Running head: GENDER DIFFERENCES IN SELF-EFFICACY AND MODELING TASKS
Gender Differences in Self-Efficacy Beliefs and Mathematical Modeling Tasks
Anu Sharma
University of Florida, Gainesville
Author Note
Anu Sharma, School of Teaching and Learning, University of Florida.
Anu Sharma is now at the Center for Educational Testing and Evaluation (CETE),
University of Kansas.
This manuscript is based on data previously used in a doctoral dissertation.
Correspondence concerning this article should be addressed to Anu Sharma, Center for
Educational Testing and Evaluation, 1122 West Campus Road, Room # 431, Joseph R. Pearson
Hall, University of Kansas, Lawrence, KS-66045.
Email: [email protected]
GENDER DIFFERENCES IN SELF-EFFICACY AND MODELING TASKS
2
Abstract
The present study investigated the relationship between self-efficacy judgments and students’
performance on mathematical modeling tasks by gender. Participants included 122 female and
103 male eighth- and ninth-grade students. Self-efficacy beliefs were measured using a selfreport measure, modeling self-efficacy scale. Modeling outcomes were measured in terms of
participants’ success in solving six modeling problems, adapted from the PISA 2003 problemsolving assessment. The main and interaction effects were tested using structural equation
modeling techniques, which indicated that male and female participants did not differ
significantly on modeling self-efficacy beliefs (β = 2.848, p = .175). Further, the interaction
between self-efficacy beliefs and gender on modeling task success was marginally significant (β
= 0.015, p = .055). Among participants with low self-efficacy judgments about mathematical
modeling tasks, female participants outperformed male participants. However, among
participants with high self-efficacy judgments, male participants outperformed female
participants. The implications for future research and the limitations of this study are discussed.
Keywords: self-efficacy, mathematical modeling tasks, gender differences
GENDER DIFFERENCES IN SELF-EFFICACY AND MODELING TASKS
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Gender Differences in Self-Efficacy Beliefs and Mathematical Modeling Tasks
A central tenet of social cognitive theory is that human functioning involves reciprocal
interactions among personal, behavioral, and environmental factors (Bandura, 1997;
Zimmerman, 2000). Further, the theory states that proactive, self-reflecting, and self-regulated
learners have the capacity to take control of their thoughts, feelings, and actions. According to
Bandura (1997), learners display this sense of personal agency because of the self-efficacy
beliefs that they hold about themselves and their capabilities. In academic settings, particularly
school mathematics, self-efficacy refers to students’ judgments about their abilities to solve
mathematical problems, perform mathematics-related tasks, or engage in mathematical activities
(Pajares, 1996). These beliefs reflect students’ judgments about how successful they will be at
performing a task in the future, rather than their actual performance level.
Research shows that self-efficacy beliefs are related to and predictive of students’
mathematical achievement (Chen, 2003; Greene, Miller, Crowson, Duke, & Alley, 2004;
Nicolidau & Philippou, 2004; Pajares, 1996; Pajares & Graham, 1999; Pajares & Kranzler, 1995;
Pajares & Miller, 1994, Pajares & Valiante, 2001; Pintrich & DeGroot, 1990). Efficacy
judgments positively influence students’ engagement with complex tasks, their persistence in
completing complex tasks, and the amount of cognitive effort they exert during problem-solving
activities (Schunk & Mullen, 2012; Schunk & Pajares, 2009). Further, students’ confidence in
their abilities predicts success in mathematics better than anxiety about mathematics (Pajares &
Miller, 1994), prior math experience (Pajares & Miller, 1994), and attitudes toward mathematics
(Nicolidau & Philippou, 2004). Moreover, Pajares and Kranzler (1995) found stronger direct
effects of students’ self-efficacy beliefs on mathematical problem-solving performance when
general mental ability was controlled for. With regard to gender differences in self-efficacy
GENDER DIFFERENCES IN SELF-EFFICACY AND MODELING TASKS
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beliefs, researchers have found mixed results. For example, some researchers have reported that
female students have lower confidence in their abilities to solve mathematical tasks or perform
mathematical activities than male students do (Pajares, 2005; Pajares & Miller, 1994; Pajares &
Graham, 1999; Sadker & Sadker, 1994; Seegers & Boekaerts, 1996). Some researchers (e.g.,
Fouad & Smith, 1996; Middleton & Midgley, 1997; Pajares & Graham, 1999; Pajares &
Kranzler, 1995), however, have not found any gender differences in self-efficacy beliefs or
students’ academic performance.
Given this literature, the present study investigates whether gender differences in selfefficacy beliefs exist for students engaged in real-world mathematical modeling tasks. Modeling
with mathematics is the process of using knowledge and skills from across and within a
curriculum to solve problems arising in everyday life, society, and workforce (National
Governors Association Center for Best Practices, Council of Chief State School Officers, 2010).
Mathematical modeling has been regarded as an effective platform for providing students with
experiences that support the development of mathematical knowledge and skills essential to
succeed in life beyond school (English & Sriraman, 2010; Galbraith, 2012; Lesh & Zawojewski,
2007). While solving mathematical modeling problems, students work with tables of values,
graphs, and charts to “describe, explain, or predict patterns or regularities associated with
complex and dynamically changing systems” (Lesh, 2000, p. 179). Students make sense of
realistic situations by engaging in processes of mathematization such as quantifying, organizing,
sorting, weighting, and coordinating data. Because of the current emphasis in mathematics
education on engaging students in mathematical modeling tasks, it is important to understand the
gender differences in self-efficacy beliefs in understanding and completing modeling tasks, and
in modeling-task success. Further, as mathematical modeling activities promote the development
GENDER DIFFERENCES IN SELF-EFFICACY AND MODELING TASKS
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of 21st skills and abilities (English & Sriraman, 2010; Galbraith, 2012; Lesh & Zawojewski,
2007), information about students’ self-efficacy beliefs about modeling tasks and their success in
solving these tasks may be helpful in understanding their decisions to pursue careers in science,
technology, engineering, and mathematics. The present study was guided by two research
questions:
1. To what extent are there gender differences in students' perceived capabilities to
understand and solve mathematical modeling tasks?
2. To what extent the relationship between self-efficacy beliefs and modeling outcomes is
mediated by gender?
Methods
Participants
The current study recruited 225 eighth- (n = 88, 39.11%) and ninth-grade (n = 137,
60.8%) students from a local research developmental school affiliated with the researcher’s
university. The average age of the participants was 14.22, with a standard deviation of 0.85. The
number of female participants (n = 122, 54.2%) was slightly higher than the number of male
participants (n = 103, 45.8%). Participants reported their ethnicity as White (n = 111, 49.3%),
African American (n = 46, 20.44%), Hispanic (n = 33, 14.6%), Asian (n = 12, 5.33%), and
Native Hawaiian (n = 1, 0.44%). The remaining participants reported their ethnic background as
either a combination of the listed ethnicities (n = 19, 8.4%) or as “others” (n = 3, 1.33%).
Materials and Procedure
Two instruments were used to measure the desired constructs. First, a modeling selfefficacy scale was used to measure participants’ efficacy judgments about the modeling tasks
(Sharma, 2014). This scale was appropriate because it was especially developed for measuring
GENDER DIFFERENCES IN SELF-EFFICACY AND MODELING TASKS
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self-efficacy beliefs about mathematical modeling tasks. Participants provided judgments of their
perceived capabilities to correctly solve modeling problems on a 100-point scale. The scale was
divided into 10-unit intervals ranging from 0, representing “not at all sure”, to 100, representing
“very sure”. The self-efficacy survey consisted of four items:
(i)
How sure are you that you can understand this mathematical problem?
(ii)
How sure are you that you can determine a strategy to solve this problem?
(iii)
How sure are you that you can determine the information required to solve this
problem?
(iv)
How sure are you that you can solve this mathematical problem correctly?
The second instrument used in this study was a test composed of six real-world situations
that examined participants’ modeling success competence. The modeling test was developed by
adapting problems from the Programme for International Student Assessment (PISA) 2003
problem-solving assessment (Organization for Economic Co-operation and Development
[OECD], 2004). These problems were selected because researchers in the field of mathematical
modeling have regarded problems from PISA assessments as complex modeling tasks (Blum,
2011; Carriera, Amado, & Lecoq, 2011; MaaΒ & Gurlitt, 2011; Mousoulides, 2007;
Mousoulides, Christou, & Sriraman, 2008). The modeling test assessed participants’ modeling
performance on three different types of tasks: decision-making, system analysis and design, and
troubleshooting (OECD, 2004). The decision-making tasks measured the extent to which
participants could make appropriate decisions by choosing strategically among several
alternatives provided under a given set of conditions. The system analysis and design tasks
required participants to identify complex relationships among the variables or to design a system
by satisfying all the conditions given in a problem. The third type of task, troubleshooting
GENDER DIFFERENCES IN SELF-EFFICACY AND MODELING TASKS
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problems, required participants to diagnose, rectify, and improve a faulty or underperforming
system. The modeling test included two problems for each type of task.
Participants who returned signed consent forms completed the self-efficacy survey and
solved problems on the modeling test in two sittings during regular class periods. Participants
took approximately 15 minutes to rate their confidence in solving modeling tasks after reading
them. They solved the problems on the modeling test in approximately 30 minutes.
Results
Participants’ performance on the modeling test was evaluated in accordance with the
scoring system used in the PISA 2003 problem-solving assessment. The associations between
self-efficacy beliefs and participant’ success on modeling tasks were examined by gender using
structural equation modeling (SEM) techniques. The statistical calculations, such as estimating
fit indices, errors, and model parameters, were performed using the program, Mplus Version 7.1.
Sharma (2013) study found that self-efficacy beliefs about modeling tasks directly predict
students’ success in mathematical modeling tasks (β = .50, p < .001). That is, students who
reported higher levels of confidence in understanding and solving modeling tasks were more
successful in solving these tasks. The present study did not find any significant gender
differences in self-efficacy beliefs about understanding and solving modeling tasks (β = 2.848, p
= .175). In other words, male and female participants did not differ significantly in their
confidence in understanding and solving modeling tasks. The interaction between gender and
self-efficacy beliefs on modeling-task success was marginally significant (β = 0.015, p = .055).
The regression equations including relationships between self-efficacy and mathematical
modeling success for male participants and female participants indicated that the influence of
self-efficacy beliefs on modeling-task success was larger for male participants (β = 0.040, p =
GENDER DIFFERENCES IN SELF-EFFICACY AND MODELING TASKS
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.000) than for female participants (β = 0.025, p = .000). Further, the interaction plot indicated
that female participants outperformed male participants in the group of students who reported
below about 1 standard deviation above the mean on self-efficacy, but male participants
outperformed female participants in the group of students who reported above about 1 standard
deviation above the mean on self-efficacy (see Figure).
Discussion
The present study is focused on understanding whether male and female participants hold
different self-efficacy beliefs about their ability to understand and solve mathematical modeling
tasks. The study also considers whether the relationship between self-efficacy beliefs and
participants’ modeling outcomes is mediated by gender. The male and female participants in this
study did not differ significantly in their confidence in solving real-world modeling tasks. This
finding contradicts earlier assertions made by Pajares and Miller (1994), Sadker and Sadker
(1994), and Seegers and Boekaerts (1996), who found male students to be more self-efficacious
than female students for solving mathematical tasks. One of the possible explanations for the
contradictory findings is that the participants in this study reported their self-confidence in
solving real-world modeling tasks, rather than general mathematical problems. Further, the
modeling problems used in this study did not require participants to learn and master
mathematical concepts and skills (OECD, 2004). As a result, gender differences typically find in
self-efficacy about solving mathematical tasks are not replicated in the present study.
On the actual PISA problem-solving assessment, the difference between the mean
performance of male and female U.S. students was not statistically significant (OECD, 2004). In
contrast to the present study, the gender differences found in the PISA problem-solving
assessment were not investigated by controlling for self-efficacy beliefs about these tasks. The
GENDER DIFFERENCES IN SELF-EFFICACY AND MODELING TASKS
9
present study found only a marginal relationship between self-efficacy and gender in
participants’ success in solving modeling problems correctly. Among the group holding low selfefficacy beliefs about their ability to solve modeling problems, female participants performed
better than male participants; and among the group holding high self-efficacy beliefs about their
ability to solve modeling tasks, male participants outperformed female participants. These results
show that male students can more accurately assess and report their levels of self-efficacy about
modeling tasks than female students can. Additionally, the study found the influence of selfefficacy beliefs on students’ performance in modeling tasks to be greater for male participants
than for female participants.
The present study, however, has two limitations. First, the present study asked
participants to report their confidence in their ability to solve modeling tasks. Because students
are seldom engaged in real-world problem solving in school, it is likely that participants failed to
understand the complexity involved in the tasks and the cognitive demands posed by them. Thus,
participants may have underestimated or overestimated their judgments about their own
competence in solving the modeling tasks. Second, the modeling problems were adapted from
the PISA 2003 problem-solving assessment. These problems were situated within real-world
contexts and embedded within the subject-areas of mathematics, science, and reading (OECD,
2004). Participants’ performance on the modeling test may have been influenced by individual
differences in reading ability, cognitive ability, familiarity with the context of the problem,
socioeconomic status, or prior mathematics achievement. The present study did not control for
the influence of these factors on participants modeling achievement.
Despite these limitations, the results of the present study have important implications for
educators and for future research. The study provided evidence that the influence of self-efficacy
GENDER DIFFERENCES IN SELF-EFFICACY AND MODELING TASKS
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beliefs on modeling-task success was greater for male participants than for female participants
although there were no significant gender differences in self-efficacy beliefs about understanding
and solving modeling tasks. This implies that female students who are confident in their ability
to understand modeling task do not benefit from this confidence as much as male students do.
Therefore, teachers should not only support students in raising their self-efficacy beliefs about
complex modeling problems, but also educate students to self-reflect, self-monitor, and selfevaluate their solution processes. This is because metacognitive behaviors, such as monitoring
actions, evaluating solutions, and regulating strategies, support students in solving modeling
problems (Magiers & Zawojewski, 2011). Furthermore, teachers should encourage students to
participate in classroom discussions and explain their thought processes when they are engaged
in real-world modeling tasks.
Because analytical reasoning skills have been found to correlate strongly with students’
problem-solving success (OECD, 2004), future researchers might study gender differences in
analytical reasoning skills and the influence of these skills in correctly solving modeling tasks.
Researchers may study relationships between self-efficacy beliefs and mathematical modeling by
adding analytical reasoning skills to the statistical model. Because the present study was
conducted with participants from a research developmental school, future researchers should
consider replicating this study with public school students, and compare the self-efficacy beliefs
and mathematical modeling performance of male and female students from the research and
public schools.
GENDER DIFFERENCES IN SELF-EFFICACY AND MODELING TASKS
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Manuscript submitted for publication.
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Figure: Regression of mathematical modeling achievement on self-efficacy about modeling tasks
by gender