Baughman 1
Self-Efficacy in Mathematics
HSRC#05110801
By
Allyson Baughman
455-95-9691
APPROVAL:
__________________________________
Chair, Graduate Advisory Committee
__________________________________
Member
__________________________________
Member
______________________________________
Dean, West College of Education
______________________________________
Date
Baughman 2
Self-efficacy in Mathematics
A Research Paper
Presented to
the Faculty of the West College of Education
Midwestern State University
In Partial Fulfillment
of the Requirements for the Degree
Master of Education
By
Allyson Baughman
April, 2006
Baughman 3
Abstract
The
purpose
of
this
study
was
to
describe
the
relationship
between self-efficacy and academic performance in my upper level
mathematics classes. A t-test of statistical significance was
used
to
explore
whether
there
was
a
difference
in
semester
averages and mathematics self-efficacy scores of male and female
advanced
placement
math
students.
A
Pearson’s
correlation
coefficient was also used to seek a relationship between selfefficacy and semester average. The data showed that there was
not a statistically significant difference in the averages of
males and females, yet there was a significant difference in
self-efficacy.
The
data
did
not
show
a
between self-efficacy and semester average.
linear
correlation
Baughman 4
Introduction
Bandura (1994) defined self-efficacy as a person’s belief
about his/her capability to produce at a level of performance
that will influence events that affect their lives. Selfefficacy can affect the classes students choose to take, their
field of study in college, and also their career choices as
adults.
As a female mathematics major at Oklahoma State University,
I was in the minority in each of my math classes. Of the nine
mathematics teachers at Burkburnett High School, I am one of
only three women. I believe many female students view
mathematics careers as male dominated and choose different
paths.
During my ten years of teaching, I have realized that my
female students perform quite well, especially those in my
upper-level math classes. I have had more female students earn a
passing score on the Advanced Placement Statistics exam than
male students. Even though my female students are succeeding in
mathematics, I hear more of them complain about their ability to
do math than their male counterparts.
The purpose of this study was to describe the relationship
between self-efficacy and academic performance in my upper level
mathematics classes. I felt this would give me some insight on
Baughman 5
why students perform the way they do in math classes, and why
students choose to take or not take more math classes in high
school. As an educator of mathematics, I would like to do my
part in encouraging more female students to choose math-based
careers.
My paper includes a review of literature, a description of
my research methods, my results, and a discussion concerning the
results.
Baughman 6
Review of Literature
The purpose of my research was to evaluate self-efficacy
among high school math students. Self-efficacy is how a person
feels about his/her ability to achieve success in specific
areas. Research shows that males have a higher self-efficacy and
perform better than females in mathematics (Bandura, 1994). My
review of literature explores mathematics self-efficacy as it
pertains to school, gender, and career choice.
Self-efficacy
Bandura (1994) defined self-efficacy as a person’s belief
about his/her capability to produce at a level of performance
that will influence events that affect their lives. Selfefficacy has an effect on one’s feelings, thinking, motivation,
and behavior. People with high self-efficacy approach difficult
tasks as challenges to overcome instead of threats to be
avoided. Shim and Ryan (2005) surveyed 361 college students from
a large midwestern university at the beginning of the semester
and immediately after receiving their first major grade. The
authors examined the role of goals in the change in motivational
constructs associated with performance feedback. Shim and Ryan
found self-efficacy and preference for challenges to be related
to achievement goals. Bandura also stated that students with a
strong sense of self-efficacy set high goals and make a
Baughman 7
commitment to achieving those goals. Even when faced with
failure, those with high self-efficacy recover quickly from
setbacks and move forward. The students with high self-efficacy
attribute failure to a lack of effort, knowledge, and skills,
but they know these things are acquirable. Having a strong sense
of self-efficacy helps produce personal accomplishments and also
reduces stress and depression.
According to Bandura (1994), students with low self-efficacy
doubt their ability, and in turn, back away from difficult
tasks. They view these tasks as personal threats and have very
little commitment in accomplishing these tasks. When a difficult
task presents itself, students with low self-efficacy dwell on
their own deficiencies instead of concentrating on how to
successfully perform the task. They are prone to slacken their
efforts and give up when faced with difficult situations. Those
with such low self-efficacy have a hard time recovering from
setbacks and view failure as inept performance and a deficiency
in aptitude. They lose faith in themselves and become stressed
and depressed. Shim and Ryan (2005) extend Bandura’s position by
suggesting that future learning and achievement is undermined
when one loses confidence, interest, and avoids challenges.
Bandura (1994) stated that four main components influence
one’s self-efficacy. Mastery experiences are the most important
Baughman 8
components needed to effectively create self-efficacy. Social
models provide another. If a person sees someone similar to them
succeeding because of the effort being put forth, they believe
they too can succeed and master comparable activities. An
important component to this modeling idea is strongly influenced
by one’s perception of the similarity to the models. If people
see the models as quite different from themselves, self-efficacy
is not influenced much by the model’s success. The third way to
strengthen self-belief is through social persuasion. If people
receive verbal persuasion that they have the ability to attain
certain goals, they are more likely to put forth more effort and
determination in mastering those goals. They are less likely to
doubt their abilities in mastering the activity. The final way
to promote self-efficacy is to reduce stress and negative
thoughts about being able to adequately perform certain tasks.
The idea of reducing stress and negative thoughts holds very
true in the case of careers. A person who is more efficacious
will explore a broader range of career paths. They will better
prepare themselves for certain occupations because they are not
afraid to face adversity. They, in turn, will achieve greater
success and gain a sense of personal growth through their
occupation.
Baughman 9
Bandura (1994) suggests that the creation of a learning
environment that ensures cognitive development relies heavily on
the talents and self-efficacy of teachers. Teachers who are
efficacious about their abilities are able to motivate students
and enhance their cognitive development. A student’s belief
about their capabilities to master certain subjects affects
their aspirations, their level of interest, and also their
academic accomplishments.
Mathematics Self-efficacy and School
Bong (2004) stated that students form motivational beliefs
that relate to specific academic tasks. The author also stated
that too many parents and teachers believe that motivation is
just part of a global personality trait. Some parents and
teachers mistakenly believe that students are motivated or not
motivated across all academic domains. In a study, Bong assessed
academic self-efficacy, task value, and achievement goals in
several subjects, including mathematics. Questionnaires were
given to 389 freshmen girls in a public high school in Seoul,
Korea. The author found that, on average, motivational beliefs
were more clearly defined for high school students than they
were for students in middle school. The study also found that
students hold different beliefs toward each subject matter. A
strong correlation was found to exist between self-efficacy
Baughman 10
across same subject areas, and a moderate correlation existed
between self-efficacy beliefs in different subject-matter
domains. Students neither gave credit for nor blamed ability
level for success or failure in different subject domains.
Stevens, Lan, and Tallent-Runnels (2004) observed selfefficacy and motivation across 358 Hispanic and Caucasian
students attending a West Texas high school to predict
mathematics performance and students’ plans to take additional
math classes. An intelligence test was used to measure the
general mental ability of each student and an 8-point Likerttype scale was used to measure mathematics self- efficacy. The
study found that self-efficacy indeed predicts both variables
being observed. Motivation appears to be predicted by selfefficacy, which, in turn, helps influence a student’s decision
to continue his/her involvement in math classes. Stevens et al.
also found that self-beliefs of efficacy and one’s motivation
were strongly correlated to achievement in mathematics. Students
who are more confident have greater intrinsic motivation and
welcome more challenging mathematics tasks. Those who do not
feel as efficacious in mathematics often shy away from
mathematical tasks and enroll in math classes because of
extrinsic motivators, such as parents and education
requirements. Stevens et al. also reported that students with
Baughman 11
greater intrinsic motivation chose to take additional math
classes.
Pajares and Miller (1997) studied 327 eighth grade algebra
students in a southern state by having the students complete a
survey in which math self-efficacy was measured. The authors
examined the relationship between self-efficacy and performance.
Pajares and Miller found that males were better predictors of
their performance than females at higher self-efficacy levels.
At lower self-efficacy levels, girls were better predictors of
performance.
Miller (2000) explored ways in which students become selfregulated learners by administering a 7-point Likert-type scale
to 297 midwestern public high school students. The author stated
that it is important for students to concentrate and focus on
their strengths rather than weaknesses in order to form better
perceptions of their learning. It is also crucial to not place
unrealistic expectations on students by placing them in groups
where the ability of the other group members far exceeds the
individual student. Miller believes it is important to compose
groups with like-abilities. A student is more likely to become
involved in a comparable work-group than one whose ability far
exceeds his/her capabilities. Stevens et al. (2004) suggested
Baughman 12
that teachers should focus on mathematics self-efficacy to
improve mathematics performance of all students.
Lopez and Lent (1992) explored the relation of four
different sources of self-efficacy of 50 math students taking
Algebra II at a public high school. Survey measures were used to
study the four sources that included personal background, math
self-efficacy, academic self-concept, and math/science
interests. The authors found that prior performance was the best
predictor of self-efficacy and that global academic self-concept
did not explain one’s self-efficacy variation beyond prior
performance. The study also showed that the effect of selfbeliefs of efficacy on the perceived importance of math to
future plans was mediated by students’ math/science interests.
Lopez and Lent discovered that emotional arousal was a strong
prediction of mathematics self-efficacy.
Mathematics Self-efficacy and Gender
Malpass, O'Neil, and Hocevar (1999) examined the effects of
gender, self-efficacy, learning goal orientation, selfregulation, and worry on the Advanced Placement calculus exam.
They studied 144 students from six public high schools in
Southern California. This study showed that self-efficacy is
positively related to math achievement, and that males were less
worried and had higher self-efficacy than females. Much research
Baughman 13
continues to support gender differences in mathematics in favor
of males. Research has also indicated that achievement in
mathematics is similar in males and females in all but the most
advanced math courses.
Malpass et al. believed that males would
score better than females on the Advanced Placement calculus
exam.
The exam is considered to be high-stakes because a
passing score can help a student earn admission into certain
colleges and also receive college credit. Self-efficacy was
measured immediately after the A.P. exam by showing the students
sample problems to remind them how they felt during the test.
This study did show that self-efficacy plays an important role
in achievement for these gifted students. Self-efficacy had a
large positive effect on the Advanced Placement calculus exam.
The authors believed that stimulating self-efficacy for gifted
students would prove to be beneficial in improving performance.
Rouxel (2000) used questionnaires to examine gender
differences in motivational beliefs of 476 fourth and fifth
grade students to determine whether there were qualitative or
quantitative differences. Qualitative differences were defined
as structural or functional differences, and quantitative
differences were found by using average scores. The author found
that self-efficacy was not linked to performance, and
anxiousness before an exam was linked to performance in female
students only. On the other hand, anxiety after the exam was
Baughman 14
related to performance. There was also a negative correlation
found between self-efficacy and anxiety.
Hyde, Fennema, Ryan, Frost, and Hopp (1990) performed a
meta-analysis of studies of gender differences in mathematics
affect and attitudes, which yielded 63,229 subjects. The authors
wanted to study the magnitude of gender differences in several
aspects of mathematics attitudes and affect, find the ages where
gender differences appear or disappear, and look for trends in
the magnitude of gender differences over time. Hyde et al. found
stereotyping to be a critical factor for the fewer numbers of
females in advanced math courses and math-related careers. The
meta-analysis showed that males stereotype math as a male domain
more than females. The authors stated that educators should be
concerned that male peers, male teachers, and male employers may
be discouraging females from careers in mathematics.
Mathematics Self-efficacy and Careers
Over the past several years, research has extended the role
of self-efficacy to be a major factor in the career process
(Cooper & Robinson, 1991). O'Brien, Martinez-Pons, and Kopala
(1999) surveyed 415 eleventh grade students from twelve
parochial high schools in a large metropolitan area. The survey
assessed math self-efficacy, ethnic identity, and career
interests. O'Brien et al. found that there are two major factors
contributing to the low number of women and minorities in
Baughman 15
science and engineering. One factor is the deficiency of selfperceived skill in mathematics. Mathematics skills play an
important role in the success of a career in science or
engineering. Lower self-efficacy in mathematics is a key
component of the lowered career interest in these two areas
among women. O'Brien et al. questioned whether improved
mathematics self-efficacy among women and minorities would be
required in order to increase the numbers of female and minority
scientists and engineers. The authors hypothesized that gender
influenced a student’s career choice in math or science. The
findings were that career interest is predicted solely by
science-mathematics self-efficacy, and that self-efficacy is
predicted by academic performance and ethnic identity.
Fouad and Smith (1997) stated that efforts to encourage
females and minorities to enter math and science careers have
not made substantial gains. Students lose more and more interest
in preparing for this type of career at each point in their
education: elementary school, middle school, high school, and
college. There have been programs that have emphasized changing
students’ self-efficacy in skills required to complete an
education in math and science. Dawes, Horan, and Hackett (2000)
suggested that preventative measures must continue in order to
prevent young women from prematurely closing the door on
mathematics-based career choices.
Baughman 16
Cooper and Robinson (1991) conducted a self-efficacy study
at a public midwestern university emphasizing applied sciences
and engineering. Two hundred ninety undergraduates were asked to
indicate their ability to complete each of ten advanced math
classes with a grade of B or better. The goals of the study were
to investigate the relationship of math and career selfefficacy, perceived external support, math background and
anxiety, and math performance in males and females pursuing a
mathematics-based degree. Cooper and Robinson’s research found
that support from parents and teachers had a weak positive
relationship with both mathematics self-efficacy and career
self-efficacy. A stronger relationship was found to exist
between teacher support and self-efficacy independent of
mathematics ability. The authors suggested that external support
from parent and teachers is even more crucial for students
taking advanced mathematics classes in high school. Cooper and
Robinson believe that teachers, counselors, and administrators
should explore specific expectations about math and career selfefficacy for students who are selecting a mathematics-based
career, those having mathematics anxiety, and those who are
having difficulty in math performance. The authors suggested
that finding ways to alter self-expectations might be the key
component in reducing anxiety and enhancing math performance.
Baughman 17
Increasing external support of parents and teachers could also
lead to a greater sense of self-efficacy among female students.
Paulsen and Betz (2004) surveyed 627 undergraduate students
enrolled in an introductory psychology course at a large midwestern university. The authors hypothesized that career
decision-making self-efficacy in college students is related to
self-efficacy related to basic components of a liberal arts
education. These components consist of mathematics, English,
science, and social science. According to Paulsen and Betz,
students who lack confidence in career decision-making also lack
confidence in the basic academic skill areas. Academic selfefficacy is also related to persistence in college. Paulsen and
Betz believed that strengthening one’s self-efficacy could prove
to be useful in assisting students’ choice of a career. The
researchers also felt that strengthening self-efficacy could
help keep students in college in order to pursue their career of
choice. The authors stated that because students begin to
develop ideas about education and career decision-making in high
school and college, it is important for educators and counselors
at these institutions to be aware of the relationship of careerdecision-making self-efficacy and low confidence in basic
academic skills such as mathematics.
Baughman 18
Summary
A review of the literature revealed that mathematics selfefficacy plays an important role in whether or not students will
choose to take advanced math classes and also in the decision to
pursue a mathematics-based career. Studies have shown that the
number of females pursuing math or science degrees and those in
math-based careers continue to be much smaller than males.
Educators and employers should be aware of the lower selfefficacy felt by some females and use this knowledge to
encourage females and reduce anxiety felt toward mathematics.
Baughman 19
Methodology
Purpose
The purpose of my research was to describe the relationship
between self-efficacy and achievement among advanced placement
math students and also to compare the self-efficacy and
achievement of male participants to that of female participants.
Participants and Context
The participants for this study were high school students
enrolled in Advanced Placement Calculus and Advanced Placement
Statistics. The high school is located in the southwest United
States and has approximately 950 students enrolled in ninth
through twelfth grade.
Procedures
The first day of class I distributed a survey to measure
self-efficacy. I compared self-efficacy of male and female
students using a two-tailed t-test of statistical significance.
I also compared achievement of my male and female students
using semester averages. These averages were made up of exams,
homework, and quizzes. I again used a two-tailed t-test of
statistical significance.
I then used Pearson’s R to seek a correlation between selfefficacy and achievement using the students’ self-efficacy
scores and semester averages.
Baughman 20
Results
A t-test of statistical significance was used to compare
the semester averages of male and female students. The results
are summarized in Table 1 below.
Table 1
Males = µ1
Females = µ2
Mean = 88.05
Mean = 82.62
Standard deviation = 8.77
Standard deviation = 8.66
N = 20
N = 21
A 2-sample t-test with the null hypothesis µ1  µ2 and the
alternative hypothesis µ1  µ2 produced a t value of 1.9940 with
38.8498 degrees of freedom and a p-value of .0532. At a
significance level of .01, the null hypothesis fails to be
rejected showing that there is not a significant difference in
the semester averages of males and females in an advanced
placement math class.
A t-test of statistical significance was also used to
compare the mathematics self-efficacy score of male and female
students. The results of this test are shown in Table 2.
Baughman 21
Table 2
Males = µ1
Females = µ2
Mean = 4.333
Mean = 3.7186
Standard deviation = .4598
Standard deviation = .6257
N = 20
N = 21
A 2-sample t-test with the null hypothesis µ1  µ2 and the
alternative hypothesis µ1  µ2 produced a t value of 3.5950 with
36.6937 degrees of freedom and a p-value of .0009. At a
significance level of .01, the null hypothesis must be rejected
showing that there is a significant difference in the
mathematics self-efficacy score of males and females in an
advanced placement math class. There was an outlier in the selfefficacy data, but the results did not change after the removal
of the outlier.
Pearson’s correlation coefficient was then used to seek a
relationship between a student’s mathematical self-efficacy
score and semester average. This test produced an r of .2279 (r²
= .0520), which shows there is not a meaningful linear
relationship between the mathematics self-efficacy score and the
semester average of advanced placement mathematics students.
Baughman 22
Discussion
The t-tests comparing semester averages versus gender and
mathematics self-efficacy versus gender showed that males and
females perform at relatively the same level, yet males feel
more confident in their math skills than females. This
paralleled other studies in the review of literature (Pajares &
Miller, 1997). The low self-efficacy in mathematics that females
are feeling may be keeping very qualified women out of jobs in
the field of mathematics. Females need to be encouraged at an
early age that they are just as capable in mathematics as their
male counterparts.
The Pearson’s R did not demonstrate a linear relationship
between mathematics self-efficacy and semester average. This was
not surprising because most advanced placement math students
have high self-efficacy in mathematics. As the semester averages
increased, there was not much change in the self-efficacy score.
A more detailed self-efficacy indicator might have made a
difference. A better self-efficacy survey could have separated
the scores a little more than they were. The results were also
not surprising because the t-tests showed that the averages for
males and females were approximately the same, yet the female
self-efficacy scores were lower. A male and female with the same
semester average did not have the same self-efficacy score.
Baughman 23
Further research needs to be done to determine when girls
become less efficacious in mathematics than boys. I believe it
would be helpful to know when it starts so educators can do
their part to try and prevent it from happening. Does it happen
at school, at home, or is it a social stigma that will take
years to undo? I believe these are valid questions that need to
be answered so we do not lose qualified women in math related
fields. Women are important to the field of mathematics, and we,
as educators, need to persuade them of that.
Baughman 24
References
Bandura, A. (1994). Self-efficacy. Encyclopedia of Human
Behavior, 4, 71-81.
Bong, M. (2004). Academic motivation in self-efficacy, task
value, achievement goal orientations, and attributional
beliefs. Journal of Educational Research, 97, 287-297.
Cooper, S. E., & Robinson, D. A.G. (1991). The relationship of
mathematics self-efficacy beliefs to mathematics anxiety
and performance. Measurement & Evaluation in Counseling &
Development, 24(1), 4-11.
Dawes, M. E., Horan, J. J., & Hackett, G. (2000). Experimental
evaluation of self-efficacy treatment on
technical/scientific career outcomes. British Journal of
Guidance & Counseling, 28(1).
Fouad, N. A., & Smith, P. L. (1997). Reliability and validity
evidence for the middle school self-efficacy scale.
Measurement & Evaluation in Counseling & Development, 30,
17-31.
Hyde, J. S., Fennema, E., Ryan, M., Frost, L. A., & Hopp, C.
(1990). Gender comparisons of mathematics attitudes and
affect. Psychology of Women Quarterly, 14, 299-324.
Lopez, F. G., & Lent, R. W. (1992). Sources of mathematics selfefficacy in high school students. Career Development
Quarterly, 41(1), 3-11.
Baughman 25
Malpass, J. R., O'Neil, Jr., H. F., & Hocevar, D. (1999). Selfregulation, goal orientation, self-efficacy, worry, and
high-stakes math achievement for mathematically gifted high
school students. Roeper Review, 21, 281-289.
Miller, J. W. (2000). Exploring the source of self-regulated
learning: the influence of internal and external
comparisons. Journal of Instructional Psychology, 27, 4752.
O'Brien, V., Martinez-Pons, M., & Kopala, M. (1999). Mathematics
self-efficacy, ethnic identity, gender, and career
interests related to mathematics and science. Journal of
Educational Research, 92, 231-235.
Pajares, F., & Miller, M. D. (1997). Mathematics self-efficacy
and mathematical problem solving: Implications of using
different forms of assessment. Journal of Experimental
Education, 65(3), 213-228.
Paulsen, A. M., & Betz, N. E. (2004). Basic confidence
predictors of career decision-making self-efficacy. The
Career Development Quarterly, 52, 354-362.
Rouxel, G. (2000). Cognitive-affective determinants of
performance in mathematics and verbal domains gender.
Learning & Individual Differences, 12, 287-310.
Baughman 26
Shim, S., & Ryan, A. (2005). Changes in self-efficacy, challenge
avoidance, and intrinsic value in response to grades: the
role of achievement goals. Journal of Experimental
Education, 73, 333-349.
Stevens, T., Olevarez Jr., A., Lan, W. Y., & Tallent-Runnels, M.
K. (2004). Role of mathematics self-efficacy and motivation
in mathematics performance across ethnicity. Journal of
Educational Research, 97, 208-221.
Baughman 27
Appendix
Semester Average
Self-efficacy Score
Gender
65
2
f
92
3.67
f
70
4.83
m
75
3.5
f
87
3.83
f
85
4.67
m
80
4
f
88
4.33
m
90
2.6
f
84
5
m
90
4.5
f
93
4.67
m
97
3.83
m
85
4
m
92
4
m
95
4.17
m
86
4.5
f
90
4.5
f
71
3.5
f
71
3.5
f
Baughman 28
81
4.67
m
72
4
f
71
3.83
m
80
4
f
92
4.33
m
88
3.5
f
91
3.33
f
90
5
m
87
4.33
f
80
3.33
f
100
4.5
m
90
3.33
m
91
3.67
f
70
3.83
f
88
3.5
f
77
4.83
m
84
4.67
m
91
4.5
f
100
3.83
m
87
4
m
100
4.17
m