Gender Differences in University Students’ Perceptions of
and Confidence in Problem-Solving Abilities
Shelly L. Wismath and Maggie Zhong
University of Lethbridge,
Lethbridge, AB, Canada
Oct. 24, 2012.
Abstract:
Problem-solving skills are crucial components of an education for the 21st century, and
confidence and self-efficacy have been shown to be critical to the development and
practice of such skills. In a study of perceptions of and confidence in problem-solving
abilities by students enrolled in a university course specifically focused on teaching
problem-solving skills, we found significant gender differences in perceived confidence
and ability. The average score for all students (male and female) on these indicators
increased significantly from the pre-test to post-test. However, female students ranked
themselves much lower in both confidence and abilities at the start of the course than
male students, but also showed a remarkably larger increase in these indicators by the end
of the course. This result confirms the necessity of and potential for helping female
students develop confidence in their problem-solving abilities.
Gender Differences in University Students’ Perceptions of
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and Confidence in Problem-Solving Abilities
Introduction
There has been a long and well-documented history of under-representation of women in
the STEM fields of science, technology, engineering and mathematics (Schiebinger,
2001; Corbett, Hill & Rose, 2008; Leder, Rowley & Brew, 1999; Taylor, Leder, Pollard
& Atkins, 1996). Many theories have been advanced to explain this under-representation,
including both biological and social factors (Schiebinger, 2001). Zeldin and Pajares
(2000) have argued that confidence and self-efficacy are key factors impacting whether
women enter into or remain in STEM programs and careers: ``Women aptly competent in
mathematics often fail to pursue mathematics-related careers because they have low selfefficacy perceptions about their competence” (p. 218).
Sadker and Sadker (1994) described the gender differences in belief in math and science
abilities as a “confidence gap.” Bandura (1995) defines self-efficacy as “the belief in
one’s capabilities to organize and execute the courses of action required to manage
prospective situations” (p. 2). Various studies have shown an important correlation
between self-efficacy and student achievement (Bandura, 1996; Liu, Hsieh, Cho and
Schallert, 2006) and mathematics achievement (Stevens, Olivárez, Lan, & TallentRunnels, 2004). Bandura (2001) found that students' perceived efficacy is the main
determinant of their perceived professional self-efficacy and career choice.
Problem-solving skills are a key component of success, particularly in mathematics but
more generally in all STEM fields (NCTM, 2000). More generally, problem solving is
one of the focus areas of 21st century learning (Kay, 2010). Here too confidence plays a
large role. Zimmerman and Campillo (2003) argue that “having knowledge and skill
does not produce high-quality problem solving if people lack the self-assurance to use
these personal resources” (pp. 240-241), and that such confidence and self-efficacy “are
predictive of persistence and effort during problem solving because they assess beliefs
about personal competence and value” (pp. 241-22). In addition, more self-efficacious
people display more effort and persistence (Bandura, 1997; Schunk, 1984; Zimmerman,
2000).
Although there is a substantial literature on the development of problem-solving skills,
study has often focused on elementary and secondary level students, and on narrowly
defined mathematical problem solving (Polya, 1945; Arizpe, Dwyer & Stevens, 2012;
Zambo & Follman, 1994). A literature review of gender differences in mathematical
problem solving by Zhu (2007), while comprehensive, also shows this focus. The study
described here broadens the scope of discussion in two ways: we consider university
students, and a slightly broader context of general problem-solving and critical thinking
skills.
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Methodology
Data was collected from 38 students enrolled in a university elective science course
called Problems and Puzzles, which focused on developing students’ problem-solving
and critical thinking skills. The course involved some study of mathematical problems
(word problems using simple algebraic solution of equations) but the focus of the course
was on general problem solving. Study participants completed a pre- and post-course
attitudinal survey, consisting of 37 questions using a five-point Likert scale. They also
completed three reflection assignments during the course, in which they discussed their
progress on various components of the course.
Survey Results
Thirty-eight students (22 females and 16 males) participated in this study. We carried out
paired t-tests on the 37 attitudinal questions, comparing pre-test and post-test scores, for
all participants, and separately for males and for females. Four questions yielded
significant (α < 0.05) gender-differentiated results:
 “I have good problem-solving skills”
 “I am confident in my ability to solve problems”
 “I like doing math word problems”
 “I am nervous when I have to tackle a new problem”
The first two of these questions addressed students’ perception of their problem-solving
ability and their confidence in their problem-solving skills. These two questions indicated
a significant increase for the whole group (α < 0.001); but the gender differences are
particularly striking for these questions. The data indicates a significant change in all
students’ perception of their problem-solving abilities, and most particularly for female
students (Table 1).
Table 1: Response by Gender for Que. 32: “I have good problem-solving skills.”
Strongly
Strongly
Response
Disagree Neutral Agree
mean median
Disagree
Agree
Female,
0
3
13
6
0
3.14
3.00
Pre-Test
Female,
0
0
2
18
2
4.00
4.00
Post-Test
Male,
0
0
5
8
3
3.88
4.00
Pre-Test
Male,
0
0
2
7
7
4.31
4.00
Post-Test
t-test
sig
.000
.048
At the beginning of the course, only 6 of 22 female students (27.3%) agreed with the
statement “I have good problem-solving skills,” and none “strongly agreed.” A majority
of females, 59.1%, described themselves as neutral, while 3 (13.6%) “disagreed.” This is
in sharp contrast to the male students, where fully 50% of males agreed that they had
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“good problem-solving skills,” while another 18.8% “strongly agreed,” and no males
disagreed with this statement. Five of 16 male respondents (31.2%) rated themselves as
neutral.
On the post-test, both male and female results indicated an increase in mean score: an
increase of 0.43 for males and 0.86 for females. Although the female participants still did
not rate their problem-solving skills as highly as males did by the end of the study, they
indicated a markedly larger increase in their responses – the median response for females
increasing from 3.00 (“neutral”) to 4.00 (“agree”).
On the pre-test, female responses regarding their problem-solving skills were distributed
across the “Disagree” (14%), “Neutral” (59%) and “Agree” (27%) categories. However,
on the post-test, no female respondents selected the “Disagree” option, and the “Neutral”
group shrank to 9%. Fully 91% of female students selected “Agree” or “Strongly Agree”
(Figure 1).
Figure 1. Female participant pre-test and post-test responses for Que. 32: “I have good
problem-solving skills.”
The survey statement “I am confident about my ability to solve problems” was intended
to specifically address students’ perceived confidence in their abilities, rather than their
perception of skill. For female respondents, the mean positive response to this statement
rose by 0.72, from 3.14 to 3.86, in comparison to a increase for male respondents of 0.50,
from 3.94 to 4.44. While males indicated higher levels of confidence in their problemsolving skills than female respondents, both at the beginning of the course and at the end,
female respondents exhibited once again a greater and significant (α < 0.001) increase in
their perceived confidence in problem-solving abilities (Table 2).
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Table 2: Response by Gender for Que. 33: “I am confident in my ability to solve
problems.”
Strongly
Strongly
t-test
Response
Disagree Neutral Agree
mean median
Disagree
Agree
sig
Female 0
3
13
6
0
3.14
3.00
Pre-Test
.000
Female 0
0
5
15
2
3.86
4.00
Post-Test
Male
0
2
0
11
3
3.94
4.00
Pre-Test
.056
Male
0
0
1
7
8
4.44
4.50
Post-Test
At the beginning of the course, only 27% of female indicated that they were confident in
their problem-solving abilities, while the rest were either neutral (59%) or negative
(14%) regarding this. On post-test results for female respondents, the “Neutral” responses
shrank to 23%; while 68% of female respondents agreed that they were confident in their
abilities, and 9% strongly agreed. Thus 77% of female students either agreed or strongly
agreed that they were confident of their problem-solving skills by the end of the course
(Figure 2).
Figure 2. Female participant pre-test and post-test responses for Que. 33: “I am confident
in my ability to solve problems.”
It is important to note here that we did not conduct an objective test of actual problemsolving skills, and thus did not compare actual problem-solving performance between the
beginning and the conclusion of the course. The data reported here is based on students’
own assessment of their skills and confidence level. Thus we cannot conclude whether
male participants were in fact better problem-solvers than females, or whether students
were better problem-solvers overall by the end of the course. But they certainly
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manifested more confidence in their own abilities and perceived their skills to have
improved.
We have focused on these two questions as the key indicators of perceived ability and
confidence. It is interesting to note that on the pre-test, the female students provided an
identical breakdown of scores on both questions; and while their perceptions of both
skills and confidence increased by the post-test, the skill rankings increased more than the
confidence ones. The male students, by contrast, rated themselves slightly higher on
confidence than skills on the pre-test, and maintained this ordering on the post-test.
Two other questions related to confidence in and enjoyment of problem solving showed
gender differences. There was a significant increase for females in response to the
statement “I like doing math word problems,” (α < 0.001). Since this is a major area of
discomfort in mathematics for many people, it is encouraging to see an increase in
comfort level here. Additionally, the statement “I get nervous when I have to tackle new
problems” also indicated a gender-differentiated response. Although the pre-test to posttest change was not statistically significant, the difference between the t-test for females
(α = 0.090) and for males (α = 0.483) suggests that factors of gender may be at play
here too.
Reflection Assignment Results
The survey results discussed above indicates that students in the study perceived that they
gained both problem-solving skill and confidence in their problem-solving abilities over
the course of the semester. In addition to the survey data, we collected open-ended
responses from students from three reflection assignments (graded for completion only)
in the course.
On the final reflection assignment at the end of the semester, students were explicitly
asked “Do you think that you are a better problem-solver after taking this course?”
Nineteen of the twenty-two female students (86.4%) indicated that they felt that they had
improved their problem-solving skills. One student noted that ``I still have difficulties
with math problems but have improved a significant amount since the beginning of this
course.” For a number of female students, simply being willing to and knowing how to
start a problem was a major step, as these two student responses suggest:
I definitely think that I’m a better problem-solver after taking this course,
if not solely for the fact that I actually even attempt to solve problems
now. Before taking this course, I would simply give up or avoid entirely
any problem that hinted any form of mathematically-related thinking or
logical reasoning. This course has taught me that I’m capable of solving
these types of problems as well as helpful ways to approach problems that
intimidate me.
I believe I am a better problem solver. This class has taught me different
strategies to look at problems and different ways to solve them. It has
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taught me to think out of my thinking strategy box and outside my comfort
zone. I also have to try and attempt problems which I find really hard and
want to give up but with different strategies I am able to keep going and
find the answer.
Although the reflection assignment specifically asked students about their perception of
their problem-solving abilities, over half of the female responders also spontaneously
referred to an increase in their confidence. The following two comments were typical:
I am confident approaching problems and am able to follow through and
finish in a productive manner. Even though problems can be slightly
intimidating, I now enjoy tackling them, whether in this course or in other
areas.
When I come across a problem or a puzzle, I usually feel very anxious
because I never know where to start. After taking this course, I can finally
take a step back and find more than one approach to take. It gives me
patience and confidence to try and tackle a problem without the fear of
getting it wrong. I now know that I can use a mistake as a learning
experience.
Finally, we quote here two extended responses from students, to highlight how strongly
the female students themselves view confidence and self-efficacy as an important part of
their learning in problem solving, and in their development into good problem solvers.
I am doing very well in the course and have learned a lot of problem
solving methods that help to make problems/puzzles easier and less scary.
I feel I have the tools to tackle almost any problem. […] but most of all
I’ve realized I always had the capability to be a good problem-solver, I
had already a lot of tools and skills that contribute to better problemsolving, but I just didn’t have the know how to put the two together; the
right method with the right problem. Now, I can do that. In this class I’ve
learned how best to tackle a problem, what strategies work best with
certain kinds of problems. […] now I know that the strategies I am using
and the answers I am getting have merit and it is a process not just picking
random answers or trying random things hoping to get the right
answer/any answer. So now I feel more confident in the step-by-step
process of problem solving strategies.
The goals that I had before taking this course were to do the best I could
for a class that was outside my comfort zone and to ultimately improve my
problem solving skills. I have definitely exceeded my expectations for this
course. I thought that I would start off quite slow and then improve as the
course went on. To my surprise, I actually caught on a lot quicker than I
personally expected and excelled right away. […] I most definitely think
that I am a better problem solver after taking this course. […] I honestly
think that I have developed the confidence in my problem solving abilities
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to be better able to explain strategies and processes. […] It has taught me
that if I put my mind to a task or complicated assignment and stick to it, I
will eventually find the answer I am looking for. Trying this course that
was completely outside my comfort zone only developed characteristics
that established the self-belief that I have the ability to achieve anything I
put my mind to.
Based on societal attitudes about and pressures on females in STEM areas, one might
question whether the female students were actually as lacking in confidence as they
reported themselves to be: perhaps they simply felt that they could not acknowledge their
actual perceptions. If this is the case, it still speaks strongly to gender differences in
attitudes in STEM areas. But we also argue that statements by students such as those in
the above two extensive quotes show that the participants did indeed feel real anxiety and
lack of confidence at the start of our study.
Conclusion and Discussion
Often post-secondary STEM courses seem to emphasize the coverage and acquisition of
content, rather than focusing on increasing students’ confidence in their problem-solving
abilities. The course this study was based on was explicitly designed to provide students
with hands-on experience in problem solving, including mathematical problem solving. It
did not focus on gender as an issue, although our data has revealed significant gender
differences. The course was very much non-traditional in format (Wismath, 2012;
Wismath, Orr & Good, 2012). It offered an unthreatening and even fun atmosphere for
students to engage in a variety of problems and puzzles to build their skills. Most in-class
time involved active participation by students as they attempted to solve problems, either
individually or in groups; lecturing by the instructor was kept to a minimum, and students
were encouraged to lead the “debriefing” of a problem by sharing their strategies and
solutions with the class. Students were also introduced to metacognitive strategies of
problem-solving, and encouraged to reflect on their progress and skill development.
Despite decades of efforts to increase female success in math-related fields and female
recruitment and retention in STEM careers (AAUW, 2008), there is still debate about
gender differences in performance in areas such as problem solving. Whether such
differences are due to differences in ability or simply to differences in social climate and
attitude, it is clear that self-efficacy can make a significant difference for female students.
Perception of self-efficacy can affect whether students are willing to try courses or
programs that require math skills or general problem-solving skills. Moreover, this
perception, or lack thereof, affects the future use of such skills (Schneider and Pressley,
1989). As Zimmerman and Capillo (2003) argue, “teaching students to use problemsolving strategies does not guarantee their continued use or generalization to similar tasks
unless other self-regulation processes and a wide array of motivation beliefs are
involved" (p. 252).
In this study, we found that perception of confidence and self-efficacy in problem solving
increased among students taking a course in problem-solving skills, with lower
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confidence and self-efficacy levels at the start for female students but a larger increase in
these indictors for females than for male students by the end of the course. This is
especially important for female students, as confidence is known to affect their
participation in STEM areas (Zeldin & Pajares, 2000).
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