The Expectancy-value theory is grounded in the social cognitive perspective of motivation. Psychologists in this tradition argue that individuals' choice, persistence, and vigor expended in performance can be predicted and explained basically by expectations of achievement and the value attributed to a task; i.e., by their beliefs about how well they will do in the task and the extent to which they value the task (Atkinson, 1957; Wigfield and Eccles, 1992; Wigfield, 1994). Apart from the components noted above, some theorists from this tradition have introduced a third construct related to the feelings experienced by students when they do a task (Pintrich and De Groot, 1990). We name this third construct “process expectancy.” In the course/subject matter context, we understood process expectancy to be the positive feelings that students expect to experience in their interaction with their teacher during the course (How will I feel studying this subject?). Indeed experience tells us that no-one starts something that is not worthwhile or when expectations of success are very poor because completing the task in such circumstances is considered a waste of time. Finally, nobody starts a task if they do not expect be feel well during the performance process. Hence these beliefs are considered three important indicators of students' motivation (Pintrich and De Groot, 1990), which specify some underlying motivational mechanisms that lead to the initiation and maintenance of action (Pintrich and Schunk, 1996). Centered on a course-subject and based on the above arguments, we herein used three types of beliefs that can make adolescent students decide on striving to learn a subject or not: (a) the subject value (What value does this subject have for me?), (b) the achievement expectancy (Will I be able to pass this subject?), and (c) process expectancy (How will I feel studying this subject?).

The modern Expectancy-value theory (Eccles and Wigfield, 2002; Eccles, 2009) distinguishes four task-value components: attainment value, intrinsic value, utility value and cost. For the present study, which centered on a course subject, we used extrinsic value (which encompasses utility, importance, and interestingness) and cost-benefit components to assess the subject matter value. Eccles and Wigfield (2002) identified cost as a critical component of value, which was conceptualized as a negative determinant in engaging a task due, for instance, to performance anxiety and fear of failure, and to the amount of effort needed to succeed (Eccles and Wigfield, 2002). However, when we centered on a course, we understood that being involved in a specific subject depends not only on the time and effort invested, but also on the benefits (e.g., in terms of results, reinforcements, enjoyment, etc.) that students can obtain. In short, the subject value items employed in this work refer to: (a) the extrinsic subject value, i.e., the perceived utility, importance, and interestingness of the subject (What value does this subject have for me?); (b) the expected cost-benefit relationship to pass the subject (Will it be worth the time and effort that I will have to invest to pass the subject?).

Students' expectancy-value beliefs may have been generated before classes began, from previous experiences, or may arise on the first days of class when students meet the teacher and find out about the study syllabus, evaluation requirements, teacher methodology, etc. (Doménech, 2006, 2011, 2012, 2013). This means that these beliefs can be evaluated at the beginning of the course after some days/week of class.

According to the aforementioned rationale, the main aim of this study was to examine if the motivational beliefs derived from the Expectancy-value theory play a mediator role between academic self-efficacy and learning outcomes (achievement and satisfaction). At the same time, another aim was to identify some of the motivational processes through which students' academic self-efficacy affects student achievement and satisfaction (see Figure 1). Accordingly, we hypothesized that expectancy-value beliefs would have a direct effect on academic achievement and satisfaction, whereas academic self-efficacy would have an indirect effect on academic achievement and satisfaction through expectancy-value variables. In other words, we predicted that expectancy-value variables would play a mediator role between self-efficacy and achievement (H1), and between self-efficacy and satisfaction (H2). The hypothesized connections were addressed and tested by the Structural Equation Modeling (SEM) procedure with the EQS program (Bentler, 2006). Self-efficacy and expectancy-value variables were all measured in the first academic term after some weeks of class, and student achievement and satisfaction were all measured in the third and last terms of the course. This study can provide new data to improve the motivational theories that integrate self-efficacy, expectancy, and value constructs in the educational setting context, focused on a subject matter as a unit of analysis. It may also help identify the motivational connections that mediate between academic self-efficacy and students' achievement/satisfaction. Important implications for educational practice may derive from these findings since they can provide valuable information to design instructional actions and programs that can improve student achievement and satisfaction. Student achievement and satisfaction are two of the most important learning outcomes, and are also considered key indicators of education quality.

The sample consisted of 797 Spanish secondary education students from 36 classes with different subjects, of whom 404 were male (50.7%) and 393 were female (49.3%), and they were aged between 12 and 17 years. Most of their teachers (N = 23, 63.88%) also participated in the study, of whom 11 were males (average experience = 29 years) and 12 were females (average experience = 32 years). About 80% of the participating students were Spanish, while the parents of the rest had come from other counties (the majority from Romania, Ecuador, and Morocco) to Spain as emigrants some years ago. One private and two state secondary schools located in east Spain took part in this study, which was carried out at the first four levels of compulsory secondary education: 1st ESO (12–13 years old), 2nd ESO (13–14 years old), 3rd ESO (14–15 years old), and 4th ESO (16–17 years old; ESO is the Spanish acronym for Educación Secundaria Obligatoria—Compulsory Secondary Education). Table 1 displays sample distribution according to levels of education and centers. This study was approved by the Ethics Committee of the Regional Valencian Government, Spain. Consent for students to participate was required from students' parents or legal tutors. Confidentiality and personal data protection were guaranteed in accordance with current Spanish law.

The scales used to measure the variables considered herein have been reviewed and refined in previous studies (Doménech, 2006, 2012, 2013; Doménech-Betoret et al., 2014). As most had been designed for university students, they had to be adapted to secondary education in order to use them herein. The scales that referred to self-efficacy and expectancy-value beliefs were administered at time 1 (halfway through the first term), and student satisfaction and achievement were measured at time 2 (halfway through the third term). See Table 2 for item examples.

The hypothesized connections were tested by the SEM procedure. The ML and ML robust method of estimation (if the assumption of multivariate normal distribution was violated), developed by Satorra and Bentler (1988, 1994), was used with the EQS program (Bentler, 2006) to calculate the fit indices of the hypothesized models. Since the Chi-square test is sensitive to sample size, using relative fit indices like CFI, the NNFI, and RMSEA is highly recommended (Bentler, 1990). Values below 0.05 for RMSEA indicate a good fit, whereas values up to 0.08 denote an unacceptable fit (Browne and Cudeck, 1993). NNFI- and CFI-values above 0.90 (Hoyle, 1995), or even 0.95 (Hu and Bentler, 1999), were fixed as the cutting-off point.

Hypothesized covariance structure models represent only approaches of reality because the obtained indices may be driven by the sample characteristics on which the model was tested (Cudeck and Browne, 1983). One approach to mitigate this limitation is to employ the cross-validation strategy (Byrne, 2012). To apply this strategy, the total sample (N = 797) was randomly split into two equivalent subsamples (the calibration sample and the validation sample), following the recommendations of Cudeck and Browne (1983). First, with subsample 1 (n = 399), a separate explorative factor analysis (EFA), using the principal component method with varimax rotation, was conducted on all the scales to estimate their factorial structure. Second, by taking the factors extracted in the EFA as the observational variables, a separate confirmatory factor analysis (CFA) was performed with subsample 2 (n = 398) to test the goodness of fit and stability of the measurement models of these scales. These two-handed factorial analyses (exploratory and confirmatory) approach provide strong evidence for the reliability of the factors used as latent variables, and improve the validity of the measurement model (Cudeck and Browne, 1983). Finally, the total sample (N = 797) was then used to examine the structural model; i.e., the relationships among the latent variables (see Table 2 for details). When data analyses were performed, the initial sample slightly reduced because 23 students did not complete the entire scales. Missing values were not calculated given the large number of participants.

The structural equation analysis was carried out with the whole sample to firstly test the mediation role of the expectancy-value beliefs between the self-efficacy–achievement relationship, and secondly the mediation role of the expectancy-value beliefs between the self-efficacy–satisfaction relationship. The procedure followed to test the mediation effect of the expectancy-value beliefs between self-efficacy and achievement, and also between self-efficacy and satisfaction, was conducted in two steps: first by testing the significant direct effects of latent variable self-efficacy on latent variables achievement (M1A model) and satisfaction (M1S model); second by testing the mediated role of the latent variable expectancy-value beliefs on the self-efficacy–achievement relationship (M2A), and also on the efficacy–satisfaction relationship (M2S). In this case we considered the direct and indirect effects between self-efficacy and achievement/satisfaction simultaneously.

The M1A model was first tested (direct effects) for the mediation role of the expectancy-value beliefs between self-efficacy and achievement. The fit indices values obtained by the ML method (χ² = 194.52; p = 0.0000, d.f. = 34; NNFI = 0.93; CFI = 0.95; GFI = 0.92; RMSEA = 0.078) and the ML Robust method of estimation (χ² = 173.19; p = 0.0000, d.f. = 34; NNFI = 0.93; CFI = 0.95; RMSEA = 0.073) indicated that the model satisfactorily fitted the data. According to the data, academic self-efficacy had a significant effect on achievement. So this prerequisite for mediation to exist was met (Baron and Kenny, 1986).

Next the mediated model M2A was tested. The fit indices values obtained by the ML method (χ² = 329.77; p = 0.0000, d.f. = 74; NNFI = 0.92; CFI = 0.94; GFI = 0.94; RMSEA = 0.067) and the ML Robust method of estimation (χ² = 293.87; p = 0.0000, d.f. = 74; NNFI = 0.92; CFI = 0.94; RMSEA = 0.062) indicated that the model fitted the data well. According to the data, latent variable academic self-efficacy had a significant effect on expectancy-value beliefs, which, in turn, had a significant effect on achievement. On the contrary, the path between academic self-efficacy and achievement was not significant. See Figure 2 for details.

The M1S model was first tested (direct effects) for the mediation role of the expectancy-value beliefs between self-efficacy and satisfaction. The model was optimized when a covariance between two variable errors (E10–E12) from the self-efficacy latent variable was introduced, following the recommendations of the Wald and Lagrange test in the EQS program. Then the model was tested again. The fit indices values obtained by the ML method (χ² = 197.88; p = 0.0000, d.f. = 52; NNFI = 0.926; CFI = 0.942; GFI = 0.959; RMSEA = 0.060) and the ML Robust method of estimation (χ² = 163.57; p = 0.0000, d.f. = 52; NNFI = 0.931; CFI = 0.946; RMSEA = 0.053) indicated that the model fitted the data well. According to the data, Academic Self-Efficacy had a significant effect on teaching process satisfaction. So this prerequisite for mediation to exist was met (Baron and Kenny, 1986).

Second the mediated model M2S was tested. The model was optimized when a covariance between two variable errors (E10–E12) from the self-efficacy latent variable was introduced, following the recommendations of the Wald and Lagrange test in the EQS program. Then the model was tested again. The fit indices values obtained by the ML method (χ² = 399.86; p = 0.0000, d.f. = 100; NNFI = 0.891; CFI = 0.909; GFI = 0.938; RMSEA = 0.062) and the ML Robust method of estimation (χ² = 343.17; p = 0.0000, d.f. = 100; NNFI = 0.894; CFI = 0.912; RMSEA = 0.056) indicated that the model fitted the data well. According to the data, the latent variable academic self-efficacy had a significant effect on expectancy-value beliefs which, in turn, had a significant effect on teaching satisfaction. On the contrary, the path between academic self-efficacy and teaching satisfaction was not significant. See Figure 3 for details.

The description and fit indices of the tested models are provided in Table 3, which summarizes the structural equation analyses results.

Based on the results obtained in this study, the following educational implications can be made:

First, the expectancy-value beliefs generated during the first weeks of the course are capable of predicting student achievement and their satisfaction with the teaching process followed throughout the course. Therefore, we wish to stress the importance of making a diagnostic evaluation at the beginning of the course of secondary students' expectancy-value beliefs in order to: (a) detect possible shortcomings that students may present in relation to students' expectancy-value beliefs formed at the beginning of the course, after some days of class; (b) design an action plan to overcome or improve these shortcomings.

Second, the obtained results provide evidence that general academic self-efficacy is capable of explaining to a great extent the expectancy-value beliefs formed by secondary students about a specific subject some days after the course starts. Therefore teachers should also take it into account at the very beginning of the course. Accordingly, implementing actions and programs at schools is recommended to improve students' academic skills to, in turn, improve academic self-efficacy. These programs should include a variety of components that fall in line with the sources of self-efficacy beliefs proposed by Bandura (1997) in academic contexts. According to Bandura (1997), self-efficacy beliefs are developed when individuals interpret information from four major sources, such as mastery experience, vicarious experience of observing others, social persuasions that students receive from others, and emotional and psychological states. In the school context, mastery experience refers to the way students interpret and evaluate obtained results, and self-beliefs of competence are revised and created according to these interpretations. Accordingly, teachers should provide instructional scenarios in which students are able to succeed in challenging tasks. Students' judgments of competence are also created by vicarious experience; i.e., by evaluating their capabilities in relation to other students' performance. Another source of self-efficacy is the social persuasions that students receive from others. Accordingly, a supportive message from parents and teachers is important to empower students' self-confidence. Finally, students' self-efficacy is created by their emotional and psychological states as students tend to interpret negative psychological states (stress, anxiety, bad mood, depression, etc.) as evidence for lack of skills, and positive psychological states as indicators of personal competence. Accordingly, promoting students well-being and reducing negative emotional states strengthen students' self-efficacy. For more details about sources of self-efficacy, see the review by Usher and Pajares (2008). In short, the actions and programs that aim to develop students' self-efficacy should be based on these four sources.

We defend the notion of quality education based on a preventive view. Accordingly, we suggest secondary school teachers taking specific actions on the first days of the T–L process to improve adolescent students' beliefs as regards academic self-efficacy (self-beliefs), achievement expectancy, process expectancy and subject value.

Although the results obtained herein are satisfactory, some limitations and suggestions for future research should be pointed out.

First, the results were obtained from schools located in a specific socio-cultural context. Thus, replicating this study in other educational and cultural contexts is recommended to generalize the findings.

Second, extending the tested model should be considered first by introducing other types of self-efficacy, such as metacognitive self-efficacy (Moores et al., 2006) or emotion regulation self-efficacy (Gross and John, 2003); second by including other motivational variables as mediators. Regarding the motivational process, Bandura (1986) distinguished three types of cognitive motivators: (a) causal attributions; (b) outcomes expectations; (c) goals, whose corresponding theories are Attribution theory, Expectancy-value theory, and Goal theory. Accordingly, including new variables as mediators in future research, such as, goal orientation (Pintrich, 2000) or achievement goals, would be interesting (Liem et al., 2008).

Third, although academic self-efficacy and expectancy-value beliefs were measured in the same data collection wave, we provide enough evidence and theoretical support to consider general academic self-efficacy as an antecedent of the students' expectancy-value belief generated in the classroom context.

Fourth, according to Wigfield and Cambria (2010), most of the measures used by researchers to assess motivational beliefs are student self-report measures. However, self-report measures can be problematic, especially for young children or for students who state that school is not important to them. Consequently, we wish to emphasize the importance of combining quantitative and qualitative methods to reduce biases and to obtain more complete information about students' belief.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.