Does amotivation matter more than motivation in predicting mathematics learning gains? A longitudinal study of sixth-grade students in France

Contemporary Educational Psychology 44-45 (2016) 41–53

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Contemporary Educational Psychology j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / c e d p s y c h

Empirical study

Does amotivation matter more than motivation in predicting mathematics learning gains? A longitudinal study of sixth-grade students in France Nadia Leroy a,*, Pascal Bressoux a,b a b

University Grenoble Alpes University Institute of France

A R T I C L E

I N F O

Article history: Available online 13 February 2016 Keywords: Self-Determination Theory Autonomous motivation Amotivation Motivational changes Mathematics achievement Multilevel growth model

A B S T R A C T

This study examines the change trajectories of different types of motivation proposed by selfdetermination theory and their relationships with mathematics achievement during the first year of junior high school. Multilevel growth models were used to describe the trajectories of motivation regulation in 1082 students over the course of one year. On average, all types of motivation, whether selfdetermined or non-self-determined, declined throughout the school year. Conversely, the trajectory of amotivation increased continuously. The growth parameters of these trajectories extracted and utilized as covariates in explaining mathematics achievement at the end of the school year. The mean initial levels of motivation contributed to the explanation of the variance in mathematics performance, as did their rates of change during the school year. Second, amotivation was the only motivation type to be significantly associated with mathematics achievement over the school year. Theoretical and applied implications are discussed. © 2016 Elsevier Inc. All rights reserved.

1. Introduction Achievement in mathematics is a growing matter of interest. Mathematics competences appear to be crucial in many countries, where key skills include active citizenship, social inclusion, and employability in a society of knowledge (OJL 394, 30.12.2006). However, with a 16-point decline score from 2003 and a growing gap in mathematics performance between high and low achievers, France now ranks 25th in the PISA 2012 index. Moreover, for many years, French youth have shown a serious decline in their interest toward mathematics and sciences (Keskpaik & Salles, 2013; Merle, 2003). To improve France’s competitiveness in mathematics in the world, strict measures must be encouraged at the national level. To be effective, these measures should be based on studies addressing factors that have been demonstrated to have an impact on performance or on students’ career choice in mathematical and scientific domains (Lubinski & Benbow, 2006). One such factor, motivation, has proved to play a role in how students select mathematics-relevant fields of study and research careers (European Commission, 2004). Although motivation is considered as a crucial factor for academic achievement, there is little agreement

* Corresponding author. Laboratoire des Sciences de l’Education, Université Pierre-Mendès-France, (EA n° 602) 1251 Avenue Centrale, BP 47, 38040 Grenoble Cedex 9, France. E-mail address: [email protected] (N. Leroy). http://dx.doi.org/10.1016/j.cedpsych.2016.02.001 0361-476X/© 2016 Elsevier Inc. All rights reserved.

regarding which type of motivation should be promoted (Taylor et al., 2014). One way to understand why some students experience difficulties in the mathematics domain is to address how the different types of motivation contribute to mathematics achievement over time.

1.1. Self-Determination Theory Although prior mathematics achievement scores and grades are often considered as the most powerful predictors of subsequent mathematics achievement (e.g., Duncan et al., 2007; Hemmings, Grootenboer, & Kay, 2010; Reynolds & Walberg, 1992), motivation has been recognized for over three decades as a crucial factor in explaining school achievement. According to Self-Determination Theory (SDT; Deci & Ryan, 1985, 2002; Ryan & Deci, 2009), behaviors can be motivated either intrinsically or extrinsically, or they can be amotivated. Whereas intrinsic motivation refers to an engagement in a task for the pleasure inherent in it, extrinsic motivation refers to an engagement in a task to obtain a reward or avoid external pressure (Ryan & Deci, 2002). This definition, which contrasts two kinds of motivation, has been enriched by a multifaceted conceptualization of motivation. This conceptualization distinguishes four forms of extrinsic motivation that vary in degree of autonomy (Deci & Ryan, 1985). From the least to the most autonomous, these four forms are external, introjected, identified, and integrated regulation. External regulation refers to the behaviors adopted

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by an individual in order to obtain a consequence external to the task, such as being offered a reward. Introjected regulation refers to behaviors that are slightly more internalized by the individual since he or she is motivated by an internal pressure or coercion such as avoidance of shame or guilt. Identified regulation is a more autonomy driven form of extrinsic motivation. In this case, action is accepted as personally important. Finally, integrated regulation, which is considered as the most autonomous kind of extrinsic motivation, occurs when regulations are fully assimilated with the self. However, some debate and inconsistent results have called into question the empirical distinction between the identified and integrated regulation subscales (Lonsdale, Hodge, & Rose, 2008; Mouratidis, Lens, & Vansteenkiste, 2010) and Vallerand (1997) asserted that integrated regulation is a type of motivation that is not prevalent until adulthood. SDT proposes the existence of amotivation, which means to be neither intrinsically nor extrinsically motivated. This state occurs when individuals lack the intention to act or when behaviors are executed without intention or unknown reason (Legault, Green-Demers, & Pelletier, 2006; Ryan & Deci, 2002). According to Cheon and Reeve (2015), “with amotivation the students have no reason to act—not intrinsic motivation, identified regulation, external regulation or introjected regulation” (p. 100). More generally, amotivation refers to a complete lack of volition with respect to a particular task or domain. In this case, individuals cannot see the motive behind their behaviors (Ryan & Deci, 2000). This lack of perceived contingency implies a dereliction of intention to act (Legault et al., 2006) and results from different reasons (e.g., Cheon & Reeve, 2015; Green-Demers, Legault, Pelletier, & Pelletier, 2008; Legault et al., 2006). For example, individuals may think that whatever they do, they are unable to achieve desired outcomes either because they lack the desire to expend the energy necessary to enact the task (i.e., amotivation low-effort belief), because they believe they lack sufficient ability or competence to perform the task (i.e., amotivation low-ability beliefs), because they do not value the activity (i.e., amotivation low task value) or because the task is perceived as unappealing or unattractive (i.e., amotivation unappealing task). In the classroom context, amotivated students lack confidence in controlling their learning process and tend to exhibit inappropriate behaviors (Yates, 2009). Amotivated students interpret failure as a sign of personal lack of ability and doubt they can do anything to overcome their difficulties (Montagne & Van Garderen, 2003). This loss of behavioral agency also renders the school environment particularly unpredictable and leads students to perceive any attempt to learn or improve as vain (Bandura, 1993; Pintrich, 2003; Weiner, 1984, 1985). They question the usefulness of engaging in the activity (e.g., ‘‘I can’t see the use of doing school work in mathematics”). In turn, these pessimistic attitudes and negative reactions interfere with their ability to learn (Cheon & Reeve, 2015) and may lead students to quit the activity (Dweck, 1999).

motivational regulations are, the more strongly they correlate with positive consequences. By contrast, the controlled forms of motivation and amotivation are highly associated with negative consequences (Deci & Ryan, 2002). On the basis of this simplex pattern, SDT posits that the different kinds of motivation fall along a relative autonomy continuum in which amotivation is contrasted with both autonomous motivation and controlled motivation (Ryan & Deci, 2000). This idea of a motivational continuum has however recently been questioned by Chemolli and Gagné (2014) who stated that, “the continuum argument has muddled the description of the different regulations, such that they are alternatively described as different in kind or as varying in terms of their level of self-determination” (p. 576). In other words, they point out that the definition that Ryan and Connell (1989) gave to the simplex actually merged the concepts of kind and degree as being one and the same thing. Indeed, contrary to autonomous actions, which are initiated by a sense of choice and personal volition, or controlled actions, which are regulated by external or internal pressures (Taylor et al., 2014), amotivation refers to the absence of contingency between actions and outcomes. More specifically, when people are more or less autonomously motivated, they perceive why they do what they do, whereas in the case of amotivation, they cannot find the reasons for engaging in an activity. For example, Chemolli and Gagné (2014) pointed out that in SDT, only the different types of internalization (i.e., intrinsic, identified, introjected and external) differ in the degree to which they are autonomously regulated. This conceptual difference would imply that one cannot contrast amotivation to other forms of motivational regulation insofar as amotivation would be a qualitatively different construct from the other regulations. Other researchers using analytical methods to verify factorial structures, such as CFA, have not found a single dimension, but have rather showed that items from the amotivation subscale and items from the other subscales load on separate factors (Fernet, Senécal, Guay, Marsh, & Dowson, 2008; Gagné et al., 2013; Guay, Vallerand, & Blanchard, 2000; Millette & Gagné, 2008; Tremblay, Blanchard, Taylor, Pelletier, & Villeneuve, 2009; Vallerand & Bissonnette, 1992; Vallerand, Blais, Brière, & Pelletier, 1989; Vallerand et al., 1992, 1993). This was furthermore supported by Rasch analysis, which showed that evidence for the continuum is actually quite weak (Chemolli & Gagné, 2014). A final argument against the continuum is that the different regulations produce different affective, cognitive, and behavioral consequences (Koestner & Losier, 2002). These seemingly qualitatively different types of regulation led researchers to assert that the simplex pattern does not provide sufficient evidence for a continuum. Chemolli and Gagné (2014) advocate that the simplex pattern cannot be described using a continuum but rather using the concept of contiguum. In other words, as motivation types do not only vary in degree of autonomy but also in quality, they should not be described as falling along a continuum of autonomy but rather as a succession of adjacent constructs.

1.2. Amotivation and the continuum of autonomy

1.3. Motivation as a predictor of academic adjustment

Another characteristic of SDT is the simplex pattern of correlations among the motivational forms. According to Deci and Ryan (1985, 2002), individuals scoring higher on the subscales measuring autonomous forms of motivation (i.e., intrinsic, integrated and identified) are expected to score lower at controlled forms of motivation (i.e., introjected, external) and amotivation. Moreover, the correlations between regulations that are near each other on the continuum should be higher than the correlation between regulations that are far apart. For example, individuals’ scores on the external regulation subscale are more highly related to their scores on the introjection subscale than on the intrinsic motivation subscale. This simplex pattern also implies that the more autonomous

The vast array of literature on what motivates students in the classroom has repeatedly demonstrated the benefits of selfdetermined regulations in the academic setting from childhood through adolescence (e.g., Broussard & Garrison, 2004; Elliot & Dweck, 2005; Gottfried, 1985, 1990; Harter & Connell, 1984; Henderlong & Lepper, 1997, April; Lloyd & Barenblatt, 1984). Autonomous types of motivation are associated with positive academic (Gottfried, Fleming, & Gottfried, 1994; Gottfried, Marcoulides, Gottfried, Oliver, & Guerin, 2007; Steinmayr & Spinath, 2009), behavioral, cognitive and emotional consequences (e.g., Vallerand, 1997). Students who show higher intrinsic motivation report more interest in school (Vallerand et al., 1989) and are less likely to drop

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out (Vallerand, Fortier, & Guay, 1997). In addition, studies have reported that from childhood through adolescence, students showing the highest levels of intrinsic motivation perform best at school, hold the most positive self-perceptions, and are less anxious at school (Gottfried, Gottfried, Cook, & Morris, 2005). By contrast, controlled forms of motivation are associated with negative consequences (Deci & Ryan, 2002). Although these relations have been observed for all subject areas, they are particularly significant for mathematics (e.g., Gottfried & Gottfried, 2004; Uguroglu & Walberg, 1979). It must however be emphasized that other studies have reported inconsistent results, and some researchers argue that extrinsic motivation is most important (Wigfield & Eccles, 2000). Others argue for a combination of autonomous and controlled forms of motivation (Lepper, Corpus, & Iyengar, 2005). Although many studies have examined the relation between autonomous or controlled forms of motivation with academic adjustment, considerably much less attention has been directed toward the role of amotivation in predicting academic achievement. Indeed, there is a great need to look into academic amotivation because, except for some studies treating amotivation as an antecedent of school boredom (Vallerand et al., 1993), school dropout (Hardre & Reeve, 2003; Vallerand et al., 1997), lack of effort and persistence (e.g., Ratelle, Guay, Vallerand, Larose, & Senecal, 2007) or poor students’ classroom engagement (Aelterman et al., 2012), the link between amotivation and performance is still underexplored. Instead, studies have reported associations between amotivation and mediator processes such as higher perceived stress at school (Baker, 2004), poor concentration in class (Vallerand et al., 1993), difficulties to process complex information in mathematics (Dweck, 1986) and little hope for academic success (Covington & Beery, 1976; Diener & Dweck, 1978; Weiner, 1979, 1984). Studies that have addressed the link between amotivation and academic achievement are quite scarce and should be further developed. For example, Karsenti and Thiebert (1995) showed that amotivation is the type of motivation most significantly related to GPA. Their results indicate that the relationship between amotivation and GPA for junior-high school students were higher (r = −.30) than those obtained for senior-high school students (r = −.25). However, these results are limited because they are based on correlations and analyses that failed to take the different forms of motivation or the baseline performance into account. Another study from Legault et al. (2006) has reported such a negative relationship. However, in this study, academic performance was a self-reported measure and may risk being positively biased. Although these studies shed some light on the role of amotivation by showing that it is potentially more harmful for younger students’ school achievement (Taylor et al., 2014), these limitations must be considered when interpreting results. 1.4. Students’ lack of motivation in the mathematics domain Another factor that may partly explain the students’ poor performance in mathematics is their lack of interest for this academic subject. Compared to many other school domains, mathematics has the least positive level of student motivation (Pintrich, Wolters, & De Groot, 1995). This lack of motivation may be explained by several features of the mathematics domain. First, as an area of the curriculum in which success and failure are highly salient (Dweck & Licht, 1980), with answers to questions that are right or wrong (McLeod, 1992) and the frequent introduction of new concepts, mathematics is often perceived negatively. In addition, as it is a logical deduction domain in which new concepts are built on prior concepts, it is considered as a stressful discipline with an accumulative dimension (Cook, 2009). For example, when one goes from arithmetic to algebra or from geometry to calculus and so on (Licht & Dweck, 1984), the relevance of

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past learning may not be evident. These characteristics can create stressful learning situations that are more frequent in mathematics than in other subject areas such as verbal domains. Second, as mathematics is often perceived as a domain in which only gifted and smart students with a “mathematical” mind have what it takes to learn (Kloosterman, 1988, 2002; McLeod, 1992), many struggling students attribute success to ability (Kloosterman & Gorman, 1990; Middleton & Spanias, 1999). They also believe that hard work cannot compensate for this (Tobias, 1993) and decide early in their school career that they cannot do well at math. As they reach junior high school, they consolidate and internalize the attributional pattern that failure is due to a lack of ability (Eccles, Wigfield, & Reuman, 1987) and consequently view success as unattainable. In addition, because of its cumulative and complex nature, students feel nervous and insecure and progressively develop anxiety and helplessness (Miller & Mercer, 1997). As a consequence, their attitudes toward mathematics become more and more negative. They tend to rate mathematics as less fun (Middleton, Littlefield, & Lehrer, 1992), report more discouragement, reduce their efforts, and adopt a variety of work avoidance strategies (Covington, 1992). As in a vicious circle, this negative pattern prevents amotivated students from attempting to complete a task they would otherwise be capable of coping with. Other interesting results show that the motivational orientation endorsed by students interacts with the demands of academic material in relations to students’ performance (Licht & Dweck, 1984). In other words, academic performance appears to be a function of how well the motivational orientation fits with the demands of the domain. When a task involves confusing concepts as is often the case in mathematics, amotivated students show more marked difficulties than in other disciplines. As amotivation has been shown to have more predictive power in mathematics performance than in other domains, this reveals how particularly susceptible amotivated students may be to poor mathematics performance. 1.5. Temporal changes in motivation and their effects on academic achievement Researchers have repeatedly reported that students’ motivation gradually declines from elementary to high school. Studies that have examined motivation using longitudinal designs evidenced a particularly steep decline in intrinsic motivation across the school years (e.g., Gottfried, Marcoulides, Gottfried, & Oliver, 2013; Lepper & Henderlong, 2000; Spinath & Spinath, 2005; Spinath & Steinmayr, 2012). In addition to this temporal decline, a qualitative change characterized by a shift from decreasingly autonomous types of motivation to increasingly controlled types was also observed (Harter, 1981). In other words, students’ motivation, which is strongly selfdetermined during the first years of schooling, becomes more and more non-self-determined as students progress through school (Eccles, Lord, & Buchanan, 1996; Nishimura & Sakurai, 2013). The intensity of this general temporal decline varies between subjects, depends on the subject area (Eccles, Wigfield, Harold, & Blumenfeld, 1993; Haladyna & Thomas, 1979; Wigfield, Eccles, MacIver, Reuman, & Midgley, 1991), and is particularly striking in science and mathematics (e.g., Gottfried, Fleming, & Gottfried, 2001; Koballa, 1995; Middleton & Spanias, 1999; Pajares & Graham, 1999; Wigfield, Eccles, Schiefele, Roeser, & Kean, 2006). Some researchers have also been interested in studying how students’ motivational change over time can contribute to academic achievement. For example, Otis, Grouzet, and Pelletier (2005) examined the effects of motivational changes on students’ intention to drop out, absenteeism, homework completion, and future aspirations during the transition from junior to senior high school. Their results revealed that students’ intrinsic motivation and extrinsic motivation decreased gradually over time. Students who experienced

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a decline in intrinsic motivation and those who experienced a decline in external or identified regulation had more difficulty in their educational adjustment over time. By contrast, students who were intrinsically motivated at the end of junior high school were less exposed to the adverse effects of the senior high school transition. Unsurprisingly, students who were amotivated were those who experienced the most negative long-term effects. In a recent longitudinal study, Gottfried et al. (2013) used latent change modeling to show that the longitudinal decline in mathematics intrinsic motivation relates significantly to mathematics achievement. Thus, students who are low in mathematics intrinsic motivation and who experience a steeper decline in motivation over time also report less mathematics enjoyment over time. Guay, Ratelle, Roy, and L’italien (2010), using a cross-lagged model, showed that over the course of one year in high school, students’ autonomous motivation was positively associated with academic achievement. Similarly, Garon-Carrier et al. (2014) showed that the association between intrinsic motivation and achievement in mathematics became stronger from the first to the sixth year of primary school. Other longitudinal studies that have estimated the contribution of each type of motivation on academic achievement at university have reported contrasting results, however. For example, Burton, Lydon, D’Alessandro, and Koestner (2006) showed that identified regulation significantly and positively predicted final grades in a psychology course, whereas intrinsic motivation did not. By contrast, Baker (2003) and Taylor et al. (2014) quasi-longitudinal studies (study 2) reported that intrinsic motivation was the only type of motivation to significantly predict academic achievement. The research described above has provided a first step at considering motivation as a dynamic process that influences academic achievement. However, despite this essential contribution, the results remain inconsistent or fragmented and some aspects remain underexplored. Whereas some researchers have examined the relationships between autonomous or controlled motivation changes and school adjustment, to our best knowledge, no study based on longitudinal repeated measures has jointly examined the longitudinal effect of motivation and amotivation on mathematics performance. As a consequence, there is little evidence regarding which type of motivation should be promoted in this academic domain. 1.6. Study objectives and hypotheses The main research question of the present study is to investigate whether it is better for students’ mathematics performance to promote autonomous and controlled forms of motivation or to reduce amotivation. More specifically, this study investigates (a) whether developmental changes in the different kinds of motivation are related to mathematics performance and, if so, (b) which motivational change is the most predictive of mathematics performance? The aim of this study is then twofold. Our first objective was to analyze the development of all types of motivation as described by SDT (i.e., autonomous and controlled types of motivation and amotivation) by examining the intra-individual changes occurring during the first year of junior high school in the French context. The second objective was to examine the effect of the varying trajectories of each type of motivation on students’ mathematics achievement, controlling for prior performance. In other words, we investigate whether the interindividual differences in mathematics achievement are explained by changes occurring in these different motivational constructs throughout the year. We tested two groups of hypotheses. The first concerns hypothesized growth trajectories of the different kinds of motivation over the school year. The second concerns the hypothesized effects of these motivational changes on students’ mathematics performance.

Hypothesis 1. We hypothesize that the autonomous forms of motivation would decrease while the controlled ones and amotivation would increase over the school year. Hypothesis 2a. We expect to observe an effect of the initial status of motivation and amotivation on mathematics achievement as well as a significant relationship between their rates of change and mathematics achievement. In line with SDT, we predict that autonomous forms of motivation will have a positive effect on mathematics achievement. By contrast, we expect that controlled forms of motivation and amotivation will be negatively associated with mathematics achievement. Thus, we predict that, controlling for initial mathematics achievement, the less rapidly the autonomous regulations decline, the better the end-of-year learning will be. By contrast, the more rapidly the controlled motivations and amotivation increase, the poorer the end-of-year learning will be. Hypothesis 2b. Finally, we hypothesize that the positive development of amotivation would have the most predictive and negative effect on mathematics performance at the end of the school year. 2. Method 2.1. Participants The sample consisted of 1082 first-year junior high school students from 47 classes located in 15 schools in suburban Grenoble (France). This school year was chosen because it can be considered as the transitional year from elementary school to junior high school, which is the most crucial year with regard to motivational decline (e.g., Gottfried et al., 2001; Reuman, Mac Iver, Eccles, & Wigfield, 1987; Yoon, Eccles, Wigfield, & Barber, 1996, March). Students were evenly distributed across gender (50.2% and 49.8% girls) and were aged between 10 and 12 years old. Regarding academic progression, 75.74% of students were “on track,” 17.96% had repeated a grade, and 3.8% had skipped a grade (no birth year was available for 2.5% of participants). The socioeconomic status of the sample represented a diverse middle-class range from semiskilled workers through professionals (17% of the fathers were employed as business executives; 20% in middle management; 14% were artisans; 0.2% farmers; 3.5% white-collar employees; 14.7% bluecollar employees and 5% were from other professions; 25.6 % N/A). All schools were public and enrolled between 220 and 717 students. A total of 33% of these schools were enrolled in Priority Education Zones and received additional resources such as funds or personnel to encourage the development of new teaching projects. 2.2. Procedure The school principals, mathematics teachers, and parents filled out a consent form containing information about the study. The students completed a survey on a voluntary basis with the authorization of the principal and the teachers. Parental consent was obtained through letters distributed to students’ families. All participants were informed that their answers would remain anonymous and confidential. Unlike other longitudinal studies that assess motivation at only one or two time points per year, the present study aims at providing a more fine-grained picture of the evolution in motivation. Consequently, students were invited to answer a questionnaire four times during the year (i.e., at the beginning of the year and at the end of the three school terms). Students also took a mathematics test at the end of the school year. At each time point, the researcher went to each classroom to administer the questionnaire for one hour during a regular class session. Oral and written instructions were given to help children understand the questionnaire.

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Students’ data were matched across time point by using a pseudoanonymized identification code generated from the date of birth and a code assigned to each class. From the initial sample of students who were invited to participate in the study (i.e., N = 1082), 874 answered the questionnaire at all time points (i.e., four times); the others were absent at one (n = 150), two (n = 25) or three (n = 33) of the four time points. Missing data resulted from usual factors in longitudinal research with adolescents, such as absence on the day of assessment or refusal to complete the questionnaire. The comparison of mean scores obtained at the beginning of the study from students who answered the questionnaire at all time points and the others revealed no significant differences for intrinsic motivation, Pillai’s Trace = .0001, F(2, 1018) = .82, p > .05; identified regulation, Pillai’s Trace = .0001, F(2, 1017) = .09, p > .05; introjected regulation, Pillai’s Trace = .0004, F(2, 1017) = 2.08, p > .05; external regulation, Pillai’s Trace = .0003, F(2, 1018) = .19, p > .05; or national mathematics tests, Pillai’s Trace = .003, F(2, 1027) = 1.8, p > .05. However, for amotivation, a significant difference was found between the different groups, with the group of students who were present at two of the survey administrations having a higher mean score (M = 2.46) than the students who were present at 3 or 4 of the survey administrations (M = 1.75 and M = 1.67, respectively).

2.3. Measures 2.3.1. Academic motivation The students’ motivation was assessed using an adapted version of the Academic Self-Regulation Questionnaire (SRQ-A) developed by Ryan and Connell (1989). The SRQ-A uses four subscales: external regulation, introjected regulation, identified regulation, and intrinsic motivation. It asks questions about why students do various school related behaviors in four main areas: “Why do I do my homework?”, “Why do I work in class?”, “Why do I try to answer hard questions in class?” and “Why do I try to do well in school?” In its original version this questionnaire assesses class-specific individual differences in the types of motivation. Because context cannot be ignored in the study of teaching and learning (Romberg & Carpenter, 1986) and because student motivation and learning can be better understood by domain-specific analyses (Middleton & Spanias, 1999; Vallerand, 1997), we adapted the questionnaire by specifying these four questions to the mathematics domain (i.e., “Why do I do my homework in mathematics?”, “Why do I work in mathematics?”, “Why do I try to answer hard questions in mathematics?” and “Why do I try to do well in mathematics?”). The multiple choices corresponded to the different motivational regulations: external regulation (e.g., “because I was promised rewards if I do well”); introjected regulation (e.g., “because I will feel bad about myself if I don’t do well”); identified regulation (e.g., “because it’s important for me”); intrinsic motivation (e.g., “because I enjoy doing my school work well”). Additional items were used to identify amotivation as a single dimension having to do with behaviors that are executed for unknown reason (i.e., “honestly I do not know why I should do math homework, I really feel I am wasting my time”; “frankly, I do not see what’s the aim of working in mathematics, if I could, I would not come”; “frankly, I can’t see the use of doing well in mathematics” and “I don’t know, I wonder what I’m doing in math class”). For each area, students rated each alternative explanation on a five-point Likert scale ranging from 1 “strongly disagree” to 5 “strongly agree.” Because this multiple choice response format allows students to rate each type of motivation, it is assumed that each motivational regulation does not align along a single dimension. In addition, using separate scores for each type of regulation better reflects the reality that students can have more than one type of

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motivation for a particular activity (Chemolli & Gagné, 2014; Koestner & Losier, 2002). The SRQ-A has been extensively used in the educational domain, and its validity and reliability have been tested and shown to be sound. For example, test–retest reliability score was high (r = .94, p < .0001) and internal consistency of the scale was quite high (α = .91) (Aubrey, Brown, & Miller, 1994). Extensive evidence for construct validity has also been shown (Ryan & Connell, 1989). In a previous study, Leroy, Bressoux, Sarrazin, and Trouilloud (2013) used this adapted version of the SRQ-A and demonstrated good internal consistency for the different subscales, ranging from .72 to .84. 2.3.2. Mathematics learning scores To assess students’ baseline level in mathematics, we collected their scores on the national mathematics test, which is administered at the beginning of the school year to all French students entering junior high school (M = 67.4; SD = 17.32; no information available on Cronbach’s alpha). This standardized test was developed by the Direction de l’Evaluation de la Prospective et de la Performance (French Ministry of Education). It was given over two separate 45-minute periods and included exercises in geometry, algebra and calculus. Because students are not required to take a standardized test at the end of the sixth year in France, we developed a test to assess students’ performance at the end of the school year. As the French curriculum is centralized, students from all participating schools have been exposed to the same content. The end-of-year test was organized into two parts: one grouping geometry exercises, the other algebra and calculus exercises. It reviewed the objectives outlined in the mathematics curriculum for the whole school year (M = 11.04; SD = 4.62; Cronbach’s Alpha = 0.86). This type of evaluation seemed much more accurate than self-reported performance. 2.4. Modeling intra-individual change using multilevel growth models We used multilevel growth models (Singer & Willett, 2003), which provide great flexibility for testing a large set of hypotheses on developmental trends. Assuming that the series of four repeated time points on motivation are represented as Yij (the value of motivations for student i at time t as a function of time), the longitudinal model equation for describing the development of motivations across the time points (also called the Level 1 model or intra-individual model) is written as follows:

Yti = π 0i + π1i TIMEti + eti where π0i represents the intercept (i.e., the initial status) of an individual’s change trajectory, π1i represents the slope (i.e., the rate of change) of the change trajectory, and eti corresponds to the model residual for each individual at each time point. As we recentered TIME on the first time point, the intercept represents the initial status of the motivation score. The rate of change associated with the time variable indicates the change in the motivation scores associated with the increase in one temporal unit. Since the temporal unit used here was the school term, we are referring to the term-based rate of change. Given that π0i and π1i are random variables, these parameters can be represented by a group mean intercept (β00) and a group mean slope (β10) plus an intercept variation component (u0i) and a slope variation component (u 1i ) as indicated by the following interindividual models (or Level 2 models):

π 0i = β00 + u0i π1i = β10 + u1i

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shows that the mean scores for all the motivational regulations dropped over the course of the school year. By contrast, amotivation seems to increase continuously. At each time point, identified regulation was the most prevalent motivational regulation among students, and amotivation was the least common.

Integrating the two levels of the model gives:

Yti = β00 + β10 TIMEti + (u0i + u1i TIMEti + eti ) As in our study students were nested within classes, we tested a three-level model with repeated measures at Level 1, students at Level 2, and classes at Level 3. Our three-level unconditional growth model can be described as follows:

3.2. Coefficients of temporal stability

Ytij = β000 + β100 TIMEtij + (u0ij + u1ijTIMEtij + v 00 j + v10 jTIMEtij + etij )

Table 2 presents the coefficients of stability between the different time point, two by two. The coefficients of temporal stability were highest between Time 3 and Time 4, which shows that each of the motivational regulations tended to become more stable over the course of the school year.

where subscribe t represents the measures (time), subscript i represents the students, and subscript j represents the classes. We found evidence for relationships between some observed variables and missing data. As the missingness is related to the observed variables, we considered missing data are Missing at Random (Enders, 2010; Schafer & Olsen, 1998). The growth model used Maximum Likelihood estimation to approximate missing values. These analyses were completed using the “mixed” procedure of SAS version 9.3.

3.3. Simplex pattern Correlations among the five types of motivational regulations and with the mathematics test scores from the beginning and at the end of the school year were examined separately for each time point (Table 3). The expected relations were generally found for each of the time points. It can also be noted that between the autonomous forms of motivation and both external regulation and amotivation, the correlation coefficients were negative. In terms of the correlations between motivational regulations and achievement, we found that at no time point was introjected regulation associated with end-of-year scores. External regulation and amotivation were negatively associated with performance at all time points. Conversely, the correlation was positive between intrinsic motivation and end-of-year performance at the first, third and fourth time points. The positive correlations between identified regulation and end-of-year performance were significant at the last two time points.

2.5. Data analytic strategy In the first step of the analysis, we estimated the growth models for each type of motivation. In the second step, the parameters from the growth models (i.e., individual initial status π0ij and rate of change π1ij) were extracted and used as covariates in a multilevel model of mathematics performance, with students at Level 1 and classes at Level 2. This approach (e.g., used by Kim, Petscher, Schatschneider, & Foorman, 2010 to study the relationship between growth trajectories of fluency and reading comprehension) aims to reveal which type(s) of motivation significantly contributes to explained variance in mathematics performance. Specifically, it will assess the relationships between the different kinds of motivation growth trajectories and mathematics achievement.

3.4. Multilevel growth models for the different motivational regulations

3. Results As described previously, multilevel growth models were used to depict the change trajectories for each motivation type (i.e., motivational regulation and amotivation). We first tested several unconditional models not only to distinguish, within the variance of each regulation, the components from each level, but also to obtain

3.1. Descriptive statistics and internal consistency of scales Table 1 presents the descriptive statistics and Cronbach’s alpha coefficients for all variables at the four time point. A first examination

Table 1 Descriptive statistics of variables and internal consistency of scales. Variables

Intrinsic motivation Identified regulation Introjected regulation External regulation Amotivation Beginning-of-year score End-of-year score

Wave 1 (October)

Wave 2 (December)

Wave 3 (March)

Wave 4 (June)

M

SD

Alpha

M

SD

Alpha

M

SD

Alpha

M

SD

Alpha

3.14 3.95 3.19 3.13 1.69 67.38 —

0.9 0.92 0.94 0.91 1.01 17.32 —

0.79 0.79 0.81 0.72 0.75 — —

3.08 3.76 2.93 2.93 1.68 — —

0.96 1.02 0.99 0.95 1.04 — —

0.83 0.83 0.83 0.76 0.81 — —

2.99 3.59 2.76 2.82 1.72 — —

1.04 1.11 0.99 0.97 0.84 — —

0.87 0.86 0.85 0.79 0.84 — —

2.88 3.43 2.6 2.76 1.76 — 11.04

1.03 1.12 0.98 0.98 1.11 — 4.62

0.87 0.86 0.85 0.81 0.87 — 0.86

Table 2 Longitudinal stability correlation coefficients for motivational regulation subscales. Subscale

Intrinsic motivation Identified regulation Introjected regulation External regulation Amotivation

T1–T2

T1–T3

T1–T4

T2–T3

T2–T4

T3–T4

October–December

October–March

October–June

December–March

December–June

March–June

0.63 0.54 0.59 0.54 0.53

0.59 0.52 0.55 0.52 0.54

0.53 0.46 0.46 0.45 0.49

0.68 0.61 0.66 0.64 0.64

0.62 0.58 0.59 0.57 0.59

0.74 0.69 0.67 0.66 0.67

Note: All coefficients are significant at the α = .001 threshold.

N. Leroy & P. Bressoux/Contemporary Educational Psychology 44-45 (2016) 41–53

47

Table 3 Zero-order correlations among variables for the four measurement times. Variables

October

December

1.

2.

1. Intrinsic motivation 2. Identified regulation 3. Introjected regulation 4. External regulation 5. Amotivation 6. Beginning-of-year score 7. End-of-year score

— .67** .38** −.15** −.51** .08** .13**

— .44 ** −.08 ** −.54 ** −.03ns .04ns

Variables

March

1. Intrinsic motivation 2. Identified regulation 3. Introjected regulation 4. External regulation 5. Amotivation 6. Beginning-of-year score 7. End-of-year score

— .76 ** .38 ** −.29 ** −.55 ** .03ns .12 **

1.

3.

— .36 ** −.18 ** −.06ns −.03ns

4.

— .33** −.22** −.22**

5.

— −.12** −.20**

6.

— .71**

7.

1.

2.

3.

4.

5.

6.

7.

—

— .74 ** .37 ** −.18 ** −.54 ** .001ns .017ns

— .41 ** −.13 ** −.57 ** −.07 ** −.03ns

— .37 ** −.20 ** −.11 ** −.05ns

— .30** −.17** −.17**

— −.06ns −.15 **

— .71**

—

June 2. — .46 ** −.21 ** −.61 ** −.002ns .09 **

3.

— .28 ** −.24 ** −.05ns .04ns

4.

— .33** −.12** −.15**

5.

— −.04ns −.16 **

6.

— .71**

7.

1.

2.

3.

4.

5.

6.

7.

—

— .76 ** .46 ** −.18 ** −.56 ** .02ns .15 **

— .47 ** −.15** −.60 ** −.003 ns .12 **

— .30 ** −.23 ** −.07 * .02ns

— .33** −.11** −.14**

— −.07 * −.23**

— .71**

—

* p < .05. ** p < .01.

the most accurate parameter estimates (Table 4). A three-level model was specified for each regulation type with repeated observations at Level 1 nested within students (Level 2) and within classes (Level 3). A four-level model with schools at Level 4 was also tested but, as it did not better fit the data than the three-level model, the school level was not included in subsequent analyses. Table 5, which presents the variance decomposition for each motivational regulation, shows that the largest proportion of the variance was found at the interindividual level, ranging from 46% for introjected regulation to 52% for intrinsic motivation. The smallest proportion of variance was found at the interclass level, ranging from 4.35% for external regulation to 10.2% for intrinsic regulation. Regarding intra-individual variability, the proportions of variance were also considerable, ranging from 37% for intrinsic motivation to nearly 46% for introjected, identified and external regulation. Introducing the time variable (Table 4) significantly reduced the intra-individual variability. Line R2ε indicates the proportion of intraindividual variance explained by time. For most variables, this value was substantial, ranging from 11% for amotivation to 28% for introjected regulation. The model estimates (Table 4) and the graphical representations (Fig. 1) show that all the motivational regulations declined during the year. Regarding amotivation, a continuous increase was observed throughout the year. It should be emphasized that these change trajectories represent average patterns around which we found sizeable heterogeneity. The Level 2 and Level 3 variance components reveal that students do not all present the same profile. The significance of the random effects associated with the intercept indicates that the initial status of each motivational regulation differed significantly from one student to another and across classes. Similarly, the significant variance in slopes indicates that the rate of change in motivational regulations was not the same for every student or for every class. In other words, the scores did not change over time in the same way for all students from different classes. 3.5. Effect of the development of the different motivational regulations on mathematics learning The second part of our analysis involved examining the effects of interindividual changes on end-of-year mathematics performance. In a growth model, each student is represented by his unique trajectory and therefore by two growth parameters: an initial status

and the rate of change. We extracted these growth parameters produced by the growth model for each student and introduced them as covariates in a hierarchical model explaining variations in mathematics performance. This technique allowed us to test whether the mean initial status and the mean rate of change of motivation contribute to the explanation of variance in student mathematics performance at the end of the school year. This thus enabled us to account for the effect of motivation as a truly dynamic process. We first tested an empty model (Model 0, Table 6) that does not include any predictors. The interindividual and interclass variances estimates were 82.35% and 17.65%, respectively. Next, we included only the control variables (i.e., socio-demographic characteristics, student’s gender, type of academic progression, and score on national mathematics tests at the beginning of the year). Since father’s occupation had no significant effect, this variable was not retained in subsequent analyses. The fact of being a girl brought about a significant gain of .97 points in the end-of-year mathematics test. In addition, students who had repeated a grade at least once during their schooling had a mean end-of-year mathematics score that was .71 points lower than those who had never repeated. The inclusion of these variables explained 53.73% of the interindividual variance and 38.82% of the interclass variance. This is considered to be our baseline model, which we then specified by successively introducing the growth parameters produced by the previous growth models (i.e., initial status and rate of change). A comparative analysis was performed, in which the fits of several competing models were assessed. Model 2 included the covariates from the baseline model (Model 1) and the growth parameters derived from the change trajectories for every type of motivational regulations (i.e., intrinsic, identified, introjected and external motivation). The results indicate that there was no significant effect of growth parameters extracted from motivation growth models except for the rate of change of identified regulation (b = 2.26) revealing that, when identified motivation increases during the year, so do students’ end-ofyear mathematics scores. Introducing these parameters led to a 4.7% reduction in residual variance at the interindividual level and a 5.2% reduction at the interclass level. This model fit the data significantly better than the baseline model (i.e., the likelihood-ratio test was significant, ΔD(8) = 43, p < .001). We next tested Model 3, which included all the covariates from Model 2 and the growth parameters derived from the change

N. Leroy & P. Bressoux/Contemporary Educational Psychology 44-45 (2016) 41–53

0.11 10,355.5 — 10,427.4

— —

0.10**

ns

ns — —

— 9833.8 0.28 9592.5 — 10,136.8 0.25 10,233.5 — 10,659.5 0.21 9262

ns 0.07** 0.007**

— —

— —

0.08**

ns

ns 0.52** 0.53** 0.37** 0.51** —

*p < .05. ** p < .01.

R2ε −2 Log L

Level 3 random effects

Level 1 random effect Level 2 random effects

Intercept Linear Time Intercept Intercept Linear Time Intercept Linear time Covariance Intercept Linear Time Intercept Linear time Covariance

— 9522.8

0.04** — — 0.07** 0.004** 0.06** 0.004**

— —

— —

0.08**

0.46** 0.46**

2.88** —

3.95** −0.17** 0.39** 0.47** 0.04** 3.70** — 3.03** Fixed effects

Intrinsic motivation Identified regulation Introjected regulation External regulation Amotivation

0.19 9577.4

ns ns 0.10** 0.06** 0.004** −0.009**

— — — —

3.18** −0.20** 0.33** 0.53** 0.03** −0.03**

—

0.42** 0.46**

2.92**

ns

3.11** −0.12** 0.34** 0.42** 0.03**

—

— —

0.47** 0.57**

1.72**

ns

0.10**

1.67** 0.03** 0.42** 0.52** 0.03**

Table 5 Decomposition of variance for different motivational regulations.

3.17** −0.09** 0.29** 0.48** 0.03**

Unconditional model Unconditional growth model

External regulation

Unconditional model Unconditional growth model

Introjected regulation

Unconditional model Unconditional growth model Unconditional model Unconditional model Model fitted

Identified regulation Intrinsic motivation Variables

Table 4 Unconditional models and unconditional growth models for different motivational regulations over the 4 measurement times.

Unconditional growth model

Amotivation

Unconditional growth model

48

Level 1 intra-individual

Level 2 interindividual

Level 3 inter-class

37.7% 46% 46% 45.65% 41.22%

52% 46.9% 46% 50% 50%

10.2% 7.1% 8% 4.35% 8.78%

trajectory for amotivation. The two parameters for amotivation were significant. Both were negative, meaning that the higher the initial status of amotivation, the lower the end-of-year mathematics scores (b = −0.44). The more rapidly the amotivation progressed during the year, the lower were students’ end-of-year mathematics scores (b = −2.32). In addition, the inclusion of the growth parameters from the amotivation trajectory made the identified motivation rate-ofchange non-significant. This result is consistent with findings from Karsenti and Thiebert (1995) who found that the relationship between autonomous forms of motivation and achievement was not as strong when amotivation was controlled. We verified that this non-significance did not come from multicollinearity problem between covariates: the VIF indices ranged between 1.4 and 3, which show no multicollinearity. Although this model fit the data significantly better than did Model 2 (ΔD (2) = 10.8, p < .01), the gains in the explanation of the residual variance at the interindividual and interclass levels were weak (1.2% and 1% respectively). Given that in Model 3 only the growth parameters for amotivation were significantly related to mathematics achievement, we next specified Model 4 to include only these covariates and those from the baseline model. The effect of the growth parameters associated with the amotivation trajectory were stronger in Model 4 than in Model 3 (b = −.62 for initial status and b = −3.5 for rate of change). The results indicate that the higher the initial status and the faster the increase of amotivation, the worse the end-of-year mathematics performance. Although the deviance statistic in Model 4 is higher (−2 Log L = 4554.1) than that in Model 3, the likelihood-ratio test between these two models was not significant (ΔD (8) = 12.2, p > .05). In addition, we can consider that Model 4 fit the data better than Model 3 because it was more parsimonious (AIC = 4570.1 in Model 4 compared to 4573.9 in Model 3, and BIC = 4584.2 in Model 4 compared to 4602.1 in Model 3). Finally, as in Model 2, the rate of change of identified motivation was significantly related to mathematics achievement. We therefore tested a last alternative model (Model 5), which included the covariates from the baseline model and the growth parameters derived from the identified motivation trajectory. This was done in order to compare the relevance of a model with the only significant motivation regulation (as revealed by Model 2) to the model that includes only amotivation parameters (Model 4). This would allow us to compare two models with the same number of parameters but that only differ on the included type of regulation. The results showed that all fit indices were smaller in Model 4 than in Model 5, in particular for AIC and BIC (respectively 4570.1 and 4584.2 against 4578.2 and 4592.3) indicating that Model 4 offers a better fit. According to Raftery (1995), a difference of 8.1 points in the BIC is considered strong evidence of better fit. In addition to the fact that identified regulation becomes non-significant when amotivation is controlled (Model 3), this result indicates that amotivation is a better predictor of mathematics performance than identified motivation. Even, from a strict statistical point of view, we can argue that amotivation is the only relevant motivational construct if one wants to explain mathematics learning, at least based on data from this sample.

N. Leroy & P. Bressoux/Contemporary Educational Psychology 44-45 (2016) 41–53

49

Fig. 1. Developmental trajectories of different motivational regulations.

4. Discussion Although the autonomous and controlled forms of motivation have been well documented (Deci & Ryan, 2000; Elliot & Moller, 2003; Lepper et al., 2005; Wigfield & Eccles, 2000), no study based on longitudinal repeated measures has jointly examined the effects of the different types of motivation and amotivation on school learning over time. The objective of the present investigation was twofold. First it aimed at describing motivational patterns of change over the first year of junior high school in a French context. The second objective was to analyze the dynamic (i.e., changing) effects of the different types of motivational regulations as well as amotivation on students’ mathematics performance to determine which motivational construct is the best predictor of subsequent mathematics achievement. By measuring motivation at more than two time points, this study shows how change in motivation and amotivation over the course of the year predict end-of-year mathematics performance. 4.1. How do the different types of motivational regulations change during the first year of junior high school? This study offers an extension to previous results by improving our understanding of the developmental trajectories of motivation and amotivation during the first year of junior high school. Whereas previous studies have generally reported a decrease in intrinsic motivation (Lepper et al., 2005; Wigfield & Eccles, 2002) and an increase in extrinsic motivation (Eccles et al., 1996; Nishimura & Sakurai, 2013), our results are more similar to those obtained by Gillet, Vallerand, and Lafrenière (2012) for elementary school students and those by Otis et al. (2005) for senior high school students who showed a decline in both the autonomous and controlled forms of motivation over time. However, identified regulation appeared to be the most reported type of motivation. Thus, if students engaged in mathematics, it was mainly because they perceived this subject to be important rather than because they perceived it to bring them pleasure and satisfaction. Regarding amotivation, an increase in scores over the course of the year was noted, indicating that the more students progressed through the school year, the more likely they were to state that mathematics is a waste of time and a useless subject. However, this result needs to be considered with some caution given that students’ scores on this variable were lower than they were on the other types of motivation investigated throughout the school year. In addition, an increase in amotivation did not

necessarily coincide with a decline in the other kinds of motivational regulations. As previously noted, amotivation should not be considered as simply capturing the opposite of autonomous motivation. Consequently, its pattern of change is independent of other kinds of motivation trajectories. It should also be pointed out that these observations involved mean developmental patterns and that the variance components for each regulation were significant, indicating that these trajectories were heterogeneous. In other words, not all students’ motivational beliefs necessarily followed the same pattern. The variability of these developmental patterns for each of the motivational regulations is primarily accounted for at the interindividual level. This result shows that it is mainly the students’ individual characteristics and processes developing over time that explain this heterogeneity. Lastly, the interclass-level variance, although modest, also indicates that environmental characteristics might explain why students did not start with the same motivational level and did not change at the same rate. 4.2. How does the development of motivational regulations and amotivation during the first year of junior high school affect mathematics achievement? Our results are consistent with previous studies that have shown that both the mean level of motivation (Wigfield et al., 2006) and the rate of change (Gottfried et al., 2013) influence students’ subsequent achievement, even when accounting for prior achievement. In line with SDT, which has shown that identified motivation is an important form of motivational regulation for school-related activities (e.g., Koestner & Losier, 2002), our study provides consistent evidence by showing that only identified regulation has a significant and positive effect on mathematics achievement when the other motivation regulation beliefs (excluding amotivation) are taken into account (Karsenti & Thiebert, 1995). Although we were encouraged by the fact that amotivation was less commonly endorsed by students than intrinsic or identified regulation, its notably detrimental effect on academic achievement gives reason for concern (Ntoumanis, Pensgaard, Martin, & Pipe, 2004; Ryan & Deci, 2000). Our study offers a particularly robust finding on this point. Indeed, contrary to previous studies that have utilized a Relative Autonomy Index (e.g., Black & Deci, 2000) or have not included amotivation at all, this study shows the unique importance of amotivation in predicting mathematics achievement over time. When accounting

50

Table 6 Explanatory models for end-of-year learning.

Fixed effects

Random effects Fit indices

* p < .05. ** p < .01.

Intercept (std error) Beginning-of-year test score (std error) [β] Repeating a grade (yes = 1; no = 0) (std error) [β] Gender (girl = 1; boy = 0) (std error) [β] Initial status of intrinsic motivation (std error) [β] Rate of change of intrinsic motivation (std error) [β] Initial status of identified regulation (std error) [β] Rate of change of identified regulation (std error) [β] Initial status of introjected regulation (std error) [β] Rate of change of introjected regulation (std error) [β] Initial status of external regulation (std error) [β] Rate of change of external regulation (std error) [β] Initial status of amotivation (std error) [β] Rate of change amotivation (std error) [β] Level 1 variance (std error) Level 2 variance (std error) −2 Log L AIC BIC

Model 0 (Empty model)

Model 1 (Baseline model)

Model 2

−2.14 (0.53)** 0.18 (0.006)** [0.67] −0.71 (0.29)** [−0.05]

10.95 (0.32)** — —

Model 3

−1.83 (1.25) ns 0.18 (0.01)** [0.67] −0.64 (0.28)* [−0.05]

0.97 (0.19)** [0.10]

Model 4

−0.19 (1.47) ns 0.18 (0.01)** [0.67] −0.64 (0.28)* [−0.05]

0.95 (0.19)** [0.10]

Model 5

−0.69 (0.61) ns 0.18 (0.006)** [0.67] −0.68 (0.28)** [−0.05]

0.86 (0.19)** [0.10]

−3.29 (0.93) ns 0.18 (0.006)** [0.67] −0.67 (0.28)** [−0.05]

0.80 (0.19)** [0.09]

0.94 (0.19)** [0.10]

— —

—

ns

ns

—

—

—

—

ns

ns

—

—

—

—

ns

ns

—

0.44 (0.18)* [0.05]

—

—

ns

—

3.17 (0.82)** [0.08]

—

—

ns

ns

—

—

—

—

ns

ns

—

—

—

—

ns

ns

—

—

—

—

ns

ns

—

—

— —

— —

— —

8.12 (0.39)** 2.30 (0.56)** 4595.7 4607.7 4618.3

7.74 (0.37)** 2.18 (0.56)** 4552.7 4580.7 4605.3

−0.62 (0.17)** [−0.08] −3.5 (1.04)** [−0.08] 7.76 (0.37)** 2.17 (0.55)** 4554.1 4570.1 4584.2

— —

17.55 (0.84)** 3.76 (0.99)** 5291.6 5297.6 5302.9

−0.44 (0.23)* [−0.06] −2.32 (1.2)* [−0.05] 7.65 (037)** 2.16 (0.55)** 4541.9 4573.9 4602.1

2.26 (1.07)* [0.06]

7.83 (0.37)** 2.17 (0.55)** 4562.2 4578.2 4592.3

N. Leroy & P. Bressoux/Contemporary Educational Psychology 44-45 (2016) 41–53

Fitted Models

N. Leroy & P. Bressoux/Contemporary Educational Psychology 44-45 (2016) 41–53

collectively for prior achievement, all types of motivation regulation, and amotivation, our analyses showed that amotivation is the only motivation type to be significantly associated with mathematics achievement at the end of the school year. This result is consistent with findings reported in the meta-analysis by Taylor et al. (2014) meta-analysis (study 1), which showed that for older students, amotivation was the most strongly related to school achievement over time. Our study extends previous quasi-longitudinal research to a younger population by indicating that for junior high school students, amotivation seems to play a more important role on subsequent mathematics achievement than any other motivation forms do. Even though amotivation was the less endorsed type of motivation, it is the only type of motivation that increased over time. In other words, poor mathematics achievement seems to be predominantly a function of academic amotivation rather than a consequence of controlled forms of motivation. As the baseline performance was controlled for in the analyses, this result cannot be attributed to interindividual differences in initial level of performance. These findings could indicate that amotivated students are less able to cope with difficulties in mathematics. In fact, it is possible that the reasons why students are amotivated are a source of explanation for the preponderance of amotivation. In addition, the behavioral pattern that amotivated students display (Dweck, 1986) could help to explain the powerful effects of amotivation. Amotivated students are reluctant to contribute to academic tasks, take few if any initiatives, and adopt work avoidance strategies (Dweck, 1975; Dweck & Reppucci, 1973). In turn, they miss numerous opportunities to learn. Because of the cumulative nature of mathematics learning, the deleterious effects of missed opportunities to learn new concepts could worsen in time. 4.3. Limitations and future directions Although this research offers insights not addressed in previous studies, it nevertheless contains a number of limitations that should be considered in order to provide directions for future studies. First, in this study, amotivation was considered as a one-dimension construct: a general state of absence of motivation. However Pelletier, Dion, Tucson, and Green-Demers (1999) argued that this onedimension conceptualization is not sufficient to reveal the whole picture of motivational deficits. It could be interesting to address the conceptual definition of amotivation as Legault et al. (2006) and Green-Demers, Legault, and Pelletier (2006) did in order to give a more precise picture of amotivation and its effects on academic achievement. Second, it should be pointed that although these results shed new light on the influence of amotivation on achievement, their specificity to the mathematics domain prompts us to be cautious about their applicability to other subject areas. Studies have shown that the effect of motivational orientations vary in function of the demands of the task and in function of the characteristics of the academic domain (Licht & Dweck, 1984). Finally, other research perspectives can emerge from this. Since this study involved a relatively limited time interval, it would be worthwhile to pursue this research using a longer time frame so as to examine the effects of motivational changes over the long term. In so doing, it would also be possible to determine whether the developmental patterns of different motivational regulations and amotivation are confirmed in subsequent school years, by focusing in particular on the consequences related to the transition from one grade level to the next. 4.4. Implications A deeper understanding of the consequences of the evolution of the different types of motivations as well as amotivation will no

51

doubt have important theoretical and applied implications. The importance of this study lies in the fact that motivation and especially the lack of motivational regulation predicts mathematics achievement more than do autonomous forms of motivation. As an impressive body of research from self-determination theorists has shown, intrinsic and identified regulation are reliable predictors of academic achievement. This work provides complementary evidence by showing the importance of the amotivation process. As Legault et al., (2006) indicated, “it seems that amotivation is itself an entity” (p. 580) that has to be considered not merely as an absence of motivation but rather as a complex process worthy of attention. By extension, it could be interesting to address which component of amotivation is the most likely to lead to poor achievement in mathematics. According to these researchers, students may experience a lack of motivation because of perceived lack of ability, incapacity of effort, the characteristics of the task or the value they place on it. More particularly they reported that amotivation relative to low ability and low effort beliefs displays negative relationships with academic achievement. Hence, students who believe they are neither smart nor capable of effort are the most likely to have poor academic achievement. To further understand the impact of motivational behavior on academic achievement, it is essential to consider the importance of motivation not merely as a declination of various degrees of self-determinated regulation but also as an absence of regulation. Indeed the passivity and disaffection with learning engendered by amotivation seem to be the cause of particularly debilitating effect on mathematics performance. To go a bit further, one could even say that behavioral deregulation seems to be as important as behavioral regulation, if not more. Although theories of amotivation have appeared as the object of recent research (Green-Demers et al., 2008; Legault et al., 2006), understanding a lack of motivation is still an underexplored conceptual and empirical field (e.g., Hidi & Harackiewicz, 2000; Pelletier et al., 1999). It seems however to be a promising research avenue for understanding how to reduce one of the most predictive factors of poor academic adjustment. Investigating more deeply the reasons that give rise to amotivation would give more insight about processes that thwart behavioral deregulation in mathematics domain. By doing that, it would undoubtedly facilitate teacher to implement effective strategies in their class. Our findings also have important practical implications; indeed they could lead practitioners to reconsider strategies and interventions to promote success in mathematics. While promoting selfdetermined forms of motivation is a strategy that has proven to be effective (e.g., Reeve, 2009), it appears that amotivation renders students more vulnerable to long-term negative effects related to school transitions (Taylor et al., 2014). If educators and teachers want to have a tighter grasp on the precise causes of academic difficulties, it might be more appropriate to turn attention to the reasons why students avoid mathematics. More efforts should be directed toward reducing amotivation (e.g., Cheon & Reeve, 2015) especially because the growth patterns revealed that amotivation increases throughout the year and that its associated negative behaviors become entrenched (Yates, 2009). Moreover, because the cumulative effects of amotivation can become more and more deleterious as amotivation, it is important to identify students early who may be susceptible to developing amotivation. This would allow teachers to immediately work with at risk students and, as a consequence, prevent them from dropping out. References Aelterman, N., Vansteenkiste, M., Van Keer, H., Van den Berghe, L., De Meyer, J., & Haerens, L. (2012). Students’ objectively measured physical activity levels and engagement as a function of between-class and between-student differences in

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