The Gender Confidence Gap in Fractions Knowledge: Gender Differences in Student Belief–Achievement Relationships
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<ul><li><p>The Gender Confidence Gap in Fractions Knowledge: GenderDifferences in Student BeliefAchievement Relationships</p><p>John A. RossUniversity of Toronto</p><p>Garth ScottKawartha Pine Ridge DSB</p><p>Catherine D. BruceTrent University</p><p>Recent research demonstrates that in many countries gender differences in mathematics achievement have virtuallydisappeared. Expectancy-value theory and social cognition theory both predict that if gender differences in achievementhave declined there should be a similar decline in gender differences in self-beliefs. Extant literature is equivocal: thereare studies indicating that the male over female advantage in self-efficacy and beliefs about math learning is as strongas ever and there are studies reporting an absence of gender differences in belief. Using data from 996 grades 710Canadian students, we found that gender differences in beliefs continued, even though gender differences in achieve-ment were near zero. Gender differences, favoring males, were larger for self-beliefs (math self-efficacy and fear offailure) and weaker for functional and dysfunctional beliefs about math learning. There were also gender differences inthe structure of a model linking beliefs about math, beliefs about self and achievement.</p><p>The achievement gap refers to a persistent advantage ofmales over females in student achievement in mathematicsthat begins in the early years and continues into high schooland postsecondary education. Research syntheses con-ducted 20 years ago (Friedman, 1989; Hyde, Fennema, &Lamon, 1990) found that the achievement gap has beengetting smaller over time, and some recent research,reviewed below, suggests that the gap has vanished entirely.The confidence gap refers to a similar male over femaleadvantage in student self-confidence and willingness toengage in mathematical tasks. In contrast with reporteddeclines in achievement, the confidence gap appears tocontinue, despite predictions that the confidence andachievement gaps would decline together (Falco & Crethar,2008; Linver & Davis-Kean, 2005). In this article, we drawon social cognition theory and recent research on genderdifferences in mathematics learning to frame an investiga-tion into the relationship between gender differences inmathematics achievement and beliefs about self and math-ematics learning.</p><p>Gender differences in self-beliefs and beliefs in math-ematics learning have short- and long-term implications. Inthe short term, beliefs affect achievement (as shown in theliterature reviewed below): A gender gap in affect mightexplain why some studies find gender differences inachievement. In the long term, beliefs influence studentwillingness to take advanced courses in mathematics(Ansell & Doerr, 1996) and to access careers that requiremathematical training.</p><p>Social cognition theory (Bandura, 1997), particularly theconstruct of self-efficacy, provides a mechanism that wouldaccount for changes in student confidence taking place atthe same time as changes in achievement. Self-efficacy isan expectancy about future performance, a set of domain-specific self-beliefs about ones ability to organize andexecute the actions required to perform particular tasks.Self-efficacy contributes to higher achievement (demon-strated in the literature review below), and higher achieve-ment is interpreted by students as evidence that they havethe ability to perform similar tasks in the future. The reviewof Usher and Pajares (2008) found that mastery experiencesare the most powerful source of self-efficacy information.The reciprocal reinforcement of achievement and self-efficacy produces an upward or downward spiral in whichchanges in one stimulate and sustain changes in the other.From this perspective, if females are becoming as success-ful as males on mathematics tasks, the self-beliefs offemales and other facets of their belief systems should be assupportive of mathematics learning as the self-beliefs andbelief systems of males. If gender differences in achieve-ment are declining, then gender differences in confidenceshould also be declining. The aim of our research was toinvestigate this proposition.</p><p>Literature ReviewGender and Mathematics Achievement</p><p>Some studies, especially those conducted in the Nether-lands (Seegers & Boekaerts, 1996; Veenstra & Kuyper,</p><p>278 Volume 112 (5)</p></li><li><p>2004), continue to find that males outperform females onmeasures of mathematics performance, especially on moredifficult items (Duffy et al., 1997). More frequently,gender differences in achievement are near zero (Else-Quest, Hyde, & Linn, 2010; Lloyd, Walsh, & Yailagh,2005; Pajares & Graham, 1999; Silver, Strutchens, &Zawojewski, 1996; Stringer & Heath, 2008). Gender pat-terns vary across countries. For example, analysis of theNational Assessment of Educational Progress data, 19902003, found that gender differences in achievement weresmall but consistent over time in the United States,growing larger in the upper grades and with White, eco-nomically advantaged and high-ability students (McGraw,Lubienski, & Strutchens, 2006). Canadian data reported inProgramme for International Student Assessment (PISA)found a male achievement advantage in 1999 (Edgerton,Peter, & Roberts, 2008) and in 2003 (Bassani, 2008; Else-Quest et al., 2010). But studies using samples drawn fromsingle Canadian provinces show a trivial male advantage,typically around .05 standard deviations (SDs), or no dif-ference at all (Lloyd et al., 2005; Ma & Klinger, 2000;Randhawa & Hunter, 2001; Rogers et al., 2006; Ross &Kostuch, 2011; Stringer & Heath, 2008).</p><p>Gender differences in achievement are moderated byassessment methods. Females receive higher report cardgrades in mathematics than males, even when there are nogender differences on standardized mathematics tests(Kenney-Benson, Pomerantz, & Ryan 2006; Lekholm &Cliffordson, 2009).A plausible explanation for the discrep-ancy in assessments is that teachers reward females withhigher grades than their test scores warrant because femalesexert more effort on assigned tasks (Lekholm & Clifford-son, 2009) and are more compliant with classroom rules.Females tend to score better on open-ended than onmultiple-choice items; the reverse is the case for males,although findings are mixed (Willingham & Cole, 1997).Gender, Beliefs About Self, and Achievement</p><p>In social cognition theory, self-efficacy mediatesbetween goals and actions. Self-efficacy contributes tohigher achievement in mathematics (e.g., Bandura, 1997;Borman & Overman, 2004; Bussiere, Cartwright, &Knighton, 2004; Kenney-Benson et al., 2006; Lee, 2006;Marsh, Dowson, Pietsch, & Walker, 2004; Pajares &Graham, 1999; Stringer & Heath, 2008). The key mecha-nisms linking self-efficacy and achievement are that stu-dents with high self-efficacy, in contrast with students withlow self-efficacy, adopt mastery goal orientations (Schunk,1996), persist through obstacles (Multon, Brown, & Lent,1991), and maintain better control of their emotions(Bandura, 1997). Achievement is further strengthened</p><p>through the links of self-efficacy to causal attributions (highself-efficacy students attribute success to ability) and otherpsychological constructs related to achievement such asmathematics anxiety and mathematics self-concept(Pajares, 1996). Because high self-efficacy students believethat they will be successful, they are less likely to bediscouraged by fear of failure, a construct inversely relatedto achievement (Caraway, Tucker, Reinke, & Hall, 2003;Eaton & Dembo, 1997; Heinze, Reiss, & Rudolph, 2005;Rao, Moely, & Sachs, 2000).</p><p>Pajares (1996) review of self-efficacy research foundthat males are consistently more confident than femalesabout their mathematical ability. More recent research ismixed: Some studies continue to find mathematics self-efficacy to be higher in males than females (Bussiere et al.,2004; Fredricks & Eccles, 2002; Friedel, Cortina, Turner,& Midgley, 2007; Preckel & Freund, 2005), while othersreport no gender differences (Kenney-Benson et al., 2006;Rao et al., 2000; Tapia & Moldavan, 2007). Because therelationship between self-efficacy and achievement isreciprocal, if the achievement gap disappears, it is possiblethat the confidence gap would decline and perhaps evendisappear. In an analysis of national data from the Trendsin Mathematics and Science Study and the PISA 2003,Else-Quest et al. (2010) found that countries with genderdifferences in achievement also had gender differences inmathematics confidence and related self-beliefs; correla-tions were in the r = .30s and .40s. The achievementbeliefs relationship is positively correlated on anindividual student basis; however, when we move to largerscale analyses, they have been found to be negatively cor-related (Shen & Tam, 2008). No studies have reportedgender differences for fear of failure, but given the corre-lation of fear of failure with self-efficacy, it is likely thatgender differences will be in the same direction.Gender, Beliefs About Mathematics, and Achievement</p><p>General attitudes toward mathematics, such as liking thesubject, are associated with higher achievement (Andersonet al., 2006; Silver et al., 1996). Researchers who focus onspecific beliefs about mathematics and its learning reportthat students tend to hold beliefs that impede success onmathematical tasks. These dysfunctional beliefs includethe assumption that mathematical ability is fixed (Schoe-nfeld, 1989), that problems are solved quickly or not at all(Lampert, 1990; Schommer-Aitkins, Duell, & Hutter,2005), that mathematical knowledge is separate fromknowledge in other domains (Buehl & Alexander, 2005),that one has to use all the numbers provided by a problemto find its solution (Hart, 1993), that some problemsrequire only calculation while others require thinking</p><p>The Gender Confidence Gap in Fractions Knowledge</p><p>School Science and Mathematics 279</p></li><li><p>(Callejo & Vila, 2009), among others. Less attention hasbeen devoted to functional beliefs about mathematics,such as participation in student discussions helps one learn(Jansen, 2006). Some studies have reported that malestend to have more positive attitudes toward mathematicsthan females (Ercikan, McCreith, & Lapointe, 2005), butgender differences on specific beliefs about mathematicsand its learning reported to date have been very small(Schoenfeld, 1989; Tapia & Moldavan, 2007).Gender and AffectAchievement Relationships</p><p>Although there is considerable research investigatinggender differences in mathematics achievement and affect,little attention has been given to whether there are genderdifferences in the relationships among achievement andaffect. Seegers and Boekaerts (1996) found the relation-ship between self-beliefs and achievement to be the samefor males and females, in a sample of 10- to 11-year-oldDutch children, as did Meece, Wigfield, and Eccles (1990)for grade 79 American students.Explanations for Discrepancies Between Beliefsand Achievement</p><p>Stereotypes that females lack mathematical ability arepersistent, even with growing evidence that there are few ifany differences in recent mathematics achievement.Gender differences in confidence occurring simultaneouslywith gender equivalence in achievement have been reportedin other stereotypical male domains such as science (Har-gittai & Shafer, 2006), engineering (Chachra & Kilgore,2009), and technology (Andre, Whigham, Hendrickson, &Chambers, 1999). According to social cognitive learningtheory, girls who observe women in their culture or societynot becoming engineers or scientists or mathematiciansavoid, and are anxious about, these subjects because theyare perceived as outside the realm of what is possible(Bussey & Bandura, 1999). Females who hold stereotypicalbeliefs about mathematics as a male domain have lowerperformance on examinations than females who do not holdsuch views and are less likely to seek careers requiringmathematics competence (Kiefer & Sekaquaptewa, 2007;Schmader, Johns, & Barquissau, 2004). The discrepancybetween confidence and achievement might be attributableto support for gender stereotyping.</p><p>Social cognition theory also provides a second explana-tion for the discrepancy between confidence and achieve-ment, despite their correlation: Self-efficacy beliefs are aconsequence of student reflection on their achievement. It isnot the absolute level of performance that matters but thestudents interpretation of it. For example, the runner whocomes last in the race may view her performance positivelyif it establishes a personal best. The misalignment of con-</p><p>fidence and achievement might be based on the internalcomparisons that females make between their perceivedperformance in mathematics and in subjects emphasizingliteracy skills.</p><p>Research QuestionsOur study was guided by two research questions:1. To what extent do gender patterns in mathematics</p><p>achievement on fractions tasks match gender patterns inself-beliefs and beliefs about mathematics learning? Wepredicted that gender differences would be near zero, but ifthere were differences, males would score higher thanfemales. Gender differences might be visible in oursample because we measured performance on number andoperations tasks associated with gender differences inNational Assessment of Educational Progress (McGrawet al., 2006), and the sample had a high proportion ofWhite students that were relatively advantaged economi-cally. However, individual ethnic and socioeconomicstatus information was not available. We anticipated thatgender differences in affect would be aligned with genderdifferences in achievement, that is, that the differenceswould be small or nonexistent and, if present, would favormales over females. Specifically, we predicted that maleswould have higher self-efficacy and lower fear of failurethan females. We also anticipated that males wouldexpress greater support than females for functional beliefsabout mathematics (i.e., beliefs that contribute to studentlearning) and would hold dysfunctional beliefs aboutmathematics less strongly than females. In contrast, weanticipated that females would report exerting greatereffort in mathematics class than males, in line with previ-ous findings about the greater compliance of females thanmales with classroom requirements (Cole, 2010).</p><p>2. To what extent is the relationship between studentbeliefs and achievement on fractions tasks moderated bygender? Because prior research was limited on this issue,we made no specific predictions.</p><p>MethodSample</p><p>Complete data sets were obtained from 996 grade 710students (aged 1316 years) (N = 500 males and 496females) participating in a technology-based unit on frac-tions in 20072008. Eighty-two percent of the sample wasin grades 78, with the remainder in grades 910. Thespecific features of the fractions instruction are notdescribed because they are not relevant to the researchquestions addressed here (see Bruce & Ross, 2009 forinformation on the fractions instruction).The students were</p><p>The Gender Confidence Gap in Fractions Knowledge</p><p>280 Volu...</p></li></ul>
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