Gender Differences in University Students’ Perceptions of and Confidence in Problem-Solving Abilities

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 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 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, 13 3.14 3.00 Pre-Test Female, 0 18 4.00 4.00 Post-Test Male, 0 3.88 4.00 Pre-Test Male, 0 7 4.31 4.00 Post-Test t-test sig 000 048 At the beginning of the course, only 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 (13.6%) “disagreed.” This is in sharp contrast to the male students, where fully 50% of males agreed that they had “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 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) 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 13 3.14 3.00 Pre-Test 000 Female 0 15 3.86 4.00 Post-Test Male 11 3.94 4.00 Pre-Test 056 Male 0 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 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 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 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 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 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 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 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) References American Association of University Women (2008) Women and girls in STEM Washington, DC: Author Arizpe, Barry J., Dwyer, Jerry, and Stevens, Tara (2012) Mathematical self-efficacy of middle school students solving the Rubiks cube International Journal for Mathematics Teaching and Learning Available online at http://www.cimt.plymouth.ac.uk/journal/dwyer2.pdf (July 23, 2012) Bandura, A (1995) Self-Efficacy in Changing Societies New York: Cambridge University Press Bandura, A., Barbaranelli, C., Caprara, G.V., & Pastorelli, C (1996) “Multifaceted Impact of Self-Efficacy Beliefs on Academic Functioning.” Child Development, Vol 67, No 3, 1206-1222 Bandura, A., Barbaranelli, C., Caprara, G.V., & Pastorelli, C (2001) “Self-Efficacy Beliefs as Shapers of Children’s Aspirations and Career Trajectories”, Child Development, Vol 72, No 1, 187-206 Corbett, C., Hill, C., & Rose, A (2008) Where the girls are The facts about gender equity in education Washington: American Association of University Women Kay, K (2010) 21st Century Skills: Why they matter, what they are, and how we get there Foreword in: 21st Century Skills: Rethinking how students learn, J Bellanca and R Brandt (eds.) 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