PREDICTION OF 8 TH GRADE STUDENTS MATHEMATICS SELF-EFFICACY BY THEIR ACHIEVEMENT MOTIVATION AND SOCIAL COMPARISON

Selçuk Üniversitesi Ahmet Keleşoğlu Eğitim Fakültesi Dergisi Sayı 30, Sayfa 143-156, 2010 PREDICTION OF 8 TH GRADE STUDENTS MATHEMATICS SELF-EFFICACY BY THEIR ACHIEVEMENT MOTIVATION AND SOCIAL COMPARISON Şahin Kesici 1, Ahmet Erdoğan 2, İsmail Şahin 3 1 S. Ü. Ahmet Keleşoğlu Education Faculty, Department of Educational Sciences, sahinkesici@selcuk.edu.tr 2 S. Ü. Ahmet Keleşoğlu Education Faculty, Department of Secondary Sciences and Mathematics Education, ahmeterdogan@selcuk.edu.tr 3 S. Ü. Ahmet Keleşoğlu Education Faculty, Department of Computer and Instructional Technologies Education, isahin@selcuk.edu.tr ABSTRACT The purpose of this study was to examine whether 173 8 th grade students achievement scores in motivation and social comparison predict their mathematics self-efficacy in Turkey. Three different scales were provided to measure students social comparison, achievement motivation, and mathematics self-efficacy. Analyses indicated that while both social comparison and achievement motivation predicted mathematics self-efficacy subscale, achievement motivation predicted students awareness of their own behaviors concerning mathematics subjects and ability to transform mathematics efficacy into life skills subscales. Key Words: Mathematics Self-efficacy, Achievement Motivation, Social Comparison

Selçuk Üniversitesi Ahmet Keleşoğlu Eğitim Fakültesi Dergisi Sayı 30, Sayfa 143-156, 2010 BAŞARI GÜDÜSÜ VE SOSYAL KIYASLAMANIN SEKİZİNCİ SINIF ÖĞRENCİLERİNİN MATEMATİK ÖZ- YETERLİK ALGILARINI YORDAMASI Şahin Kesici 1, Ahmet Erdoğan 2, İsmail Şahin 3 1 S. Ü. Ahmet Keleşoğlu Eğitim Fakültesi, Eğitim Bilimleri Bölümü, sahinkesici@selcuk.edu.tr 2 S. Ü. Ahmet Keleşoğlu Eğitim Fakültesi, Ortaöğretim Fen ve Matematik Alanlar Eğitimi Bölümü, ahmeterdogan@selcuk.edu.tr 3 S. Ü. Ahmet Keleşoğlu Eğitim Fakültesi, Bilgisayar ve Öğretim Teknolojileri Eğitimi Bölümü, isahin@selcuk.edu.tr ÖZET Bu çalışmanın amacı, Türkiye deki 173 sekizinci sınıf öğrencisinin başarı güdüsü ve sosyal kıyaslama düzeylerinin öz-yeterliklerini yordayıp yordamadığını araştırmaktır. Bu amaçla, öğrencilerin başarı güdülerini, sosyal kıyaslama düzeylerini ve matematik öz-yeterliklerini ölçmek için üç farklı ölçek kullanıldı. Yapılan regrasyon analizi sonucunda öğrencilerin hem sosyal kıyaslama düzeylerinin hem de başarı güdülerinin matematik öz-yeterliğin matematik konularında davranışlarındaki farkındalık ve Matematiği yaşam becerilerine dönüştürebilme alt boyutlarını yordadığı görüldü. Anahtar Kelimeler: Matematik Öz-yeterliği, Başarı Güdüsü, Sosyal Kıyaslama

Prediction of 8 th Grade Students Mathematics Self-Effıcacy 145 INTRODUCTION Relationships have been found between students mathematics competence and self-efficacy (Hacket & Betz, 1989; Stevens, Olivarez, & Hamman, 2006; Spence & Usher, 2007). Therefore, students first should perceive their selfefficacy to gain mathematics self-efficacy. Thus, it will be useful to make an analysis related to the concept of self-efficacy, the features of students with low and high self-efficacy, and mathematics self-efficacy. Umay (2001) states that mathematics self-efficacy consists of three components: 1) mathematics self-concept, 2) awareness in behaviors concerning mathematics subjects, and 3) ability to transform mathematics efficacy into life skills. Especially, mathematics self-concept may have a significant role in forming mathematics self-efficacy. Reyes (1984) uses the terms mathematics confidence and mathematics self-concept as synonyms. Felson (1984) mentions academic self-concept as self-perceptions of ability and he puts forward the idea that these perceptions affect the effort, persistence, and anxiety of students; hence, it affects their performance as well. Bandura (1986) indicates that self-concept, perceived usefulness, and anxiety concepts are common mechanisms of personal agency like self-efficacy beliefs and they affect the results, too. Also, these mechanisms are, to a great extent, largely due to the confidence with which individuals approach a task. On the other hand, Bong and Skaalvik (2003) claim that selfconcept has a cognitive and an affective element; however, self-efficacy is related to cognitive appraisals of competence. Self-concept is partially formed by reflection of others evaluations. Self-efficacy is based on perceptions of mastery rather than normative criteria (Zimmerman, 1995). Academic self-concept mentions perception of the individual, based on school success (Reyes, 1984). A person s mathematical self-concept mentions perception, belief, mathematics competence, or confidence in learning mathematics. Felson (1984) describes academic self-concept as competence perception and states that one of the reasons why this perception affects students performance is that it also influences students efforts, persistence, and anxiety. Students may develop awareness in behaviors concerning mathematics subjects to raise their mathematics self-efficacy. This is because mathematics is perceived as more difficult and requires more effort compared to many other subjects (Eccles, Adler, & Meece, 1984; Stodolsky, Salk, & Glaessner, 1991). According to Gottfried (1990), mathematics requires a very powerful intrinsic motivation. Concepts like perceptions of mathematics usefulness (Armstrong, 1985), and positive attitudes and interest towards mathematics (Ashcraft, Kirk, & Hopko, 1998; Utsumi & Mendes, 2000) are related to high mathematics performance. Kloosterman (1988) indicates that students who trust their mathematics competence are more relaxed when they come across mathematics cases; thus, developing self-confidence is important in its own right. Students with mathematics confidence are more apt to choose mathematics when schools provide optional mathematics courses (Perl, 1979; Reyes, 1984; Hunt, 1985).

146 Ş. Kesici, A. Erdoğan, İ. Şahin Students' perceived usefulness of mathematics is also related to the confidence they have (Hackett & Betz, 1989; Lent, Lopez, & Bieschke, 1991). Math selfefficacy is influential in solving specific mathematics problems (Betz & Hackett, 1983). Collins (1982) indicates that when previous performance is checked, students with high self-efficacy outperform to solve mathematics problems, create more effort and persistence, and retry longer to solve incorrect problems compared to students with low self-efficacy. The ability to transform mathematics efficacy into life skills may be effective in students developing mathematics self-efficacy. Mathematics self-confidence is determined a conceptual predictor of mathematics self-efficacy and consistent in the prediction of mathematics performance (Hackett, 1985). In the past, mathematics self-efficacy used to be evaluated globally by asking general questions about students perceived abilities. Recently, students have been required to solve specific mathematics problems, perform mathematics-related tasks, or succeed in mathematics-related courses for evaluation (Betz & Hackett, 1983). Bandura (1986) expresses that self-efficacy strongly influences the choices people make, the efforts they expend, and how long they persevere in the face of challenge. In Social Comparison Theory, Festinger (1954) assumes that people have a drive to evaluate their views and competencies. People need to know their own capacities and limitations, and they have to confirm their opinions of objects and other people (Jones & Gerard, 1967). Wood (1989) suggests that people, who harbor goals other than accurate self-evaluation and social environment, cannot be always obliging. Gilbert, Giesler, and Morris (1995) state the social comparison process is "spontaneous, effortless, and unintentional" and "relatively automatic" (p. 227). Festinger (1954) states that engaging social comparison is a spontaneous response of humans. When social comparisons with others is very high or very low, engaging social comparison is probable (Gilbert, Giesler, & Morris, 1995). Bandura (1997) suggests that when one lacks relevant prior experiences with the task at hand, social comparison is critical and significant. Festinger (1954) expresses that individuals make social comparisons to decrease indefiniteness and evaluate their own abilities accurately. Festinger (1954) puts forward hypotheses to explain the basis and process of social comparison. The hypothesis in the focus of social comparison is There exists, in the human organism, a drive to evaluate his opinions and his abilities (p. 117). Social comparison may exist automatically and is an inevitable element of social interaction (Brickman & Bulman, 1977). In case there is not an objective criteria available, individuals may eliminate indefiniteness of the evaluation criteria by comparing their own views, competencies, and performance with that of others. The situation which occurs in the absence of social comparison is put forward in another hypothesis as: In the absence of both a physical and a social comparison, subjective evaluations of opinions and abilities are unstable. In upward comparison, an individual may compare him/herself with the highest ones and may learn from the superior other. On the other hand, if one assumes

Prediction of 8 th Grade Students Mathematics Self-Effıcacy 147 similarity on surrounding dimensions, the upward comparison may be selfenhancing (Berger, 1977). When individuals experience no luck or no achievement, they frequently compare themselves with inferior or less advantaged ones (Wills, 1981). In Sarafino, Russo, Barker, Consentino and Titus (1982) study, in the case of a comparison made by taking an average as the reference, social comparison praise was contrasted with feedback, indicating that children were average. This may have been discouraging for some highachieving children. Marsh (1986) dwells upon social and external comparisons and argues that students base their academic self-concepts in a particular subject not only on how their ability compares with those of other students (i.e., social or external comparison), but also on how their ability in that subject compares with their abilities in other subjects (i.e., internal comparison). He also states that internal comparison is presumed to create a negative relationship between achievement in one domain and self-concept in other domains. In their study, Thwaites and Dagnan (2004) underline the effect of social comparison on the individual and other individuals. Findings from this study support the prediction that the relationship between social comparison on a particular dimension and depression is moderated by the perceived importance of dimension in attracting the interest of others. Michinov (2001) states that upward or downward social comparison may affect well-being and self-esteem negatively and positively. While upward comparison may have a negative effect, downward comparison may have a positive effect. Sarafino et al. (1982) indicate that when socialcomparison praise is contrasted with feedback indicating that children are average, some of the more successful students may be disappointed. Corpus, Ogle, and Love-Geiger (2006) argue that social-comparison praise enhances the perceptions of competence and afterwards intrinsic motivation continues to increase. In Achievement Motivation Theory, Atkinson suggests that while tasks of moderate difficulty are preferred in positively motivated subjects (i.e., subjects with motive to achieve success stronger than motive to avoid failure), too easy or too hard tasks are preferred in negatively motivated subjects (i.e., subjects with motive to achieve success weaker than motive to avoid failure). Atkinson (1974) notes that an individual can be motivated to avoid failure, depending upon the expectancy and the incentive value of failure, and this inhibits achievementoriented behavior. In McClelland s (1962) Achievement Motivation Theory, three needs (success, power, and close relationship) are underlined as the significant predictors of individuals behaviors. The basic element of motivation is to head towards a goal or intentionality, the determinant of dealing with a specific behavior (Atkinson, 1964). Murayama and Elliot (2009) conceptualize achievement goals as the goal of competency- related pastimes of individuals or the focus of their cognitive-dynamics (Maehr, 1984; Dweck & Leggett, 1988; Nicholls, 1989; Elliot, 1997). An individual with a high need for achievement is described as the one who is willing to achieve difficult tasks, maintain high criteria, work for distant goals, put forth effort to attain excellence, and react to competition positively (Jackson, 1974; 1999). Intrinsic motivation is the

148 Ş. Kesici, A. Erdoğan, İ. Şahin satisfaction from the own nature of the activity and performance in the activity for oneself (Berlyne, 1965; Eccles, Wigfield, & Schiefele, 1998). Students with high intrinsic academic motivation achieve better and they have more positive competence perception and lower academic anxiety from childhood through adolescence (Gottfried, 1985, 1990; Gottfried, Fleming, & Gottfried, 1994). According to Hart, Stasson, Mahoney, and Story (2007), conscientiousness, openness, and extraversion are positively associated with intrinsic achievement motivation; whereas, extraversion, conscientiousness, and neuroticism are positively related to extrinsic achievement motivation. Agreeableness is also found to be negatively associated with extrinsic achievement motivation. Social comparison and achievement motivation are significant for students to improve their mathematics efficacy. This study aims to investigate if social comparison and achievement motivation predict students mathematics efficacy. In this respect, the following hypotheses are tested in this study: 1. Achievement motivation and social comparison are significant predictors of 8 th grade students mathematics self-concepts. 2. Achievement motivation and social comparison are significant predictors of 8 th grade students awareness in behaviors concerning mathematics subjects. 3. Achievement motivation and social comparison are significant predictors of 8 th grade students ability to transform mathematics efficacy into life skills. METHOD Achievement motivation and social comparison are independent variables and mathematics self-efficacy is the dependent variable. In this study, the extent to which achievement motivation and social comparison scores serve as predictors of mathematics self-efficacy is analyzed. Participants Participants of the study are 8 th grade students in Konya City, Turkey. The study group consists of a total of 173 students 101 boys (58.4%) and 72 girls (41.6%). Measures Self-efficacy Scale toward Mathematics, Achievement Motivation Scale, and Social Comparison Scale were administered. Achievement Motivation Scale. Developed by Umay (2002), this scale has 14 items and is three-dimensional. This scale is used to measure the achievement

Prediction of 8 th Grade Students Mathematics Self-Effıcacy 149 motivation of the students expected to have high achievement motivation. The internal reliability of this scale was high (omega =.84). Social Comparison Scale. Social Comparison Scale, developed by Gilbert, Allan, and Trend (1991), was adapted to Turkish by Şahin and Şahin in 1992 (Gilbert et al., 1991; Şahin, & Şahin, 1992; adapted by Savaşır & Şahin, 1997). This self-evaluation scale measures how individuals perceive themselves when they compare themselves with others, based on various dimensions. It is twodimensional and consists of 18 items. The internal reliability was calculated as.87. Self-efficacy Scale Toward Mathematics. Developed by Umay (2001), the Selfefficacy Scale Toward Mathematics consists of 14 items on a 5-point Likert-type scale. The internal reliability of this scale was high (omega =.88). The validity coefficient of items is determined as 0.64. This value can be taken as a criterion that can measure the validity of the entire scale. The scale consists of three dimensions mathematics self-concept, awareness in behaviors concerning mathematics subjects, and ability to transform mathematics efficacy into life skills. Procedure and Analysis Multiple linear regression analysis was used to estimate the relationship between students mathematics self-efficacy (mathematics self-concept, awareness in behaviors concerning mathematics subjects, and ability to transform mathematics efficacy into life skills), and the predictor variables, achievement motivation, and social comparison. Data were analyzed using SPSS 15.00 (Statistical Package for Social Sciences) software. RESULTS A stepwise regression analysis method was used to determine whether 8 th grade students achievement motivation and social comparison are predictors of mathematics self-concept, a dimension of mathematics self-efficacy. Findings from the stepwise regression analysis are summarized in Table 1. According to the findings from this study, achievement motivation and social comparison are significant predictors of 8 th grade students mathematics self-concept (p <.01). However, 6.3% of the variance in mathematics self-concept is explained by social comparison, while 9.8% of its variance is explained by social comparison and achievement motivation. Table 1. Summary for Stepwise Regression Analysis of Mathematics Self-concept Model a R R 2 R 2 adj SE R 2 chg F adj df F chg 1.262 b.069.063 3.71.069 12.63 1/171.000 2.329 c.109.098 3.64.040 7.57 1/170.007 a: Dependent variable: Mathematics self-concept. b: Predictors: (Constant), social comparison. c: Predictors: (Constant), social comparison and achievement motivation.

150 Ş. Kesici, A. Erdoğan, İ. Şahin A stepwise regression analysis was used to determine whether 8 th grade students achievement motivation is a predictor of awareness in behaviors concerning mathematics subjects, a dimension of mathematics self-efficacy. Findings summarized in Table 2 showed achievement motivation was a significant predictor of 8 th grade students awareness in their own behaviors concerning mathematics subjects (p <.01). However, only 6.6% of the variance in awareness in behaviors concerning mathematics subjects is explained by achievement motivation. Table 2. Summary of Stepwise Regression Analysis for Awareness of Behaviors Concerning Mathematics Subjects Model a R R 2 R 2 adj SE R 2 chg F adj df F chg 1.268 b.072.066 3.28.072 13.18 1/171.000 a: Dependent variable: Awareness in behaviors concerning mathematics subjects. b: Predictors: (Constant), achievement motivation. A stepwise regression analysis method was used to determine whether 8 th grade students achievement motivation is a predictor of ability to transform mathematics efficacy into life skills, a dimension of mathematics self-efficacy. Results summarized in Table 3 show achievement motivation is a significant predictor of 8 th grade students ability to transform mathematics efficacy into life skills (p <.01), Overall, about 12.7% of the variance in ability to transform math efficacy into life skills is explained by achievement motivation. Table 3. Summary for Stepwise Regression Analysis of Ability to Transform Mathematics Efficacy into Life Skills Model a R R 2 R 2 adj SE R 2 chg F adj df F chg 1.364 b.132.127 1.98.132 26.07 1/171.000 a: Dependent variable: Ability to transform mathematics efficacy into life skills. b: Predictors: (Constant), achievement motivation. DISCUSSION AND CONCLUSIONS Mathematics self-efficacy beliefs cannot be thought of as one-dimensional when related to mathematics, a course requiring calculations, problem-solving skills, and performance. According to the Self-efficacy Scale Toward Mathematics, mathematics efficacy is a multidimensional (mathematics self-concept, awareness in behaviors concerning mathematics, and ability to transform mathematics efficacy into life skills) concept. Social comparison and achievement motivation are predictors of students mathematics self-efficacy. Students may prefer to make social comparisons, while gauging their own self-perception related to mathematics. Bong and Skaalvik s (2003) argument, self-concept has a cognitive and an affective

Prediction of 8 th Grade Students Mathematics Self-Effıcacy 151 component, is important. The self-concept is partially formed through reflected appraisals of others (Zimmerman, 1995). On the other hand, an individual needs achievement motivation to develop a positive self-concept through social comparison. Achievement motivation is a significant predictor of 8 th grade students awareness of their own behaviors concerning mathematics subjects. Students should recognize their mathematics efficacy, while transforming their mathematics knowledge into behavior. In addition, they should transform this efficacy into performance, while accomplishing school tasks. Also, moderate predictive correlations between perceived self-efficacy and school task performance have been found in several studies (Bandura & Schunk, 1981; Schunk, 1981). According to various studies, the correlation between selfconfidence and achievement has been moderately strong (Fennema & Sherman, 1977; Fennema, 1984; Hackett, 1985; Meyer & Fennema, 1986). Self-efficacy belief is one of the concepts related to students self-esteem and the ability to recognize behaviors concerning mathematics subjects. Pietsch et al. (2003) indicate that self-efficacy beliefs should be more highly related to academic achievement than self-concept. Achievement motivation is a significant predictor of 8 th grade students ability to transform mathematics efficacy into life skills. Efficacy belief plays a significant role on students ability to transform mathematics efficacy into life skills because students should perceive themselves efficient in math to be able to achieve academic performance. Self-efficacy belief is pervasive as a significant predictor of academic performance (Bandura, 1997). When prior performance was controlled, students with high self-efficacy scores surpass those with low selfefficacy in the completion of novel math problems, have better performance, and insist more to rework incorrect problems (Collins, 1982). In conclusion, to increase mathematics efficacy, students may develop a positive self-concept related to mathematics. Also, they may be aware of their behaviors concerning mathematics subjects and may have an ability to transform their mathematics efficacy into life skills. At the same time, students should compare their achievement motivation and self-concept with peers positively. They should avoid negative comparisons. Students should recognize task values necessary to perform well in mathematics tasks and they should recognize the effort required to achieve these tasks, as well. Students, who show more effort, are also more aware of behaviors concerning mathematics subjects and their ability to transform mathematics efficacy into life skills.

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