1. Introduction

in their academiclly proposed thatese expectations

self-efcacy. For, task values, and

International Journal of Educational Research 72 (2015) 129136

Article history:

Received 18 March 2015

Received in revised form 15 June 2015

Accepted 17 June 2015

Available online 1 July 2015

Keywords:

Mathematics

Self-efcacy

Teacher support

Intrinsic motivation

Effort

Persistence

Help-seeking behavior

In this study we analyzed if teacher support and student self-efcacy mediated the

relations between students grades in mathematics and different measures of

mathematics motivation. Participants in the study were 823 Norwegian middle school

students. Indicators of motivation were intrinsic motivation, effort, persistence, and help-

seeking behavior. Data were analyzed by means of multiple regression and SEM analysis.

The relations between students grades and motivation were partly mediated through

emotional support and self-efcacy.

2015 Elsevier Ltd. All rights reserved.

Contents lists available at ScienceDirect

International Journal of Educational Research

jo u r nal h o mep age: w ww.els evier .c o m/lo c ate / i jed ur espersistence (see, Bong & Skaalvik, 2003). Both researchers and educators have also been concerned with the quality of thestudentteacher relationship and recent studies have also documented that students motivation for schoolwork ispositively related to their perception of the teachers as emotionally supportive (e.g., Federici & Skaalvik, 2014a,b; Furrer &Skinner, 2003). The present study tested if mathematics self-efcacy and the perception of mathematics teachers asemotionally supportive predicted motivation and if these constructs mediated the relation between students achievement(grades) and their motivation for schoolwork.A common belief among educators is that students self-perceived abilities play an important role motivation. A central construct related to self-perceived abilities is self-efcacy. Bandura (1977) originaself-efcacy would affect peoples choice of activities, effort and persistence. In accordance with thnumerous studies have shown that students motivation for schoolwork is related to their academicinstance, self-efcacy beliefs have been found to relate positively to intrinsic motivation, choice of tasksMathematics achievement and self-efcacy: Relationswith motivation for mathematics

Einar M. Skaalvik a,*, Roger A. Federici a, Robert M. Klassen b

aDepartment of Education, Norwegian University of Science and Technology, N-7491 Trondheim, NorwaybUniversity of York, York, UK

A R T I C L E I N F O A B S T R A C T* Corresponding author. Tel.: +47 97169572; fax: +47 735 91 890.

E-mail addresses: einar.skaalvik@svt.ntnu.no (E.M. Skaalvik), roger.federici@ntnu.no (R.A. Federici), robert.klassen@york.ac.uk (R.M. Klassen).

http://dx.doi.org/10.1016/j.ijer.2015.06.008

0883-0355/ 2015 Elsevier Ltd. All rights reserved.

E.M. Skaalvik et al. / International Journal of Educational Research 72 (2015) 1291361302. Theoretical perspectives

2.1. Self-efcacy beliefs

In social cognitive theory self-efcacy is conceptualized as peoples expectations of being capable of conducting speciedtasks. For instance, Bandura (1977, p. 3) dened self-efcacy as . . . beliefs in ones capabilities to organize and execute thecourses of action required to produce given attainments. Thus, students self-efcacy refers to beliefs about what they arecapable of accomplishing, rather than what skills and abilities they think they possess (Bandura, 1986; Zimmerman & Cleary,2006). As pointed out by Skaalvik (1997) self-efcacy addresses questions like Can I do it? as opposed to self-concept,which addresses questions like Am I good at it?

Bandura (1986) considers self-efcacy as a unique human capability that affects motivation, for instance the choices peoplemake, the effort that they expend on different activities, and how long they will persevere when confronting challenges. Previousresearch conrms that students self-efcacy beliefs are related to different measures of motivation. Students academic self-efcacy has been shown to be positively related to intrinsic motivation (Fan & Williams, 2010; Skaalvik & Skaalvik, 2004;Zimmerman & Cleary, 2006), choice of activities (Bandura & Schunk, 1981; Pajares & Miller, 1995), career selection (Betz &Hackett, 1983), persistence (Multon, Brown, & Lent, 1991; Schunk, 1981), and task-value (Bong, 2001). Also, Klassen and hisassociates found that self-efcacy for self-regulation predicted lower levels of procrastination for both university students(Klassen, Krawchuk, & Rajani, 2008) and secondary school students (Klassen et al., 2009). Because past performance affects bothself-efcacy and motivation (Bandura, 1997), an important question is if self-efcacy predicts motivation over and above theprediction that can be made from students previous achievements. In this study we also tested if students self-efcacy beliefs inmathematics mediated the effect of past math achievement on students motivation for mathematics.

2.2. Teacher emotional support

Recent educational research shows a growing interest in the quality of the teacherstudent relationship. Relationshipsbetween teachers and students reect the potential of classroom interactions to foster student development. Several studiesreveal that positive relations between teachers and students are positively associated with student motivation, engagement,and well-being (Furrer & Skinner, 2003; Marchand & Skinner, 2007; Niehaus, Rudasill, & Rakes, 2012; Sakiz, Pape, & Hoy,2012).

In most research the teacherstudent relationship is measured by asking the students about their relationship with theirteachers. Such measures cannot be clearly distinguished from measures of the students perceptions of the teachers asemotionally supportive. Emotional support is often dened in terms warmth, friendliness, respect, empathy and care(Patrick, Kaplan, & Ryan, 2011). Research reveals that students perceptions of the teachers as emotionally supportive areassociated with a range of motivational measures such as intrinsic motivation (Skaalvik & Skaalvik, 2012a,b; Wentzel, 1994),engagement (Patrick et al., 2011), academic initiative (Danielsen, Wiium, Wilhelmsen, & Wold, 2010), effort (Goodenow &Grady, 1993; Wentzel, 1994), and help-seeking behavior (Newman, 2000; Newman & Schwager, 1993).

Students perceptions of the teachers as emotionally supportive are also positively related to the students level ofacademic achievement (Federici & Skaalvik, 2014b). In the present study we therefore also tested if perception of theteachers as emotionally supportive mediated the relation between students past mathematics achievement and theirmotivation for mathematics.

2.3. Mathematics motivation

In this study we used four measures of motivation for mathematics: intrinsic motivation, effort, persistence, and help-seeking behavior. Intrinsic motivation was conceptualized as interest and the inherent satisfaction of working withmathematics (Deci & Ryan, 2000; Ryan & Deci, 2000). Intrinsic motivation has in previous research been shown to be positivelyrelated to behavioral measures of motivation, for instance effort and help-seeking behavior (Skaalvik & Skaalvik, 2004, 2005).

Effort, persistence, and help-seeking behavior are behavioral indicators of motivation. Effort and persistence whenencountering difculties are assumed to be positively related to self-efcacy (Bandura, 1997; Schunk & Pajares, 2009). Help-seeking behavior is a self-regulatory strategy but also a behavioral indicator of motivation for mastering the task in question.If students are given optimal challenge at school they are also likely to encounter difculties and need help and guidance(Karabenick, 2004; Karabenick & Sharma, 1994). As an indicator of motivation or motivated behavior help-seeking differsfrom effort and persistence in that it requires social interaction and the admittance of needing help. Compared to effort andpersistence it may therefore be more dependent on the perception of the teachers as emotionally supportive. We assumethat all the behavioral measures of motivation are inuenced by the students interest in mathematics or their intrinsicmotivation for mathematics.

3. The present study

Understanding the factors that inuence the relationship between past achievement and current motivation is especiallyimportant to explore in mathematics, because these factors may lead to interventions that move students away from a

E.M. Skaalvik et al. / International Journal of Educational Research 72 (2015) 129136 131downward spiral of failure (Bobis, Anderson, Martin, & Way, 2011). Hence, the present study seeks to understand themediating effects of self-efcacy and perceptions of teachers emotional support on the relationship between pastachievement and current motivation for schoolwork.

4. Method

4.1. Participants and procedure

The participants in the present study were students from ve middle schools (810th grade) located in a large city inNorway. Compulsory schooling in Norway is ten years and includes primary and middle school. The educational system ispredominantly public and a curriculum is dened on a national basis. The private sector is small with 3% of students inprimary and middle schools. The children start school at the age of six. Culturally the population of Norway is fairlyhomogeneous and the schools recruit students from a diversity of socioeconomic statuses.

A total of 823 students in eight (37%) ninth (27%) and tenth (36%) grade responded to the survey. The sample consisted of49.3% males and 50.7% females. The data were collected by means of a questionnaire administered in the school classes byresearch assistants.

4.2. Instruments

The instruments used in the present study were developed by the studys authors and administered in Norwegian. Theexamples of items represent translations into English. The responses on all items were given on a 6-point scale ranging fromAbsolutely disagree (1) to Absolutely agree (6).

Students perception of the teachers as emotionally supportive was measured by a four-item scale modied from apreviously tested scale (Skaalvik & Skaalvik, 2013). Examples of items are: I feel that my math teacher cares about me andMy math teacher encourages me when I have problems with my school work. Cronbachs alpha for the scale was .882.

Mathematics self-efcacy was also measured by four items, for example: I am certain that I can manage everything thatwe shall learn in mathematics and I am certain that I can manage even the most difcult problems in mathematics.Cronbachs alpha for the scale was .916.

Intrinsic motivation was dened as enjoying working with mathematics and nding working with mathematics fun. Theconstruct was measured with four items. Examples of items are: I enjoy working with mathematics and Working withmathematics is fun. Cronbachs alpha for the scale was .931.

A combined effort and attention scale included three items: I pay attention to the math teachers explanations, I payattention in math lessons, and I always do my best when I am working with mathematics. Cronbachs alpha for this scalewas .831. Persistence was measured with two items: Even if I get a difcult problem in math, I do not give up and When weare working with difcult math problems, I quickly give up. Cronbachs alpha for this scale was .750.

Help-seeking behavior was measured by a scale developed by Skaalvik and Skaalvik (2005). The scale consisted of fouritems, for instance: If there is something I do not understand in math, I ask the teacher for help and In mathematicslessons, I do not ask for help even if I do not understand the problem I am working with. Cronbachs alpha for the scale was.893. We used a 5-point response scale ranging from Strongly disagree (1) to Strongly agree (5).

4.3. Data analyses

The data were analyzed by means of zero order correlations, regression analysis and SEM-analysis for latent variables. Weconducted a series of regression analysis predicting intrinsic motivation, effort, persistence, and help-seeking behaviorseparately. For each of these constructs we estimated three models. In Model 1 (M1) grades and gender were entered aspredictor variables. In Model 2 (M2) we added teacher emotional support and in Model 3 (M3) we added self-efcacy aspredictor variables.

The regression analysis shows both changes in explained variance (R2) and the direct association with grades whenadding emotional support and self-efcacy into the equations. However, a limitation in the regression analyses is that theyshow how grade, gender, emotional support, and self-efcacy are related to intrinsic motivation, effort, persistence, andhelp-seeking behavior when these constructs are analyzed separately. A reasonable assumption is that intrinsic motivation the enjoyment of working with mathematics inuences students motivated behavior (effort, persistence, and help-seeking behavior. We therefore conducted a SEM analysis with grades and gender as exogenous variables. In this model welet intrinsic motivation predict effort, persistence and help-seeking behavior.

The theoretical model is shown in Fig. 1. In this model we expected students grades to be positively related to theirperception of teacher emotional support and self-efcacy, but only indirectly related to the motivational constructs.Following previous research (Lloyd, Walsh, & Yailagh, 2005) we expected male students to have higher mathematics self-efcacy and effort compared with female students. Both emotional support and self-efcacy were expected to be positivelyrelated to all motivational constructs. We also expected the association between emotional support and the behavioralmeasures of motivation would to be partly mediated through self-efcacy and intrinsic motivation.

E.M. Skaalvik et al. / International Journal of Educational Research 72 (2015) 1291361325. Results

5.1. Correlations and descriptive statistics

Correlations between the study variables as well as statistical means, standard deviations, and Cronbachs alphas areshown in Table 1. Self-efcacy was positively and strongly related to grades (r = .635), intrinsic motivation (r = .664), andpersistence (r = .677). Moreover, self-efcacy was also positively and moderately related to effort (r = .475) and help-seekingbehavior (r = .434). Emotional support was positively related to all measures of motivation but particularly strongly relatedto help-seeking behavior (r = .524). Also, grades were positively and moderately related to students experiences of receivingemotional support. Male students also showed higher self-efcacy than female students (r = .224) even though math gradeswas not signicantly related to gender (r = .030). The four measures of motivation were all signicantly correlated, with arange of r = .447 to r = .586.

5.2. Regression analysis

Fig. 1. Theoretical model of the relations between the constructs.To further investigate the relations between the variables we conducted a series of regression analysis. The results of theseanalyses are shown in Table 2. The analysis of all four motivational constructs (intrinsic motivation, effort, persistence, andhelp-seeking behavior) showed that when entering grades and gender as predicting variables (M1), grades were moderatelyand positively related to all measures of motivation. The strongest associations were found for intrinsic motivation andpersistence (b = .47) whereas weaker associations were found for effort (b = .33) and help-seeking behavior (.28).

Table 1

Correlations and descriptive statistics of the study variables.

Variable 1 2 3 4 5 6 7 8

1. Grades

2. Gender .030

3. Emotional support .284*** .074*

4. Self-efcacy .635*** .224*** .392***

5. Intrinsic motivation .472*** .136*** .439*** .664***

6. Effort .333*** .013 .398*** .475*** .579*** 7. Persistence .472*** .136*** .398*** .677*** .586*** .574***

8. Help-seeking behavior .287*** .016 .524*** .434*** .444*** .447*** .538***

Maximum possible score 6 2 20.00 20.00 20.00 15.00 10.00 20.00

Number of items 1 1 4 4 4 3 2 4

Mean 3.85 15.32 12.46 11.19 11.61 7.41 15.65

Standard deviation 1.12 3.57 4.54 4.62 2.14 2.05 3.73

Cronbachs alpha .882 .916 .931 .831 .750 .893

Note. * p < .05, *** p < .001.

E.M. Skaalvik et al. / International Journal of Educational Research 72 (2015) 129136 133When teacher emotional support was added into the equation (M2) all four analysis showed a similar pattern of change:(a) Adjusted R2 increased substantially and (b) the beta values for grade were reduced. This indicates both that emotionalsupport adds to the prediction of motivation and that the relation between grades and motivation is partly mediated throughstudents perception of emotional support. The association with emotional support was particularly strong when predictinghelp-seeking behavior.

When self-efcacy was added as a predictor variable (M3) grades no longer were signicantly related to two of themotivational constructs (effort and help-seeking behavior). The associations with intrinsic motivation and persistence werealso dramatically reduced (b = .09 and .07, respectively). This indicates that the impact of grades on motivation to a largeextent is mediated through self-efcacy. Moreover, compared with M2, adjusted R2 increased strongly when adding self-efcacy into the equation, showing that self-efcacy also had independent predictive value over and above the predictionmade by grades, gender, and emotional support. The models predicting intrinsic motivation and persistence revealed higherR2 values than the models predicting effort and help seeking behavior. These models also showed the strongest R2 changewhen adding self-efcacy into the equations. These results indicate that the models predicting intrinsic motivation andpersistence t the data slightly better than the models predicting effort and help-seeking behavior.

Table 2

Regression analysis predicting intrinsic motivation, effort, persistence, and help-seeking behavior.

2(a) 2(b)

Predicting variables Intrinsic motivation Predicting variables Effort

M1 M2 M3 M1 M2 M3

Grade .47*** .38*** .09** Grade .33*** .23*** .01

Gender .12*** .10*** .00 Gender .03 .05 .12***Support .33*** .22*** Support .33*** .24***

Self-efcacy .52*** Self-efcacy .40***

Adjusted R2 .240 .340 .482 Adjusted R2 .104 .204 .286

2(c) 2(d)

Predicting variables Persistence Predicting variables Help-seeking behavior

M1 M2 M3 M1 M2 M3

Grade .47*** .39*** .07* Grade .28*** .15*** .02Gender .11*** .09** .01 Gender .00 .03 .09**Support .27*** .15*** Support .48*** .41***

Self-efcacy .58*** Self-efcacy .30***

Adjusted R2 .232 .299 .471 Adjusted R2 .079 .286 .333

Note. * p < .05, ** p < .01, *** p < .001. Standardized regression coefcients reported.5.3. Structural model

The testing of the SEM model (Fig. 2) revealed that the model had acceptable t to the data (x2 (212, N = 823) = 743.37,p < .001, CMIN/DF = 3.506, RMSEA = .052, IFI = .965, TLI = .954, and CFI = .965). The strong R2 values also indicates that themodel t the data well. We should particularly note that as much as 73% of the variance in persistence could be explained bythe variables in the model.

In accordance with the correlations and the beta values (Tables 1 and 2) grades were moderately and positively related tostudents perceptions of the teachers as emotionally supportive and strongly related to students self-efcacy. Also, self-efcacy was the strongest predictor of intrinsic motivation.

Intrinsic motivation positively predicted all behavioral measures of motivation and was particularly strongly related toeffort. The direct relations between self-efcacy and the behavioral measures of motivation was weaker than the relationsrevealed in Table 2, indicating that the association between self-efcacy and students behavior is partly mediated throughintrinsic motivation. We should note however, that the direct relation between self-efcacy and persistence was particularlystrong whereas the strongest predictor of effort was intrinsic motivation and the strongest predictor of help-seekingbehavior was perceived teacher support.

6. Discussion

We tested how mathematics self-efcacy and the perception of the emotional support from mathematics teachersmediated the relationship between previous achievement and three measures of motivation in a large sample of middleschool students. Mathematics self-efcacy was positively related to all measures of motivation that were included in thestudy: intrinsic motivation, effort, persistence, and help-seeking behavior. This was shown both through the zero-ordercorrelations (Table 1) and when controlled for students grades and teacher emotional support (Table 2 and Fig. 2). Teacher

E.M. Skaalvik et al. / International Journal of Educational Research 72 (2015) 129136134emotional support was also positively related to all measures of motivation and particularly strongly related to help-seekingbehavior.

The regression analyses showed that when entering self-efcacy into the equation grades in mathematics were notdirectly related to effort and help-seeking behavior and were only negligibly related to intrinsic motivation and persistence.The SEM analysis even showed that when controlled for gender, emotional support, self-efcacy and intrinsic motivationstudents grades were weakly but negatively related to effort and help-seeking behavior. The analyses also showed that theassociations between grades and the motivational constructs decreased when entering emotional support into theequations. These results highlight the nding that the positive relations between grades in mathematics and studentsmotivational responses were mediated both through students perception of emotional teacher support and through thestudents self-efcacy for mathematics. In addition to the mediational effect of teacher support and self-efcacy, theseconstructs also had an independent effect on motivation. This can be seen by the increase on the explained variance of theemotional constructs when including teacher support and self-efcacy into the analysis. The strong association betweenself-efcacy and a range of motivational variables in our study may explain why self-efcacy has been shown to predict

Fig. 2. Structural model of the relations between the constructs. (Standardized regression weights reported.)subsequent achievement.The SEM analysis also revealed that motivated behavior was moderately predicted by intrinsic motivationthe

enjoyment of working with mathematics and that the associations between self-efcacy and motivated behavior as well asbetween teacher support and motivated behavior were in part mediated through intrinsic motivation.

It is worth noting that the motivational constructs were differently predicted by teacher support and students self-efcacy. Self-efcacy was the far strongest predictor of intrinsic motivation and persistence when working with difculttasks whereas teacher support was the strongest predictor of help-seeking behavior. We suggest that these ndings may beexplained by the different nature of the motivational constructs. Both the enjoyment of working with mathematics (intrinsicmotivation) and the persistence when facing challenges seem primarily to depend on the individual students competencyjudgments. As underscored by Bandura (2006), beliefs about ones capability determine if people think optimistically orpessimistically about tasks, and students with low efcacy beliefs tend to give up more quickly in the face of difculties.

The strong direct association between self-efcacy and persistence is particularly interesting because Schunk (1991)suggests that self-efcacy may not always lead to greater persistence. Schunk reasoned that self-efcacy is positively relatedto skills and that students with high academic skills do not have to persist as long as students with lower skills in order toanswer questions or to solve problems. Nevertheless, in the present study we found a strong positive relation between self-efcacy and self-perceived persistence. This does not necessarily mean that students with high self-efcacy spend more timewith their schoolwork or work longer hours, but that they perceive themselves as not giving up easily when or if they areworking with difcult problems. We do not know, however, to what extent the highest achieving students are givenchallenging problems in school. The relation between self-efcacy and persistence therefore also needs to be examinedthrough experimental studies.

Help-seeking behavior deviates from the other motivational constructs in this study. By its very nature help-seekingbehavior requires social interaction. As we discussed in the introduction, asking the teacher for help may therefore be moredependent on the teacher-student relationship or the students perception of the teachers as emotionally supportive than isthe case for effort and persistence.

E.M. Skaalvik et al. / International Journal of Educational Research 72 (2015) 129136 135An interesting nding in this study was also that the best achieving students perceived the teachers as most supportive.The correlation between grades and perceived emotional support was .30. Our impression when talking with teachers is thatthey spend most time helping and instructing students with learning problems (e.g., Skaalvik & Skaalvik, 2012a,b). It istherefore possible that students with mild learning problems get the most attention from the teachers and still experiencethe teachers as less emotional supportive compared to other students. We can only speculate about the reason for this.Possible explanations may be that the content and the working assignments are insufciently tailored the students needsand abilities, that the teachers in spite of spending much time with these students also send signals that they are impatient,or that these students perceive signals that they are not meeting the teachers expectations. However, these are merelyspeculations and the problem should be investigated with methods tailored to the research question.

In this study we found only small gender differences. Although there were no gender differences in grades we found thatboys had signicantly higher mathematics self-efcacy compared to girls. This nding is in accordance with a genderstereotype perspective where mathematics is perceived as more suited for males than for females (Eccles, Adlre, & Meece,1984; Skaalvik & Rankin, 1994; Skaalvik & Skaalvik, 2004).

There are some important limitations of the present work. The study has a cross-sectional design. Thus, the regressioncoefcients merely reveal the relations between the constructs when all of the constructs are controlled for. The present datado not support interpretation of the results in causal terms, even though such interpretations are based on theoreticalanalyses of the relations among the observed constructs. Longitudinal studies of the same constructs are called for in futureresearch.

7. Conclusion

The results of this study have both theoretical and practical implications. They clearly demonstrate that studentmotivation both interest and motivated behavior is strongly predicted by self-efcacy and moderately predicted byteacher emotional support. Moreover, these constructs almost entirely mediate the association between grades (or level ofperformance) and students motivational responses. Although this study was designed as a cross-sectional survey areasonable interpretation is that the effect of grades on motivation is mediated through emotional support and self-efcacy,with self-efcacy as the stronger mediator. Thus, this study adds to previous studies demonstrating the central role of self-efcacy for students academic motivation. An important question is through which processes students self-efcacy predictsubsequent achievement or grades. This study suggests that student motivation is one such process through which self-efcacy affects performance.

This study also shows that perceived emotional support from the teachers is positively associated both with studentsself-efcacy and with motivational responses. This nding supports a wide range of recent research that shows theimportance of teachers being warm, friendly, respectful, and empathetic.

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Mathematics achievement and self-efficacy: Relations with motivation for mathematics1 Introduction2 Theoretical perspectives2.1 Self-efficacy beliefs2.2 Teacher emotional support2.3 Mathematics motivation

3 The present study4 Method4.1 Participants and procedure4.2 Instruments4.3 Data analyses

5 Results5.1 Correlations and descriptive statistics5.2 Regression analysis5.3 Structural model

6 Discussion7 ConclusionReferences