Effect
Value
F
Hypothesis df
a
Intercept
Pillai's Trace
.98
1207.88
3.00
Wilks' Lambda
.02
1207.88a
3.00
a
Hotelling's Trace
45.87
1207.88
3.00
Roy's Largest Root
45.87
1207.88a
3.00
Emotional
Support
Pillai's Trace
Wilks' Lambda
Hotelling's Trace
Roy's Largest Root
.14
.86
.16
.16
4.22a
4.22a
4.22a
4.22a
*p < .05
61
3.00
3.00
3.00
3.00
Error df
79.00
79.00
79.00
79.00
Sig.
.00
.00
.00
.00
79.00
79.00
79.00
79.00
.01
.01
.01
.01
Follow-up ANOVA Test
ANOVA was conducted on each dependent variable as a follow up test to MANOVA.
A)
Effect of Emotional Support on Math Anxiety
Follow up ANOVA revealed that emotional support had a significant effect on math
anxiety, F (1, 81) = 7.82, p < .05 as shown as table 4.9. Emotional support group (M = 2.64, SD
= .73) reported significantly lower math anxiety than no emotional support group (M = 3.12, SD
= .84). The effect size estimate was d=.61 which is a moderate effect size (Cohen, 1988).
Table 4.9: ANOVA table: Effects of Emotional Support on Math Anxiety
Sum of Squares
df
Mean Square
Between Groups
4.84
1
4.84
Within Groups
50.17
81
.62
Total
55.01
82
F
7.82
Sig.
.01
*p < .05
B)
Effect of Emotional Support on Self-efficacy
Emotional support had no significant effect on self-efficacy, F (1, 81) = 1.41, p > .05 as
shown as table 4.10.
Table 4.10: ANOVA table: Effects of Emotional Support on Self-efficacy
Sum of Squares
df
Mean Square
Between Groups
1.52
1
1.52
Within Groups
87.49
81
1.08
Total
89.01
82
F
Sig.
1.41
.24
*p < .05
C) Effect of Emotional Support on Math Problem Solving
There was a significant difference between groups in math problem solving based on
presence and absence of emotional support, F (1, 81) = 5.02, p < .05 as shown as table 4.11.
Emotional support group (M = 2.27, SD = 2.12) scored significantly higher in the post-test of
62
math problem solving than no emotional support group (M = 1.32, SD = 1.74). The effect size
estimate was d=.49 which is a moderate effect size (Cohen, 1988).
Table 4.11: ANOVA table: Effects of Emotional Support on Math Problem Solving
Sum of Squares
Df
Mean Square
F
Sig.
Between Groups
18.99
1
18.99
.03
Within Groups
306.48
81
3.78
Total
325.47
82
5.02
*p < .05
Hypothesis 2: Effects of Cognitive Motivational Messages on Math Anxiety, Self-efficacy,
and Math Problem Solving
Students who will receive cognitive motivational messages will have low math anxiety,
high self-efficacy, and better performance on math problem solving. Specifically, it is
hypothesized that students’ math anxiety will be alleviated, self-efficacy will be enhanced, and
math problem solving among will be improved those receiving cognitive motivational messages
than the students not receiving such strategies.
Descriptive Statistics
Table 4.12 presents descriptive statistics regarding the effects of cognitive motivational
messages on math anxiety, self-efficacy, and math problem solving. The mean score for the
students in the cognitive motivational messages group (M=2.73, SD=.77) was lower than the
mean score for the students in the no cognitive motivational messages group (M=3.02, SD=.85)
on the Math Anxiety Scale. Cognitive motivational messages group (M=3.94, SD=.78) scored
higher than no cognitive motivational messages group (M=2.90, SD=1.02) on Self-efficacy
Survey. Students in the cognitive motivational messages group (M=2.11, SD=2.15) scored
higher than students in the no cognitive motivational messages group (M= 1.49, SD=1.79) on
math problem solving tests.
63
Table 4.12: Means and Standard Deviations: Effects of Cognitive Motivational Messages on
Math anxiety, Self-efficacy, and Math Problem Solving from MANOVA
Cognitive
Motivational
Messages
Mean
Std. Deviation
N
Absent
3.02
.85
41
Math Anxiety
Present
2.73
.77
42
Total
2.88
.82
83
Self-efficacy
Absent
Present
Total
2.90
3.94
3.43
1.02
.78
1.04
41
42
83
Math Problem
Absent
Present
Total
1.49
2.11
1.80
1.79
2.15
1.99
41
42
83
Solving
*Maximum possible score for Math Anxiety, Self-efficacy, and Math Problem Solving was 5, respectively.
Univariate MANOVA Test
A Univariate MANOVA test was conducted to determine group difference between
cognitive motivational messages group and no cognitive motivational messages group in the
combined DV of math anxiety, self-efficacy, and math problem solving. MANOVA result
revealed significant differences between cognitive motivational messages group and no cognitive
motivational messages group on the dependent variables, (Wilks' Lambda = .74, F (3, 79) = 9.12,
p < .05) as shown as table 4.13.
Table 4.13: MANOVA results: Effect of Cognitive Motivational Messages
Hypothesis
Effect
Value
F
df
Error df
a
Intercept
Pillai's Trace
.98 1310.17
3.00
79.00
Wilks' Lambda
.02 1310.17a
3.00
79.00
a
Hotelling's Trace
49.75 1310.17
3.00
79.00
Roy's Largest Root
49.75 1310.17a
3.00
79.00
Cognitive
Pillai's Trace
Motivational Wilks' Lambda
Messages
Hotelling's Trace
Roy's Largest Root
.26
.74
.35
.35
9.12a
9.12a
9.12a
9.12a
*p < .05
64
3.00
3.00
3.00
3.00
79.00
79.00
79.00
79.00
Sig.
.00
.00
.00
.00
.00
.00
.00
.00
Follow-up ANOVA Test
ANOVA was conducted on each dependent variable as a follow up test to MANOVA.
A) Effect of Cognitive Motivational Messages on Math Anxiety
Follow up ANOVA revealed that cognitive motivational messages had no significant effect on
math anxiety, F (1, 81) = 2.66, p > .05 as shown as table 4.14.
Table 4.14: ANOVA table: Effects of Cognitive Motivational Messages on Math Anxiety
Sum of Squares
Df
Mean Square
F
Sig.
Between Groups
1.75
1
1.75
Within Groups
53.26
81
.66
Total
55.01
82
2.66
.11
*p < .05
B)
Effect of Cognitive Motivational Messages on Self-efficacy
Follow up ANOVA revealed that cognitive motivational messages had a significant effect
on self-efficacy, F (1, 81) = 27.45, p < .05 as shown as table 4.15. Cognitive motivational
messages group (M = 3.94, SD = .78) reported significantly higher self-efficacy than no
cognitive motivational messages group (M = 2.90, SD = 1.02). The effect size estimate was
d=.1.15 which is a large effect size (Cohen, 1988).
Table 4.15: ANOVA table: Effects of Cognitive Motivational Messages on Self-efficacy
Sum of Squares
22.53
Df
1
Mean Square
22.53
Within Groups
66.48
81
.82
Total
89.01
82
Between Groups
*p < .05
65
F
27.45
Sig.
.00
C) Effect of Cognitive Motivational Messages on Math Problem Solving
Follow up ANOVA indicated that there was no significant difference between groups in
math problem solving based on presence and absence of cognitive motivational messages, F (1,
81) = 2.03, p > .05 as shown as table 4.16.
Table 4.16: ANOVA table: Effects of Cognitive Motivational Messages on Math Problem
Solving
Sum of Squares
Df Mean Square
F
Sig.
Between Groups
7.96
1
7.96
2.03
.16
Within Groups
Total
317.51
325.47
81
82
3.92
*p < .05
Hypothesis 3: Interaction Effects of Emotional Support and Cognitive Motivational Messages
on Math Anxiety, Self-efficacy, and Math Problem Solving
It is expected that an interaction of emotional support and cognitive motivational
messages will result in statistically significant differences in students’ math anxiety, self-efficacy,
and math problem solving. Specifically, it is hypothesized that the presence of emotional support
and cognitive motivational messages will have the greatest positive influence on students’ math
anxiety, self-efficacy, and math problem solving.
MANOVA Test
MANOVA revealed an interaction effect (Wilks' Lambda = .87, F (3, 77) = 3.75, p < .05)
on combined DV of math anxiety, self-efficacy, and math problem solving.
Follow-up ANOVA Test
Follow up ANOVA revealed that there was an interaction effect of emotional support and
cognitive motivational messages on math anxiety, F (1, 79) = 7.17, p < .05 as shown as table
4.17. Students in both groups (no cognitive motivational messages group or cognitive
motivational messages group) reported lower math anxiety when they received emotional
support. However, students who were in the no cognitive motivational messages group showed a
bigger decrease on their math anxiety when they received emotional support than students who
were in cognitive motivational messages group as shown as figure 4.1.
66
Post-hoc analysis revealed that math anxiety of students in control group was significantly
higher than other three groups – emotional support only group, cognitive motivational messages
only group, and emotional support and cognitive motivational messages group. The difference
among emotional support only group, cognitive motivational messages only group, and
emotional support and cognitive motivational messages group was not significant in post-hoc
analysis. It means when students did not receive any support (emotional support or cognitive
motivational messages), their math anxiety was the highest. When students received any kind of
support - emotional support only, cognitive motivational messages only, and both emotional
support and cognitive motivational messages, their math anxiety was decreased.
Table 4.17: ANOVA table: Interaction Effects of Emotional Support and Cognitive
Motivational Messages on Math Anxiety
Type III Sum of
Source
Squares
Df
Mean Square
F
Sig.
a
Corrected Model
10.68
3
3.56
6.35
.00
Intercept
689.53
1
689.53
1229.05
.00
Emotional
Support
5.02
1
5.02
8.95
.00
Cognitive
Motivational
Messages
1.89
1
1.89
3.36
.07
Emotional
Support*
Cognitive
Motivational
Messages
4.02
1
4.02
7.17
.01
Error
44.32
79
.56
Total
741.29
83
Corrected Total
55.01
82
67
Figure 4.1: Interaction Effects of Emotional Support and Cognitive Motivational Messages on
Math Anxiety
Follow up ANOVA revealed that there was no interaction effect of emotional support and
cognitive motivational messages on self-efficacy, F (1, 79) = 2.949, p > .05. Also, it was
revealed that there was no interaction effect of emotional support and cognitive motivational
messages on math problem solving, F (1, 79) = 2.307, p > .05.
68
CHAPTER FIVE
DISCUSSIONS
Overview
The purpose of this study was to investigate how emotional support and cognitive
motivational messages affected students’ math anxiety, self-efficacy, and math problem solving.
Emotional support messages were designed to alleviate students’ affective dimension of math
anxiety. Emotional support messages were developed based on Shen’s (2009) study which was
based on the multidimensional coping inventory (COPE) (Carver et al., 1989). In this study,
emotional support messages included four scales related to emotion-focus coping which are
positive reinterpretation and growth (RG), focus on and venting of emotions (VE), use of
instrumental social support (IS), and use of emotional support (ES) from COPE (Carver et al.,
1989). It was expected that emotional support messages focusing on coping strategies would
have positive effects on decreasing students’ emotional conflict such as nervousness. Cognitive
motivational messages were designed to reduce students’ cognitive dimension of math anxiety
which related to worry of performing well in mathematics (Ho et al., 2000; Shen, 2009). It was
expected that cognitive motivational messages focusing on ability beliefs change messages
would have positive effects on alleviating students’ cognitive math anxiety and enhancing selfefficacy as well.
Eighty-eight GED students enrolled in GED math classes were distributed to four groups
(emotional support only, cognitive motivational messages only, emotional support and cognitive
motivational messages, and a control group) and they studied a computer based module
individually for 45 to 60 minutes. Math anxiety, self-efficacy, math problem solving was
measured before and after the treatment. Two different math anxiety questionnaires
[Mathematics Anxiety Questionnaire (MAQ) (Wigfield & Meece, 1988) and Mathematics
Anxiety Scale (MAS) (Fennema & Sherman, 1976)] were used in the pre-test and post-test to
avoid students’ recall on the previously administered math anxiety questionnaire in the pre-test.
In this study, self-efficacy refers to the student’s beliefs that he is capable of expending the
necessary effort to succeed in math problem solving and he can sustain his efforts long enough to
achieve success in math problem solving. Students’ self-efficacy was measured to examine the
69
differences among groups based on effects of emotional support and cognitive messages by pretest and post-test. Self-efficacy before treatment was measured with one item self-efficacy
questionnaire and self-efficacy toward the topic they learned from the module was measured
with two items self-efficacy questionnaires after the treatment. Self-efficacy questionnaires were
modified to be aligned with the context of this study focusing on math problem solving using
Kim’s (2004) questionnaire. Before treatment, students solved one novel item related to the
Pythagorean Theorem to measure their prior problem solving level and then they solved another
two novel items related to the Pythagorean Theorem after the treatment. Math problem solving
items were developed based on Shen (2009)’s items.
This chapter discusses the findings of this study in respect to previous research findings.
Major contributions of this study, limitations, implications, and possible directions of further
research are described in this chapter as well.
70
Overall effects of emotional support
It was revealed that emotional support significantly affected the combined DV of math
anxiety, self-efficacy, and math problem solving. This meant students who received emotional
support showed difference on their combined DV with other students who didn’t receive this
support. This result is aligned with previous research which found the main effect of the
combined DV of emotional support on math anxiety, learning, and motivation (Shen, 2009).
Specifically, it was found that students who received emotional support reported lower math
anxiety than students who did not get emotional support. Also, students who were in the
emotional support group performed better in math problem solving than students who were not
in emotional support group. These results matched with Shen (2009)’s findings. There was no
quantitative research which investigate the effects of emotional support on math anxiety and
learning before Shen (2009)’s study. This study confirmed Shen (2009)’s findings with
quantitative evidences.
Effect of emotional support on Math Anxiety
The hypothesis that emotional support would have positive effect on decreasing math
anxiety was supported in this study. Students who worked with the math module including
emotional support reported significantly lower math anxiety than students who worked with the
math module without emotional support. The positive effect of emotional support on students’
math anxiety was likely due to the fact that the students in the emotional support group had
opportunities to learn how to manage their negative emotional experience which came from
stressful situations, such as studying a new math topic and providing wrong answers on math
exercise questions (Gross, 1999). In this study, emotion-focused coping strategies were used as a
way of emotional support. Therefore, students in emotional support group had a chance to learn
how they could reduce their emotional stress associated with the stressful situation using various
emotional support messages including positive reinterpretation and growth (RG), focus on and
venting of emotions (VE), use of instrumental social support (IS), and use of emotional support
(ES).
Emotional support was provided in four situations. First, at the beginning of the module,
instructor agent (Mr. Gibbs) delivered some emotional support messages to students in the
71
emotional support group. It was expected that students’ worries on the Pythagorean Theorem
could be reduced from these messages. In many cases, students tended to start working on math
tasks with nervousness due to the unfamiliar topic. Alleviating students’ negative feelings
towards math tasks might help students continue working on the tasks rather than give up. An
example of the emotional support messages in this situation is as follows: “At this point you
might be feeling nervous. Many people do. I know I did when I studied this kind of math word
problem when I was a student. If you are feeling nervous, the best thing is to just accept this
feeling. Don’t try to make it go away. Instead, just focus on the learning task. As you make
progress you won’t feel so nervous [Social support for instrumental reasons (IS), Social support
for emotional reasons (ES)]”. Second, after students solved practice exercise questions and their
answers were incorrect, emotional support messages which aimed to decrease the students’ stress
from the failure were provided by the instructor agent (Mr. Gibbs). Shen (2009) found that
students needed emotional support in this situation from his qualitative research. Also, he found
a positive effect of emotional support from his quantitative study. Example of the emotional
support messages in this situation is as follows: “Don’t worry, this is a learning process. You
will gain understanding of the concept by doing the exercise even if you do not get it right the
first time. Stay relaxed and keep on trying [Social support for emotional reasons (ES), Positive
representation and growth (RG)]”. Third, after students finished each section, the instructor
agent (Mr. Gibbs) provided emotional support messages. Students in the qualitative research
reported they felt anxious after each section when they worked on an agent’s integrated math
computer module (Shen, 2009). Based on this result, emotional support was provided to students
after each section to decrease their math anxiety and to help them continue working on the
subsequent sections. An example of the emotional support messages in this situation is as
follows: “The Pythagorean theorem is challenging. Try to just focus on the learning and don’t
worry about the problem too much. You will get to practice [Social support for instructional
reasons (IS)]”. Fourth, when the peer agent (Trina) appeared, emotional messages especially
focusing on venting of emotions were provided to students. It was expected that if students could
have chances to vent their worries and nervousness, their math anxiety could be diminished. An
example of the emotional support messages in this situation is as follows: “I know you are
feeling anxious now. I have found math to be challenging, but I also know that having anxiety is
72
not going to help your learning. Stay relaxed and let your feelings out by typing in the text box.
When you compare how you feel now with how you felt earlier and how you will feel later on, it
might help you feel better [Social support for emotional reasons (ES), Venting of emotions
(VE)] ”.
This finding is consistent with previous research which found that emotional support
alleviated students’ math anxiety (Shen, 2009). Therefore, this study confirmed again the
positive effect of emotional support on math anxiety. By experiencing coping strategies on how
to deal with their emotional conflict toward math learning, students in the emotional support
group may have managed their stress by themselves during the module. The finding of this study
can also be supported by Hembree (1990)’s research. It was revealed that systematic
desensitization, including anxiety management and conditioned inhibition, had positive effects
on alleviating math anxiety from a meta-analysis research (Hembree, 1990).
Effect of emotional support on Math problem solving
The hypothesis that emotional support would have a positive effect on improving math
problem solving was supported in this study. Students who worked with the math module
including emotional support performed significantly better on a test applying their Pythagorean
Theorem knowledge to solve series of questions than students who worked with the math module
without emotional support. The positive effect of emotional support on students’ math problem
solving was likely due to the fact that the students in the emotional support group may try to
control their stress using various coping strategies they learned from the emotional support and
to continue working on the module. It was suggested that effective coping seems to increase
students’ own ability to cope with difficulties (Frydenberg, 2004). In this study, it seems that
emotional support was effective to students, so this intervention might have helped students
increase their own ability to manage the emotional conflict. As a result, students in emotional
support group showed lower math anxiety and performed better in math problem solving than
students in non-emotional support group. This result could be supported by previous research
that math anxiety was negatively related to math performance (e.g., Cates & Rhymer, 2003). Ho
et al. (2000) found that the affective dimension of math anxiety was significantly associated with
math achievement in a negative direction from a cross national study including China, Taiwan,
and U.S. In this study, emotional support was designed to alleviate affective dimension of math
73
anxiety. So it can be explained that emotional support decreased the affective dimension of math
anxiety and improved math problem solving at the same time. Also, it was suggested that math
anxiety might decrease math performance by distracting attention from the math task to intrusive
concerns (Ashcraft, 2002). In this line of thought, within this study, students in the emotional
support group who reported lower math anxiety after the treatment could perform better in the
math problem solving because they didn’t lose their attention from the math problem solving
task to other, non-related concerns. Students in the emotional support group might focus on the
math problem solving task itself more so than students in the non-emotional support group.
Students in the emotional support group could overcome their math anxiety better than students
who are not in the emotional support group. Also, students in the emotional support group could
concentrate on the math problem solving task better than students in the non-emotional support
group. These facts result in a significant difference in students’ math problem solving based on
the presence and absence of emotional support.
This finding is consistent with previous research which found that emotional support
enhanced students’ math learning (Shen, 2009). Even though Shen (2009) named the math
performance variable as math learning, the nature of his math learning was math problem solving
as same as this study. Therefore, this study confirmed again the positive effect of emotional
support on math learning. Students in the emotional support group may have controlled their
math anxiety and focused on learning and testing better than students who were not in the
emotional support group. This finding is also aligned with Hembree’s (1990) research which
showed the strong effect of emotional treatment on math performance.
Overall effects of cognitive motivational messages
It was revealed that cognitive motivational messages significantly affect the combined DV
of math anxiety, self-efficacy, and math problem solving in this study. It meant students who
received cognitive motivational messages showed a difference on their combined DV with other
students who did not receive cognitive motivational messages. This result is aligned with
previous research which found the effects of motivational messages on motivation and learning
(Baylor et al., 2004; Keller, Deimann & Liu, 2005; Kim and Keller, 2008; Visser & Keller,
1990 ). Even though the finding of this study is consistent with previous research, there are
74
several differences in terms of learners and treatment condition. Visser and Keller (1990)
investigated the effects of motivational messages in the form of feedback after tests and
summaries of assignments using cards, letters, and mini posters and found positive effects of
treatment on undergraduate students’ attitude and performance. Two researchers (Keller,
Deimann, & Liu , 2005; Kim and Keller, 2008) used motivational e-mail messages as a way to
deliver motivational messages and found the positive effect of motivational messages only on
undergraduate students’ confidence among the four categories of ARCS model. Baylor et al.
(2004) used a pedagogical agent as a way to deliver motivational messages and found a positive
effect on self-efficacy. These previous research studies developed motivational messages not
focusing on a specific aspect of ARCS model, instead they included various aspects of the ARCS
model.
The current study has three major differences with previous research which found same
result. First, participants of this study were GED students who had low motivation and high math
anxiety. Second, pedagogical agents were used as a way to deliver motivational messages. Third,
the motivational messages which were used in this study were developed narrowly focusing on
incremental ability beliefs under the confidence category of ARCS model.
However, this finding is inconsistent with previous research which could not find positive
effects of cognitive motivational messages on the combined DV of math anxiety, math learning,
and motivation (Shen, 2009). This inconsistency could be caused from the different nature of
cognitive motivational messages between this study and Shen’s (2009) study. In this study,
cognitive motivational messages were developed focusing on incremental ability beliefs under
the confidence category in contrast to Shen’s (2009) study, which designed cognitive
motivational messages encompassing confidence, relevance, and satisfaction. As Shen (2009)
commented in his dissertation, his cognitive motivational messages were more general than
specific, so it might cause confusion in students with regards to the emotional support messages.
In this study, cognitive motivational messages were clearly distinguished from emotional support
messages due to the specific focus on incremental ability belief (Dweck, 1999).
Specifically, it was found that students who received cognitive motivational messages
reported higher self-efficacy than students who did not get cognitive motivational messages. This
75
finding is aligned with previous research which found the positive effect of motivational
messages delivered by pedagogical agents on self-efficacy (Baylor et al., 2004; Kim et al., 2007).
Effect of cognitive motivational messages on Self-efficacy
The hypothesis that cognitive motivational messages would have positive effect on
increasing self-efficacy was supported in this study. Students who received cognitive
motivational messages during the math module reported significantly higher self-efficacy than
students who did not receive cognitive motivational messages. The positive effect of cognitive
motivational messages on students’ self-efficacy was likely due to the fact that the students in the
cognitive motivational messages group had opportunities to think about their ability beliefs and
whether their abilities were fixed or changeable with effort. In this study, incremental ability
beliefs messages were used as a form of cognitive motivational messages. Based on previous
research, it was found that incremental ability belief intervention had positive effects on students’
ability beliefs change from entity beliefs to incremental beliefs (Blackwell et al., 2007). Once
students have incremental beliefs, they tend to think of intelligence as a malleable construct
which is able to be cultivated through effort and learning (Blackwell et al., 2007; Dweck, 1999;
Kennett & Keefer, 2006). Also, students who have incremental beliefs tend to try to overcome
challenges using various strategies such as more effort and persistence (Doronh et al., 2009;
Kasimatis et al., 1996; Nussbaum & Dweck, 2008). Therefore, students who received cognitive
motivational messages had chances to reflect on their ability beliefs and change to having
incremental ability beliefs. This change might affect students’ self-efficacy toward the
Pythagorean Theorem because they could believe their ability was growing with their effort
through learning the module and they might report higher self-efficacy after treatment.
In this study, self-efficacy refers to the student’s beliefs that he is capable of expending the
necessary effort to succeed in math problem solving and he can sustain his efforts long enough to
achieve success in math problem solving. Therefore, students were asked to answer three
questions regarding how confident and competent they are to solve a Pythagorean Theorem
problem. Students in the cognitive motivational messages group received cognitive motivational
messages which emphasized that they could succeed in the Pythagorean Theorem module with
their efforts. Thus, students in the cognitive motivational messages group might believe that they
could cultivate their own ability to solve the Pythagorean Theorem problems, even though they
76
were not good at it before studying the module. This belief could affect the students’ selfefficacy in cognitive motivational messages group.
Also, there is another possible reason why students in the cognitive motivational messages
group showed higher self-efficacy than students in non-cognitive motivational messages group.
Pedagogical agents were used as a delivery method of instruction and messages in this study.
Pedagogical agents have been suggested as one of the useful strategies for improving learners’
self-efficacy in mathematics because pedagogical agent stimulates social interaction on students
(Kim et al., 2007). Cognitive motivational messages delivered by pedagogical agents played a
role as social persuasion, so students’ self-efficacy was increased in the previous research
students (Kim et al., 2007). In this study, it is possible that students in cognitive motivational
messages group experienced social persuasion from the pedagogical agents and the social
persuasion leaded to increase students’ self-efficacy same as Kim et al. (2007)’s study.
Effects of cognitive motivational messages on math anxiety and math problem solving
In this study, it was failed to find positive effects of cognitive motivational messages on
math anxiety and math problem solving. Originally, it was expected that participants who
received cognitive motivational messages that their ability could be developed with their efforts
would show lower math anxiety and higher math problem solving score than participants who
did not receive those messages. However, there was not difference between cognitive
motivational messages group and non-cognitive motivational messages group in their math
anxiety and math problem solving. These results are consistent with previous research which
failed to find positive effects of cognitive motivational messages on math anxiety and math
problem solving (Shen, 2009). He interpreted this result with three possible reasons. First reason
was the characteristics of participants. His participants were GED students as same as this study.
He thought providing both emotional support and cognitive motivational messages occurred
cognitive load to the participants. Second reason was a mismatch between participants and the
cognitive motivational messages. He suggested that there might be different types of cognitive
motivational messages which are proper to GED students. Third reason was the design of
cognitive motivational messages. He suggested if cognitive motivational messages be adaptive to
individual participants, it would be possible to find positive effects of cognitive motivational
messages on math anxiety and learning.
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In this study, one possible reason why cognitive motivational messages had no effect on
math anxiety was likely due to the nature of cognitive motivational messages. Cognitive
motivational messages were developed only focusing on incremental ability beliefs which
included people’s ability could be grown with their efforts. It was expected that cognitive
motivational messages could decrease cognitive math anxiety which means worries to perform
well on math tasks. However, it might be not enough to alleviate participants’ cognitive math
anxiety with one time treatment. Even though participants’ self-efficacy was increased with
cognitive motivational messages in this study, it might need more time to decrease their worries
about math performance. Previous research results which found positive effects of incremental
ability beliefs on students’ performance were based on long term treatments (Aronson et al.,
2002; Blackwell et al., 2007; Good et al., 2003). It means to examine the effects of incremental
ability beliefs, long term treatments would be appropriate than one time treatments.
78
Major Contributions of the Study
This study contributes to research and practice of instructional design in several aspects.
Major contributions of this study can be categorized into six areas.
First, this study supports the previous research with quantitative evidences. There were
few quantitative research studies which examined the effects of emotional support on students’
motivation and learning. Shen (2009) conducted a quantitative study and found the positive
effects of emotional supports on math anxiety and math learning. However, there was a lack of
empirical evidence which supported Shen’s (2009) findings. Thus, this study could be evidence
which confirms the positive effects of emotional support on math anxiety and math learning with
quantitative data. It is meaningful because this study may fill the gap between theoretical
evidences and empirical evidences related to the effects of emotional support.
Second, it could be suggested that emotional support would be a possible way to alleviate
GED students’ math anxiety. Math anxiety has been regarded as one of important reasons that
made students fear and avoid math. Also, many studies found that math anxiety was negatively
related to math learning. However, there were few experimental studies which investigated the
effects of certain instructional strategies on decreasing math anxiety. This gap makes this study
unique. Specifically, emotional support that used in this study was focusing on coping strategies.
In this study, emotional support refers to messages containing coping strategies to help students
overcome nervousness on math learning. It was found that emotional support was effective on
eliminating math anxiety in this study and this result aligned to previous research. Therefore, it
might be possible to suggest the emotional support which focusing on coping strategies as a
solution for alleviating GED students’ math anxiety.
Third, it was found the possibility of adopting incremental ability beliefs messages as a
form of cognitive motivational messages from this study. Many research studies confirmed the
effects of motivational messages on motivation and learning (Baylor et al., 2004; Keller,
Deimann, & Liu, 2005; Kim and Keller, 2008; Visser & Keller, 1990). However, the nature of
motivational messages in this study is unique compare to previous research. Previous studies
used motivational messages which included broad aspects of ARCS model rather than focusing
on specific aspect. In this study, cognitive motivational messages were developed focusing on
incremental ability belief under the confidence aspect of ARCS model, which was based on
79
cognitive theories of achievement motivation (Dweck, 1999; Stipek, 2002). Thus, cognitive
motivational messages in this study aimed to change students’ ability beliefs into incremental
belief. In other words, cognitive motivational messages in this study contained some messages
which encouraged students to believe their ability was not fixed and could be developed with
learning and effort. There were few experimental studies which examined the effects of
incremental ability beliefs as a form of cognitive motivational messages. It was revealed that
cognitive motivational messages had positive effects on self-efficacy. It means this study shows
a possibility that incremental ability beliefs could be adopted as the content of cognitive
motivational messages.
Fourth, empirical evidence was found to suggest cognitive motivational messages which
focusing on incremental ability beliefs messages as a way to enhance students’ self-efficacy in
this study. Previous research found the effect of incremental ability beliefs treatments on GPA
controlling for SAT scores (Aronson et al., 2002) and standardized reading test scores (Good et
al., 2003). Blackwell et al (2007) found that incremental ability belief intervention had positive
effects on students’ ability beliefs change. However, these studies did not use cognitive
motivational messages as a way to deliver incremental ability beliefs. Also, there were few
studies which examined the effects of incremental ability beliefs on self-efficacy. Low selfefficacy has been regarded as one reason of low math problem solving (Pajares & Graham, 1999;
Pajares & Kranzler, 1995; Pajares & Miller, 1994). It means increasing self-efficacy could affect
enhancing math problem solving. In this context, from the finding of this study, cognitive
motivational messages which focusing on incremental ability beliefs might be suggested as a
way to increase students’ self-efficacy.
Fifth, this study embedded motivational support into pedagogical agents and found some
positive effects from this support. Trends of agent-related studies have focused on the effects of
voice of agents (Atkinson, Merrill, & Patterson, 2002; Atkinson, Mayer, & Merrill, 2005), roles
of agents (Baylor & Kim, 2005; Ebbers, 2007), and animation of agents (Atkinson, Merrill, &
Patterson, 2002; Lester, Town, & FitzGerald, 1999). Few studies examined the effects of
motivational support from pedagogical agents on learning and motivation (Kim et al., 2007;
Shen, 2009). This study used pedagogical agents as a medium to address emotional support and
cognitive motivational messages to decrease math anxiety, to increase self-efficacy, and to
80
enhance math problem solving and found several positive results. These findings provided
empirical evidences supporting the possibility of using pedagogical agents as a method of
motivational support. This study suggested that pedagogical agents would be effective in
supporting emotional parts and not only delivering knowledge.
Sixth, this study tried to find motivational strategies to support low confidence students in
middle school level like GED students. Previous research targeted undergraduate students to see
the effects of motivational messages. Also, there were few studies which targeted middle school
students to examine the effects of pedagogical agents. Middle school level students might need
significant assistance in terms of emotional support and cognitive development. Once students
lose their motivation to learn at the middle school level, it might be hard to continue learning at a
higher level. This is why the middle school level is a critical period in need of attention by
teachers not only for knowledge, but also for emotional support. In this context, this study is
unique because it revealed that emotional support is effective to alleviating GED students’ math
anxiety and enhancing math problem solving. Also, it was found that cognitive motivational
messages had positive effect on enhancing GED students’ self-efficacy.
Limitations
This study has several limitations in terms of generalization to other populations due to the
unique characteristics of participants, short term treatment and difficulty of content area.
First, the participants of this study were GED students who had unique characteristic
including low confidence, low attention, and low math problem solving. Thus, it would be hard
to expect the same effects of emotional support and cognitive motivational messages to other
students who have different motivational characteristics. In addition, unique motivational
characteristics may cause problems to produce a positive effect of emotional support on selfefficacy and positive effects of cognitive motivational messages on math anxiety and math
learning.
Second, this study conducted during one class time with one computer based module. And
the post-test was implemented right after the treatment. It would be hard to expect a change in
students’ ability beliefs with a one-time treatment. The previous study was done over 8 weeks to
see the change of students’ ability beliefs and grades (Blackwell et al., 2007). To track the
81
change of students’ ability beliefs and the effects of this change, a longer treatment would be
necessary.
Third, the participants had trouble learning Pythagorean Theorem in this study. Even
though students already learned the pre-requisite math contents, they could not follow the
module. It may have been due to the fact that these participants had low motivation and low
achievement. Some students could not read the instructions in the screen and some could not
understand the questions because they did not possess adequate reading skills. These unique
characteristics might affect the results of this study.
Implications
This study provides empirical evidences for emotional support and cognitive motivational
messages to be used to decrease students’ math anxiety, to improve self-efficacy and math
problem solving in math education. Although there should be more research to confirm the
findings of this study and to elaborate the nature of emotional support and cognitive motivational
messages, this study made a basis to find possible ways to alleviate students’ math anxiety,
improve self-efficacy and math problem solving by implementing motivational strategies
focusing on emotional support and cognitive motivational messages. Specifically, implications of
this study could be summarized as three.
First, it was found that emotional support adopting coping strategies could be a way to
alleviate GED students’ math anxiety and improve math problem solving. These results are
aligned to a recent experimental study (Shen, 2009). Previous research suggested that behavioral
intervention which aimed to alleviate affective domain of math anxiety were effective to
decrease math anxiety and improve math problem solving (Hembree, 1990). This study used
emotion-focused coping strategies as a way of emotional support and found positive effects of
those strategies. From these results, it could be suggested to provide coping strategies to GED
students as emotional support so as to help them manage their math anxiety and continue
working on their math learning.
Second, it was found that adopting incremental ability beliefs as a form of cognitive
motivational messages could be a way to increase self-efficacy. Many studies suggested the
effectiveness of various forms of motivational messages on students’ learning, motivation, and
82
attitude (Baylor et al., 2004; Keller, Deimann, & Liu, 2005; Kim and Keller, 2008; Visser &
Keller, 1990). However, these studies developed motivational messages in broad focus of the
ARCS model in contrast to this study, which developed cognitive motivational messages in the
narrow focus of the confidence category under the ARCS model. In this line of thought, it could
be suggested that providing cognitive motivational messages while specifically focusing on
incremental ability beliefs could be a possible way to improve GED students’ self-efficacy. Even
though this study could not find a positive effect of these messages on students’ math problem
solving, it was a valuable attempt to develop cognitive motivational messages using incremental
ability beliefs.
Third, it could be suggested that adopting pedagogical agents in a computer based module
could improve GED students’ motivation and learning. Many studies investigated the effects of
pedagogical agents in terms of voice, roles, and animation of agents (Atkinson, Merrill, &
Patterson, 2002; Atkinson, Mayer, & Merrill, 2005; Baylor & Kim, 2005; Ebbers, 2007; Lester,
Town, & FitzGerald, 1999). There were few studies to examine the effects of pedagogical agents
which highlighted their possibility to provide motivational supports to students (Kim et al., 2007;
Shen, 2009). This study tried to explore the possibility of pedagogical agents to help students
overcome emotional conflicts and motivational challenges and found positive results. In
consideration of this evidence, it could be suggested that pedagogical agents would be an
effective way of motivational support to students in a computer based module.
Future Research Directions
The findings and limitations of this study provide several ideas for future research
directions.
First, it would be meaningful to examine the effects of emotional support and cognitive
motivational messages with other populations in future research. GED students have unique
characteristics, so it is hard to expect same effects of this study’s treatment with other
populations. Therefore, if other studies would investigate the effects of same treatment to K-12
students or undergraduate students, it could produce solid empirical evidence about the
effectiveness of this treatment.
83
Second, long term experiments would be valuable to determine the effects of incremental
ability beliefs as a form of cognitive motivational messages. This study was done with a onetime experiment, so it is difficult to expect a change in students’ ability beliefs. Therefore, to
conduct a long term experiment would provide valuable data about how students’ ability beliefs
could be adjusted and how these changes affect their math anxiety, self-efficacy, and math
problem solving in the long run.
Third, further research which investigates the effects of emotional support and cognitive
motivational messages within different subject area would be meaningful. This study focused on
the Pythagorean Theorem in math, but more studies built into other subject area such as science,
writing, statistics would provide evidence about the effects of the treatment on various areas.
Fourth, it would be useful to check the participants’ level of prior knowledge and reading
skills before designing a study. From the observation and interview after experiment, it was
found that some of participants had difficulties to understand languages in the module or surveys.
Brief testing, observation, and interviewing could be used to get necessary information about
participants. Even though learning analysis was done using interview with teachers in this study,
it was hard to understand the students’ level of knowledge and reading skills which would affect
the research. Therefore, consideration of learners’ readiness would be useful to design an
experiment for future studies.
Fifth, e-mail or discussion threads could be interesting medium to deliver emotional
support and cognitive motivational messages. E-mail and discussion threads are commonly used
in the face-to-face classroom. Future research could find meaningful results about the effects of
emotional messages and cognitive motivational messages delivered by various forms. These
studies would provide good reference to teachers how to use these treatments in their real
classroom.
Conclusions
This study aimed to examine the effects of emotional support and cognitive motivational
messages delivered by pedagogical agents in a computer based module on students’ math anxiety,
self-efficacy, and math problem solving. The results indicated that emotional support focusing on
coping strategies was effective in alleviating math anxiety and improving math problem solving.
84
Cognitive motivational messages embedding incremental ability beliefs were effective to
enhance students’ self-efficacy. This study shows possibilities to adapt coping strategies as a
form of emotional support and use incremental ability beliefs as the content of cognitive
motivational messages. Also, the study found that pedagogical agents could be effective as a
form of emotional and motivational support for students in a computer based module. It is
expected that further research based on this study would improve the nature of treatment and
provide more solid evidences to researcher and teachers.
85
APPENDIX A
Pre-test and Post-test on Math problem solving
Pre-test
Name: __________________
On the map below, the city of Orange is 12 miles due east of Lime. The city of Lemon is 9
miles due south of Orange. On the paper given to you, write down the equation could be used to
find the straight line distance in miles (x) between Lemon and Lime.
Please write down the steps you used to solve this problem in as much detail as possible.
Answer: ______________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
86
Post-test
Name: __________________
1. On the map below, the city of Banana is 20 miles due south of Apple, and Apple is x
miles due west Grape. The straight line distance between Banana and Grape is 45 miles. Please
write down the equation that could be used to find x? Please write down the steps or notes you
made to figure out what this formula is.
Formula: _________________________________________________________________
Notes: ___________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
87
2. On the map below, the city of Maceo is 20 miles due west of Droma. The city of Troy is
8 miles due north of Maceo. The city of Lafta is 10 miles due east of Troy. Please write down
equations could be used to find the straight line distance in miles (x) between Troy and Droma.
Please write down the steps or notes you made to figure out what this formula is.
Formula: _________________________________________________________________
Notes: ___________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
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APPENDIX B
Pre-test and post-test on Mathematics Anxiety
Pre-test
Name: __________________
Directions:
On this page you will read a series of statements. There are no correct answers for these
statements. They have been set up in a way which permits you to indicate the extent to which
you agree or disagree with the ideas expressed. Please write an X on the number from 1 to 7 that
indicates your opinion, with 1 indicating disagreement with the statement and 7 indicating
agreement with the statement.
Note: Do not spend much time with any statement, but be sure to answer every statement.
Work fast but carefully.
1. When I am in math class, I usually feel relaxed and at
ease.
2. When I am taking a math test, I usually feel nervous and
uneasy.
3. Taking math tests scares me.
4. I dread having to do math.
5. It scares me to think that I will be taking harder or more
advanced math.
6. When the teacher asks you math questions, how much do
you worry that you will do poorly?
7. When the teacher shows the class how to do a math
problem, how much do you worry that other students might
understand the problem better than you?
8. In general, how much do you worry about how well you
will do in school?
9. If you are absent from school and you miss a math
assignment, how much do you worry that you will fall
behind?
10. In general, how much do you worry about how well you
do in math?
11. Compare to other students, how much do you worry
about your performance in math?
Not at all
□
1
Not at all
□
1
Not at all
□
1
Not at all
□
1
Not at all
□
1
Not at all
□
1
Not at all
□
1
Never
□
1
Not at all
□
1
Not at all
□
1
Not at all
□
1
89
□
2
□
3
□
4
□
5
□
6
□
2
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3
□
4
□
5
□
6
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2
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3
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4
□
5
□
6
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2
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3
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4
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5
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6
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2
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3
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4
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5
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6
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2
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3
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4
□
5
□
6
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2
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3
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4
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5
□
6
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2
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3
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4
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5
□
6
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2
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3
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4
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5
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6
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2
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3
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4
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5
□
6
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2
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3
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4
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5
□
6
Very much
□
7
Very much
□
7
Very much
□
7
Very much
□
7
Very much
□
7
Very much
□
7
Very much
□
7
Very often
□
7
Very much
□
7
Very much
□
7
Very much
□
7
Post-test
Name: __________________
Directions:
On this page you will read a series of statements. There are no correct answers for these
statements. They have been set up in a way which permits you to indicate the extent to which
you agree or disagree with the ideas expressed.
Please place an X in the box that indicates your opinion:
Strongly Agree--- when you agree with the statement without any reservation
Agree--- when you agree but with reservations
Don’t know/uncertain --- when you cannot decide on the extent you agree or disagree with
the statement or when you neither agree or disagree with the statement
Disagree—when you disagree with the statement
Strongly Disagree—when you strongly disagree with the statement
Note: Do not spend much time with any statement, but be sure to answer every statement. Work
fast but carefully.
Strongly
Disagree
1. Math doesn’t scare me at all.
2. It wouldn’t bother me at tall to take more math courses.
3. I haven’t usually worried about being able to solve math problems.
4. I almost never have gotten shook up during a math test.
5. I usually have been at ease during math tests.
6. I usually have been at ease in math classes.
7. Mathematics usually makes me feel uncomfortable and nervous.
8. Mathematics makes me feel uncomfortable, restless, irritable, and
impatient.
9. I get a sinking feeling when I think of trying hard math problems.
10. My mind goes blank and I am unable to think clearly when
working mathematics.
11. A math test would scare me.
12. Mathematics makes me feel uneasy and confused.
90
Disagree
Don’t know/
Uncertain/neutral
Agree
Strongly
Agree
APPENDIX C
Pre-test and post-test on Self-efficacy
Pre-test
Name: __________________
Respond to each of the following statements by writing an X on top of the number that indicates
how well you believe you can solve each type of problem. Put down what you really believe.
There are no right or wrong answers.
1. How well can you solve a Geometry word problem?
Not at all
2. How sure are you that you can correctly solve a
Pythagorean Theorem problem?
Not at all
91
□
1
□
2
□
3
□
4
□
1
□
2
□
3
□
4
Very well
□
5
Very sure
□
5
Post-test
Name: __________________
Respond to each of the following statements by writing an X on top of the number that indicates
the strength of your agreement/disagreement with it. Put down what you really believe. There are
no right or wrong responses.
1. I can solve a Pythagorean Theorem problem.
2. I am confident in my ability to solve a Pythagorean
Theorem problem.
3. I am competent to solve a Pythagorean Theorem
problem.
Strongly Disagree
□
□
1
2
Strongly Disagree
□
□
1
2
Strongly Disagree
□
□
1
2
92
□
3
□
4
□
3
□
4
□
3
□
4
Strongly Agree
□
5
Strongly Agree
□
5
Strongly Agree
□
5
APPENDIX D
Theories of Intelligence Scale
Name: __________________
This questionnaire has been designed to investigate ideas about intelligence. There are no right
or wrong answers. We are interested in your ideas.
Using the scale below, please indicate the extent to which you agree or disagree with each of the
following statements by writing an X on top of the number that corresponds to your opinion.
1. You have a certain amount of intelligence, and you
can’t really do much to change it.
Strongly Disagree
□
□
1
2
□
3
□
4
□
5
Strongly Agree
□
6
2. Your intelligence is something about you that you can’t
change very much.
Strongly Disagree
□
□
1
2
□
3
□
4
□
5
Strongly Agree
□
6
3. No matter who you are, you can significantly change
your intelligence level.
Strongly Disagree
□
□
1
2
□
3
□
4
□
5
Strongly Agree
□
6
4. To be honest, you can’t really change how intelligent
you are.
Strongly Disagree
□
□
1
2
□
3
□
4
□
5
Strongly Agree
□
6
5. You can always substantially change how intelligent
you are.
Strongly Disagree
□
□
1
2
□
3
□
4
□
5
Strongly Agree
□
6
6. You can learn new things, but you can’t really change
your basic intelligence.
Strongly Disagree
□
□
1
2
□
3
□
4
□
5
Strongly Agree
□
6
7. No matter how much intelligence you have, you can
always change it quite a bit.
Strongly Disagree
□
□
1
2
□
3
□
4
□
5
Strongly Agree
□
6
8. You can change even your basic intelligence level
considerably.
Strongly Disagree
□
□
1
2
□
3
□
4
□
5
Strongly Agree
□
6
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APPENDIX E
STORYBOARD
No
Screen
Screen Shots & Agent Script
01
Mr. Gibbs is in
the screen and
introduces
himself.
Hello, my name is Mr. Gibbs. I will
be your teacher and guide as you
work on this lesson.
02
Mr. Gibbs
[Mr. Gibbs could go over the
directions with the student.]
Click the Next button to continue.
Before starting this lesson, I will
briefly explain how to use buttons in
the screen. When you want to go
back to the previous page, click the
Back button. If you want to go to the
next page, click the Next button.
94
Emotional Support Msg
Ability Belief Messages
No
03
Mr. Gibbs
Screen
Screen Shots & Agent Script
In this lesson you will learn how to
solve geometry word problems like
the ones you will have to solve on
the GED test. There are many types
of geometry word problems, so you
will learn how to do one specific kind
involving a strategy called the
Pythagorean theorem.
You are also going to learn
something else in this lesson that is
very important for success. You will
learn about your basic ability to learn
math.
At the end of this lesson you will
take a timed test to find out how well
you learned the material.
Click the Next button to continue.
04
Overlay Mr.
Gibbs on left part
of the geometry
problem.
Before you begin the instructional
part of this lesson, here is a sample
problem for you to solve. If you
aren’t able to do it, don’t worry about
it, because this is what the lesson
will teach you. This is just a preview.
You are given a paper and pencil to
use while working on the problem.
Please write down all of your work
as you try to solve it.
When you are finished, click the
Next button below.
95
Emotional Support Msg
Ability Belief Messages
No
05
Mr. Gibbs
Screen
Screen Shots & Agent Script
By the time you finish this lesson, I
believe you will be able to solve this
type of problem.
There is one more thing to do before
the actual instruction begins.
I want to introduce Dr. Sheila Baker.
She is an expert on psychology and
neurology and she will provide
valuable help to you. To begin, she
wants to ask you a question.
Click the Next button to continue.
06
Dr. Baker
Hello, I am Dr. Baker. There are two
statements on the screen that
represent two different attitudes
about how we learn math. Please
click on the one you agree with the
most.
Which of the following statements do
you agree with the most?
1. I believe that a person’s ability to
learn math is something you are
born with. There isn’t much you can
do about it. Some people naturally
have low (or high) ability.
2. I believe that a person’s ability to
learn math is like learning to ride a
bicycle. The more you work at it, the
better you get and the more your
ability improves.
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Emotional Support Msg
Ability Belief Messages
No
06-1
Dr. Baker
Screen
Screen Shots & Agent Script
<M>
Emotional Support Msg
Ability Belief Messages
You chose the first statement. Many
people believe this. However, it is not
true. In this lesson, I will help you learn
how to improve your math skills!
In this lesson, I will tell you several
things that will show you how your
ability to do math can be improved .
Click the Next button to continue.
06-2
Dr. Baker
<M>
You chose the second statement, and
you are correct! All humans have the
basic ability to learn math and this
ability improves based on the amount of
effort you put into learning math. The
only exceptions are people with certain
kinds of brain damage and if you were
one of these people, you would not be
here today!
In this lesson, I will tell you several
things that illustrate how your ability to
do math can improve.
Click the Next button to continue.
97
No
Screen
07
Mr. Gibbs
Screen Shots & Agent Script
1) Now, it is time to learn how to do
geometry word problems like the
one you just saw.
<E>
Emotional Support Msg
Ability Belief Messages
2) At this point you
might be feeling
nervous. Many people
do. I know I did when I
studied this kind of
math word problem
when I was a student.
3) If you are feeling
nervous, the best thing
is to just accept this
feeling. Don’t try to
make it go away.
Instead, just focus on
the learning task. As
you make progress you
won’t feel so nervous.
(IS, ES)1
Click the Next button to
continue.
1
Type of emotional support message based on COPE model (IS – Instrumental Social Support; ES – Emotional Social Support; PG – Positive
reinterpretation & growth; VE – Venting of Emotions)
98
No
08
Dr. Baker
Screen
Screen Shots & Agent Script
<M>
Emotional Support Msg
Ability Belief Messages
One reason you will feel less nervous is
your brain works like a muscle. The
more you use it, the better it performs.
Everyone can perform math well based
on the amount of time they spend
practicing and learning math skills.
Click the Next button to continue.
09
Mr. Gibbs
In the first section, I will explain and
show you some key words and
concepts related to compass
directions.
Click the Next button to continue.
99
No
10
Mr. Gibbs
Screen
Screen Shots & Agent Script
To begin, you have to understand
some key words and concepts
before you can solve the geometry
word problem you saw at the
beginning of this lesson.
One word that many people get
confused about is the word “due,” as
in “due north.”
Used in this way, the word “due,”
means “in the direction of.” So, the
phrase “due north” means “in the
north direction.”
Similarly, “due south” means in the
“south direction,” “due west” means
“in the west direction,” and “due
east” means “in the east direction.”
Click the Next button to continue.
11
Mr. Gibbs
Use the term “on
your right”
consistently from
this screen.
The diagram on your right shows
you how “due north,” “due south,”
“due west,” and “due east” are
related:
Another way to think about “north,
south, west, and east,” is by using
the words “above, below, left and
right.”
In this way, “due north” means
“directly above,” “due south” means
“directly below,” “due west” means
“directly left,” and “due east” means
“directly right.”
Click the Next button to continue.
100
Emotional Support Msg
Ability Belief Messages
No
12
Mr. Gibbs
Screen
Screen Shots & Agent Script
This picture on your right resembles
a compass, and shows you how all
of these words describing directions
are related:
Sometimes people confuse the
directions for “due west” and “due
east.” One way to avoid this
confusion is to think of the word
“we.” The letter “w” in the word “We”
is on the left, which is the direction
for “due west.” The letter “e” in the
word “wE” is on the right, which is
the direction for “due east.”
Click the Next button to continue.
13
Mr. Gibbs
Here is an example of using these
words to describe locations.
In the picture below, point A is “due
north” of point D, in other words,
point A is “directly above” point D.
Point A is also “due west” of point B,
or you could `say, point A is “directly
left” of point B.
There are many ways to describe
the locations of these four points.
Some other ways might be to say:
Point D is “due south” of point A, or
that point D is “directly below” point
A.
Point C is “due east” of point D, or
you could say, point C is “directly
right” of point D.
Click the Next button to continue.
101
Emotional Support Msg
Ability Belief Messages
No
14
Mr. Gibbs
Screen
Screen Shots & Agent Script
<[E]>
Emotional Support Msg
Many people do feel
anxious because Word
problems are confusing
at times. But the
following practice
exercises will help you
understand the
concept.
Also, it can be helpful
to hear the feelings of
someone like you who
was a GED student.
Please go to the next
page to meet Trina.
(IS)
15
Trina
<[E]>
Hi, I am Trina. I was
also a GED student. I
know you are feeling
anxious now. I know
what that’s like when I
had the same class last
year. Let your feelings
out by typing in the text
box. That might help
you feel better. Also, it
will be interesting to
compare your feelings
later in the lesson to
the way you are feeling
right now.
Click the Next button to
continue.
(ES, VE)
102
Ability Belief Messages
No
Screen
Screen Shots & Agent Script
<[M]>
Emotional Support Msg
Ability Belief Messages
Before you continue, I want to quickly
explain something. It might not seem
like it, but your math ability is actually
improving.
16
Dr. Baker
explains about
brain growing.
And then, let
students click the
video.
How do I know this? Because the inside
of your brain is like a science fiction
movie. Your brain is filled with electrochemical activity that increases when
you are thinking and solving problems.
Also, this activity leads to growth in your
brain’s abilities.
By growth, I mean there are things
happening in your brain to increase its
capability. Click on this 20 second
YouTube video to see how your brain
actually grows by creating new
connections between its parts.
After you watch the video, Click the
Next button to continue.
16-1
When students
click the link, Dr.
Baker provides
ability belief
messages.
<[M]>
The more you use your brain to apply
these math concepts, the more
connections it forms and the more you
ability grows!
Click the Next button to continue.
103
No
17
Mr. Gibbs
Screen
Screen Shots & Agent Script
Now I will guide you as you do
problems related to compass
directions.
Click the Next button to continue.
18
Mr. Gibbs
Here is a problem using direction
words to describe locations.
Type the correct word to complete
the following sentence that
describes the picture below.
Point C is “due ______” of point D.
104
Emotional Support Msg
Ability Belief Messages
No
18-1
Mr. Gibbs
Feedback on
right answer
Screen
Screen Shots & Agent Script
Emotional Support Msg
Ability Belief Messages
1) Correct.
Since point C is “directly right” of
point D, then the correct response is
“east.”
Click the Next button to continue.
18-1-1
Dr. Baker
<[M]>
2) Good job!
Based on your success at solving this
problem, your ability to solve compass
direction problems is improving!
Feedback on
right answer
This is not just my personal opinion, it is
based on brain research in my
laboratory
Click the Next button to continue.
105
No
18-2
Mr. Gibbs
Feedback on
wrong answer
Screen
Screen Shots & Agent Script
1) Incorrect.
<[E]>
2) Since point C is “directly right” of
point D, then the correct response is
“east.” Look at the problem again:
Point C is “due ______” of point D.
Imagine putting the center of a
compass at point D, as shown in the
picture below. Now look at the
location of point C, it is “directly
right” or “due east” of point D.
Emotional Support Msg
Ability Belief Messages
2) Don’t worry, this is a
learning process. You
will gain understanding
of the concept by doing
the exercise even if you
do not get it right the
first time. Stay relaxed
and keep on trying.
Click the Next button to
continue.
(IS, RG)
18-2-1
Dr. Baker
<[M]>
3) Your answer was incorrect but if you
tried to solve the problem, your math
ability is still improving because you
were using your brain to figure out the
answer to the problem. The more you
think about the problems and try to
figure out why you were wrong, the
more your brain is working and growing.
Feedback on
wrong answer
If you just took a wild guess, then your
brain is not growing.
Click the Next button to continue.
106
No
19
Mr. Gibbs
Screen
Screen Shots & Agent Script
Here is another problem using
direction words to describe
locations.
Type the correct word to complete
the following sentence that
describes the picture below.
Bill is “due ______” of Sue.
19-1
Mr. Gibbs
1) Correct.
Feedback on
right answer
Since Bill is “directly above” Sue,
then the correct response is “north.”
Click the Next button to continue.
107
Emotional Support Msg
Ability Belief Messages
No
19-1-1
Dr. Baker
Screen
Screen Shots & Agent Script
Emotional Support Msg
<[M]>
Ability Belief Messages
2) Good for you. Try to visualize what it
is like inside your brain. Imagine all of
those neural connections flashing and
growing, just like in the video!
Feedback on
right answer
Click the Next button to continue.
19-2
Mr. Gibbs
1) Incorrect.
<[E]>
Feedback on
wrong answer
Since Bill is “directly above” Sue,
then the correct response is “north.”
Look at the problem again:
Bill is “due ______” of Sue.
Imagine putting the center of a
compass on Sue, as shown in the
picture below. Now look at the
location of Bill, it is “directly above”
or “due north” of Sue.
2) Do not worry. I
understand how you
feel now. I made the
same mistake as you
did when I was learning
direction words. It just
takes a little time and
practice to grasp all
these concepts. The
good news is that you’ll
have another exercise
problem to practice. I
predict that you’ll be
fine as the learning
progresses.
Click the Next button to
continue.
(ES, RG)
108
No
19-2-1
Dr. Baker
Screen
Screen Shots & Agent Script
<[M]>
Emotional Support Msg
Ability Belief Messages
3) Are you disappointed because you
did not get the correct answer to this
question? Please don’t be.
Feedback on
wrong answer
The important thing here is to learn from
your mistakes. A mistake does not
mean you aren’t smart, it means that
there is something that you have not
learned yet. The more you try to figure
out why you made the mistake, the
more your math ability will improve.
Try hard and then just imagine all of
those neural connections flashing and
growing, just like in the video!
Click the Next button to continue.
20
Mr. Gibbs
Now try the following problem:
The map below shows four towns
connected by roads. Click the
correct words to complete each of
the following sentences that
describe the picture below.
Tarp is due ______ of Leon.
Pike is due ______ of Nard.
Leon is due ______ of Pike.
109
No
20-1
Mr. Gibbs
Screen
Screen Shots & Agent Script
Emotional Support Msg
Ability Belief Messages
1) Correct.
Click the Next button to continue.
Feedback on
right answer
20-1-1
Dr. Baker
<[M]>
2) Congratulations! If you took time to
figure out the problem and know why
you got the correct answer, your math
ability is improving with your efforts!
Feedback on
right answer
Click the Next button to continue.
110
No
20-1-2
Mr. Gibbs
Screen
Screen Shots & Agent Script
<E>
Emotional Support Msg
You got the right
answer but compass
directions can be
confusing at times.
However, just continue
to focus on the learning
and don’t worry about
the problem too much.
Feedback on
right answer
This is good time to
hear what Trina has to
say and to explain your
feelings.
Click the Next button to
continue.
(IS)
21
Trina
<[E]>
I know you are feeling
anxious now. I have
found math to be
challenging, but I also
know that having
anxiety is not going to
help your learning. Stay
relaxed and let your
feelings out by typing in
the text box. When you
compare how you feel
now with how you felt
earlier and how you will
feel later on, it might
help you feel better.
(ES, VE)
After typing your
feelings in the text box,
click the Next button to
continue.
111
Ability Belief Messages
No
21-1
Trina
Screen
Screen Shots & Agent Script
Emotional Support Msg
<[M]>
Ability Belief Messages
I also want you to know that I agree with
the things Dr. Baker has been telling
you. I used to believe that I just did not
have the ability to learn math. But, after
I learned how math ability can grow with
effort, I changed my belief. I became
convinced that I could succeed if I tried
hard.
Once I changed my belief, I did not give
up for solving math problems even
though they were really difficult.
Until recently, I was not good at math.
However, I am getting better all the time
because I keep studying hard to grow
my “math muscles”.
I hope you can also do like me.
Cheer up, friend!
Click the Next button to continue.
20-2
Mr. Gibbs
1) Incorrect.
<[E]>
Feedback on
wrong answer
Look at the problem again with a
compass. The correct answers are:
Tarp is due south of Leon.
Pike is due north of Nard.
Leon is due west of Pike.
.
112
2) That’s okay. Hang in
there and focus on the
compass on the page.
You’ll get there.
Click the Next button to
continue.
(ES, IS )
No
20-2-1
Dr. Baker
Screen
Screen Shots & Agent Script
Emotional Support Msg
<[M]>
Ability Belief Messages
3) Notice how this problem is more
complicated than the one before.
However, the ideas are basically the
same. Concentrate on understanding
this information, and your brain will keep
getting stronger and smarter.
Feedback on
wrong answer
If you feel that there is too much
information in your brain right now, take
a mental break for 30 or 40 seconds
and look around the room!
Click the Next button to continue.
20-2-2
<[E]>
Compass directions are
confusing at times.
Let’s focus on the
learning and don’t
worry about the
problem too much. You
will do better next time.
Mr. Gibbs
Feedback on
wrong answer
This is a good time to
hear what Trina has to
say and to explain your
feelings.
Click the Next button to
continue.
(IS)
113
No
Screen
Screen Shots & Agent Script
21
Trina
<[E]>
21-1
Trina
<[M]>
Emotional Support Msg
Ability Belief Messages
I know you are feeling
anxious now. I have
found math to be
challenging, but I also
know that having
anxiety is not going to
help your learning. Stay
relaxed and let your
feelings out by typing in
the text box. When you
compare how you feel
now with how you felt
earlier and how you will
feel later on, it might
help you feel better.
(ES, VE)
After typing your
feelings in the text box,
click the Next button to
continue.
I also want you to know that I agree with
the things Dr. Baker has been telling
you. I used to believe that I just did not
have the ability to learn math. But, after
I learned how math ability can grow with
effort, I changed my belief. I became
convinced that I could succeed if I tried
hard.
Once I changed my belief, I did not give
up for solving math problems even
though they were really difficult.
Until recently, I was not good at math.
However, I am getting better all the time
because I keep studying hard to grow
my “math muscles”.
I hope you can also do like me.
Cheer up, friend!
Click the Next button to continue.
114
No
22
First Mr. Gibbs,
then Dr. Baker.
Screen
Screen Shots & Agent Script
Emotional Support Msg
Ability Belief Messages
1) In the next section, I will explain
and show you some key words and
concepts related to right triangles.
Click the Next button to continue.
23
Dr. Baker
<[M]>
2) Great! You have made it through the
first section.
If this section seems to be more difficult,
do not be discouraged. As you keep
working hard to understand the
instruction, your brain will keep growing!
Be sure to listen carefully to Mr. Gibbs
and have him repeat the information
again if you are not totally clear!
Click the Next button to continue.
115
No
24
Mr. Gibbs
Screen
Screen Shots & Agent Script
Below is the four point example from
the previous section. If points A, B,
and C are all connected with straight
lines, the shape that is formed is a
triangle.
The L-shaped corner of the triangle
is called a “right angle.”
Anytime a line going north and south
crosses or meets a line going west
and east, they form an L-shape, or a
right angle.
Click the Next button to continue.
25
Mr. Gibbs
Any triangle that has a right angle is
called a “right triangle.” Right
triangles can be drawn in many
different positions. Some positions
are shown below.
Click the Next button to continue.
116
Emotional Support Msg
Ability Belief Messages
No
26
Mr. Gibbs
Screen
Screen Shots & Agent Script
Emotional Support Msg
The sides of a right triangle have
special names. The side across from
the right angle is called the
“hypotenuse.” The other two sides
are each called a “leg.”
Click the Next button to continue.
27
Mr. Gibbs
1) The sides of a right triangle are
also mathematically related through
a formula, or equation, called the
Pythagorean theorem, which says:
(leg)2 + (leg)2 = (hypotenuse)2
<[E]>
2) When I first heard of
the Pythagorean
Theorem I felt a bit
uneasy. But after I took
a deep breath and
relaxed, I practiced and
learned how the
Pythagorean Theorem
worked. So hang in
there! (IS, ES)
Click the Next button to
continue.
117
Ability Belief Messages
No
28
Mr. Gibbs
Screen
Screen Shots & Agent Script
Emotional Support Msg
Ability Belief Messages
1) Here is an example of using the
Pythagorean theorem.
In the diagram to the right, Sam is 5
feet due north of Rick, and Tom is
12 feet due west of Rick. If the
distance between Tom and Sam is
called x, then the Pythagorean
theorem says that these distances
are related by :
52 + 122 = x2
Notice that you do not have to use
parenthesis for the Pythagorean
theorem.
Click the Next button to continue.
29
Dr. Baker
<[M]>
2) Are you feeling nervous about trying
to solve a new problem? Please don’t
be. Read the problem two or three
times, make notes on a piece of paper,
and try to figure it out. As you are
working, try to visualize all the new
connections that are being made in your
brain!
If you experience difficulty trying to
understanding this example, it is okay!
You will have more opportunities to
practice similar problems during this
lesson.
Click the Next button to continue.
118
No
30
Mr. Gibbs
Screen
Screen Shots & Agent Script
1) Here is another example.
In the picture below, Pike is 11 miles
due north of Nard, and Leon is x
miles due west of Pike. If the
distance between Leon and Nard is
20 miles, then the Pythagorean
theorem says that these distances
are related by :
112 + x2 = 202
Note that x is a leg this time instead
of the hypotenuse.
<[E]>
31
Mr. Gibbs
To help better understand this
example, notice a right triangle has
been drawn with dark lines over the
map.
Recall that Pike is 11 miles due
north of Nard, and Leon is x miles
due west of Pike. If the distance
between Leon and Nard is 20 miles,
then the Pythagorean theorem says
that these distances are related by:
112 + x2 = 202
Click the Next button to continue.
119
Emotional Support Msg
2) Remember what I
said before, it’s ok to
feel a bit uneasy when
learning something
new. Just stay relaxed
and focus on
practicing. (IS, ES)
Click the Next button to
continue.
Ability Belief Messages
No
32
Mr. Gibbs
Screen
Screen Shots & Agent Script
Emotional Support Msg
<[E]>
That’s understandable.
The Pythagorean
theorem is challenging.
Try to just focus on the
learning and don’t
worry about the
problem too much. You
will get to practice.
Before you work on
more math problems,
here is Trina again.
Click the Next button to
continue.
(IS, VE)
32-1
Trina
<[E]>
I can understand how
you feel. Let me help
you ease your anxiety
and improve your
learning and
understanding. Take a
deep breath and as you
exhale, let your feelings
go out with it. Then
type in the textbox to
let me know how you
feel now. (ES, VE)
120
Ability Belief Messages
No
Screen
Screen Shots & Agent Script
33
Mr. Gibbs
1) Now I will guide you as you work
on problems related to right
triangles.
Click the Next button to continue.
34
Dr. Baker
<[M]>
Emotional Support Msg
Ability Belief Messages
2) You are making good progress! You
have accomplished a lot and are almost
finished! As you work on the next set of
problems, your math ability will continue
to improve!
Click the Next button to continue.
121
No
35
Mr. Gibbs
Screen
Screen Shots & Agent Script
Here is a problem on using the
Pythagorean theorem.
In the picture below, Marksville is 12
miles due north of Jamesville, and
Sharpsville is 15 miles due east of
Marksville. Which of the following
equations could be used to find the
straight line distance in miles (x)
between Sharpsville and
Jamesville?
(1) 152 – x2 = 122
(2) x2 + 122 = 152
(3) 152 + x2 = 122
(4) 122 + 152 = x2
35-1
Mr. Gibbs
Feedback on
right answer
1) Correct.
Since the hypotenuse in this case is
x, the correct answer choice is (4):
122 + 152 = x2
Click the Next button to continue.
122
Emotional Support Msg
Ability Belief Messages
No
35-1-1
Dr. Baker
Screen
Screen Shots & Agent Script
Emotional Support Msg
<[M]>
Ability Belief Messages
2) Good job! The problems are getting
more difficult but you got it correct. I am
happy to see how your math ability is
improving!
Feedback on
right answer
Click the Next button to continue.
35-2
Mr. Gibbs
1) Incorrect.
2) Don’t give up.
Practice makes perfect!
<[E]>
Feedback on
wrong answer
Since the hypotenuse in this case is
x, the correct answer choice is (4)
122 + 152 = x2
Look at the problem again. The
sides have been labeled with their
geometric name and with their
length.
123
Click the Next button to
continue.
(RG)
No
35-2-1
Dr. Baker
Screen
Screen Shots & Agent Script
<[M]>
Emotional Support Msg
Ability Belief Messages
3) Maybe you think this problem looks
totally new and difficult, but actually it is
related to the previous example. The
difference is that the triangle is upside
down compared to the way it was
presented before. But, the hypotenuse
is still the longest line in the triangle.
Feedback on
wrong answer
The next problem is very much like the
previous one, so give it your best effort!
Your math ability will keep improving!
Click the Next button to continue.
36
Mr. Gibbs
Try this next problem.
In the map below, Samara is 22
miles due south of Latria, and Latria
is x miles due west of Ithaca. The
straight line distance between
Samara and Ithaca is 30 miles.
Which of the following equations
could be used to find x?
(1) x2 + 222 = 302
(2) 222 – x2 = 302
(3) 302 + x2 = 222
(4) 222 + 302 = x2
124
No
36-1
Mr. Gibbs
Feedback on
right answer
Screen
Screen Shots & Agent Script
Emotional Support Msg
Ability Belief Messages
1) Correct.
Since the hypotenuse in this case is
30, the correct answer choice is (1) :
x2 + 222 = 302
Click the Next button to continue.
36-1-1
Dr. Baker
<[M]>
2) You are doing great! Your math
ability keeps improving!
Feedback on
right answer
Click the Next button to continue.
125
No
36-1-2
Screen
Screen Shots & Agent Script
<E>
Emotional Support Msg
You got the right
answer but
Pythagorean Theorem
can be difficult at times.
Mr. Gibbs
Feedback on
right answer
However, just continue
to focus on the learning
and don’t worry about
the problem too much.
Now, you can talk to
Trina one more time.
Click the Next button
to continue.
(IS)
37
Trina
<[E]>
1) I completely
understand your
feelings. We are almost
there. Don’t let your
anxious feeling take
control of you. Take a
deep breadth and let it
out. You can type them
in the textbox to my
left.
Click the Next button to
continue.
(ES, VE)
126
Ability Belief Messages
No
37-1
Trina
Screen
Screen Shots & Agent Script
Emotional Support Msg
<[M]>
Ability Belief Messages
2) I also want you to know that I had
hard time trying to understand the
Pythagorean theorem when I first
studied it. However, once I learned that
my math ability can grow, I practiced
again and again. Now, I know that I am
better than before, because my
“Pythagorean theorem related brain
muscles” are growing!
I really believe that you can have same
experience that I did!
Click the Next button to continue.
36-2
Mr. Gibbs
1) Incorrect.
<[E]>
Feedback on
wrong answer
Since the hypotenuse in this case is
30, the correct answer choice is (1) :
x2 + 222 = 302
Look at the problem again. The
sides have been labeled with their
geometric name and length.
127
2) Mr. Gibbs: Don’t
worry. You’ll learn from
your experience. If you
spend more time
analyzing the problem
and thinking about it
before you answer, I
predict that you will get
it right.
Click the Next button to
continue.
No
36-2-1
Dr. Baker
Screen
Screen Shots & Agent Script
Emotional Support Msg
<[M]>
Ability Belief Messages
3) I agree with Mr. Gibbs. Your math
ability is improving if you have been
doing your best in this lesson.
Feedback on
wrong answer
Don’t be disappointed because you
didn’t get the correct answer. Try to
understand why you got it wrong and
this will help you improve next time!
Click the Next button to continue.
36-2-2
<[E]>
Even though you are
feeling anxious that’s
OK. A little bit of
anxiety can actually
help you perform
better.
Mr. Gibbs
Feedback on
wrong answer
If you are feeling a lot
of anxiety, then try to
focus on the learning
and don’t worry about
whether you are going
to get it right or wrong.
You have the ability to
do better next time.
Now, you can talk to
Trina one more time.
Click the Next button to
continue.
(IS, VE)
128
No
37
Trina
Screen
Screen Shots & Agent Script
<[E]>
Emotional Support Msg
Ability Belief Messages
1) I completely
understand your
feelings. We are almost
there. Don’t let your
anxious feeling take
control of you. Take a
deep breath and let it
out. You can type them
in the textbox to my
left.
Click the Next button to
continue.
(ES, VE)
37-1
Trina
<[M]>
2) I also want you to know that I had
hard time trying to understand the
Pythagorean theorem when I first
studied it. However, once I learned that
my math ability can grow, I practiced
again and again. Now, I know that I am
better than before, because my
“Pythagorean theorem related brain
muscles” are growing!
I really believe that you can have same
experience that I did!
Click the Next button to continue.
129
No
38
Dr. Baker
Screen
Screen Shots & Agent Script
You are now ready for the final
problems!
Emotional Support Msg
Ability Belief Messages
Congratulations on continuing to
improve your math skills, I am very
happy for you!
<[M]>
Remember to concentrate and take
your time when trying to figure out the
math problems!
Click the Next button to continue.
39
Mr. Gibbs
On the next page you will be given
two geometry word problems to
solve.
You can use paper and pencil if you
want.
Click the Next button to continue.
130
No
Screen
Screen Shots & Agent Script
40
Mr. Gibbs
41
Great job! Keep working hard on the
next topics in your math class.
Dr. Baker
Click the Next button to continue.
131
Emotional Support Msg
Ability Belief Messages
No
42
Trina
Screen
Screen Shots & Agent Script
I hope you have leaned valuable
knowledge about Pythagorean
theorem from this lesson.
Click the Next button to continue.
43
Mr. Gibbs
Thank You for learning math with
me!!
Please click the Next button to take
a few survey questions.
132
Emotional Support Msg
Ability Belief Messages
No
Screen
Screen Shots & Agent Script
44
Mr. Gibbs
133
Emotional Support Msg
Ability Belief Messages
APPENDIX F
HUMAN SUBJECT COMMITTEE APPROVAL
Office of the Vice President For Research
Human Subjects Committee
Tallahassee, Florida 32306-2742
(850) 644-8673 · FAX (850) 644-4392
APPROVAL MEMORANDUM
Date: 4/21/2010
To: Tami Im
Dept.: EDUCATIONAL PSYCHOLOGY AND LEARNING SYSTEMS
From: Thomas L. Jacobson, Chair
Re: Use of Human Subjects in Research
The effects of emotional support and cognitive motivational messages on students' math Anxiety,
self-efficacy, and math problem solving
The application that you submitted to this office in regard to the use of human subjects in the
proposal referenced above have been reviewed by the Secretary, the Chair, and two members of
the Human Subjects Committee. Your project is determined to be Expedited per 45 CFR §
46.110(7) and has been approved by an expedited review process.
The Human Subjects Committee has not evaluated your proposal for scientific merit, except to
weigh the risk to the human participants and the aspects of the proposal related to potential risk
and benefit. This approval does not replace any departmental or other approvals, which may be
required.
If you submitted a proposed consent form with your application, the approved stamped consent
form is attached to this approval notice. Only the stamped version of the consent form may be
used in recruiting research subjects.
If the project has not been completed by 4/19/2011 you must request a renewal of approval for
continuation of the project. As a courtesy, a renewal notice will be sent to you prior to your
expiration date; however, it is your responsibility as the Principal Investigator to timely request
renewal of your approval from the Committee.
You are advised that any change in protocol for this project must be reviewed and approved by
the Committee prior to implementation of the proposed change in the protocol. A protocol
134
change/amendment form is required to be submitted for approval by the Committee. In addition,
federal regulations require that the Principal Investigator promptly report, in writing any
unanticipated problems or adverse events involving risks to research subjects or others.
By copy of this memorandum, the Chair of your department and/or your major professor is
reminded that he/she is responsible for being informed concerning research projects involving
human subjects in the department, and should review protocols as often as needed to insure that
the project is being conducted in compliance with our institution and with DHHS regulations.
This institution has an Assurance on file with the Office for Human Research Protection. The
Assurance Number is IRB00000446.
Cc: John Keller, Advisor
HSC No. 2010.4276
135
APPENDIX G
INFORMED CONSENT FORM
136
137
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143
BIOGRAPHICAL SKETCH
EDUCATION
Ph.D in Instructional Systems, August 2008 – August 2012
Florida State University: Tallahassee, Florida
Master of Arts in Educational Technology, September 2006 - August 2008
Korea University: Seoul, Korea
Bachelor of Arts in Education, March 1998 - February 2005
Korea University: Seoul, Korea
PROFESSIONAL EXPERIENCES
Teaching Assistant, Florida State University, January 2012 – August 2012
Research Assistant, Florida State University, August 2010 – August 2012
Research Assistant, Florida State University, July 2011 - August 2011
Research Assistant, Korea Education & Research Information Service, June 2010 October 2010
Online Teaching Assistant, Florida State University, August 2008 - July 2010
Research Assistant, Florida State University, December 2009
Research Assistant, Korea University, February 2008 - August 2008
Research Assistant, Center for Higher Education Policy Studies in Korea, October 2006
- February 2008
Graduate Assistant, Center for Teaching and Learning at Korea University, October
2006 - August 2007
Project Manager & Researcher, E-learning team in Korea Institute for Electronic
Commerce, May 2005 - October 2006
144
RESEARCH PROJECTS
Using 3D Virtual Reality for Social Communication Skills Development: A
Second Life-Based Learning Program for Children with Autism Spectrum Disorders
(ASD), January 2011 – August 2012
Florida State University
Florida PROMISE Training Project, July 2011 - August 2011
Florida State University
Incorporating Open Educational Resources into Higher Education in Korea, June 2010
- October 2010
Korea Education & Research Information Service
Educational Utilization of e-Portfolio-focused on Specific Functions in Elementary
School Setting, April 2008 - August 2008
Korea Education & Research Information Service
Evaluation of College Faculty, October 2006 - February 2008
Ministry of Education & Human Resources Development
Study on Statistics of College Faculty, September 2007- February 2008
Ministry of Education & Human Resources Development
Development of Faculty Achievement Evaluation Model with Associations, August 2007
- December 2007
Ministry of Education & Human Resources Development
Incorporation of National Universities and Faculty - Staff Administration, March 2007 August 2007
Ministry of Education & Human Resources Development
Study of Needs Assessment of Universities’ Enterprise Resource Planning (ERP)
System, October 2006 - March 2007
Ministry of Education & Human Resources Development
Study on u-Class Model, October 2006 - December 2006
Korea Education & Research Information Service (KERIS)
145
Industrial Sector-based e-Learning Pilot Project, December 2005 - October 2006
Ministry of Commerce, Industry and Energy
PRESENTATIONS
Im, T., & Ke, F. (2012). Mathematics Learning through Computer Educational Game
Design. Poster session at the 2012 American Educational Research Association (AERA)
Conference, Vancouver, Canada.
Im, T. (2011). The Effects of Achievement Goal Orientations and Motivational Discussion
Facilitating Strategies on Discourse Facilitation, Participation, and Satisfaction in On-line
Discussion. Full paper at the 2011 Association for Educational Communications and
Technology (AECT) International Conference, Jacksonville, USA.
Im, T. (2011). Development of Pedagogical Agents which delivering Emotional Support and
Cognitive Motivational Messages in a Computer Based Math module for GED students. Full
paper at the 2011 Association for Educational Communications and Technology (AECT)
International Conference, Jacksonville, USA.
Im, T. , & Keller, J. (2011). Possibility to Integrate Implicit Theory with Motivational
Messages. Round table at the 2011 Association for Educational Communications and
Technology (AECT) International Conference, Jacksonville, USA.
Ke, F., & Im, T. (2011). Mathematics Tutoring Anchored by Computer Games? Full paper at
the 2011 Association for Educational Communications and Technology (AECT)
International Conference, Jacksonville, USA.
Kang, M. , & Im, T. (2011). Factor Analysis of Learner-Instructor Interaction that Predict
Learning Outcomes in Online Learning Environment. Full paper at the 2011 Association for
Educational Communications and Technology (AECT) International Conference,
Jacksonville, USA.
Im, T. (2010). Roles of the Chat in a WebEx section: How is the Chat Going in a WebEx
Session? Full paper at the 2010 Association for Educational Communications and
Technology (AECT) International Conference, Anaheim, USA.
Im, T. (2010). The Effects of Emotional Support and Cognitive Motivational Messages on
Students’ Math Anxiety, Self-efficacy, and Math Problem solving. Reflection paper at the
146
2010 Association for Educational Communications and Technology (AECT) International
Conference, Anaheim, USA.
Im, T. (2010). The Effects of Emotional Support and Cognitive Motivational Messages on
Students’ Math Anxiety, Self-efficacy, and Math Problem solving. Invited presentation at the
Instructional Systems’ seminar in Florida State University, Tallahassee, USA.
Park, I., Kang, M., Im, T., & Lee, S. (2009). Relation between Learners' Participation and
Learning Achievement in e-Learning Environment of Cyber Universities. Full paper at the
International Conference for Media in Education 2008, Seoul, Korea.
Im, T. (2008). The effects of Achievement goal orientations and motivational discussion
facilitating strategy on facilitating discourse, participation, and satisfaction in on-line
discussion. Poster session at the KSET International Conference 2008, Seoul, Korea.
PROFESSIONAL SERVICE
President, Korean Instructional Systems Association, Florida State University, August
2010 - August 2011
Vice President of Operations and Finances, Instructional Systems Student Association,
Florida State University, January 2009 - July 2009
PROFESSIONAL MEMBERSHIPS
Associated for Educational Communication & Technology (AECT)
American Educational Research Association (AERA)
Korea Society for Educational Technology (KSET)
PROFESSIONAL AWARDS
2010-2011 Ruby-Diamond Future Professor Award, Florida State University, April, 2011
2010 Fall Dissertation Research Grant, Florida State University, Spring Semester, 2011
2010 Early Career Symposium funds, Association for Educational Communications and
Technology, 2010
Gagne-Briggs Scholarships, Florida State University, Fall Semester, 2008 - Spring
Semester, 2009
147
The Second Stage of BK21 Scholarships, Korea University, 2nd Semester, 2007
Administrative Assistant Scholarships, Korea University, 2nd Semester, 2006 - 2nd
Semester 2007
Research Assistant Scholarships, Korea University, 1st Semester 2008
148