Moving into adolescence is experienced by most of young people as a period of considerable stress. For many students it's considered as a major stepping-stone on the road to becoming an adult. Teens go about many physical social and emotional changes. In academic domain, for example parents and teachers often report a decline of motivation during school transition (Anderman & Maehr 1994 ; Diemert, 1992 ; Eccles & Midgley, 1989 ; Lepper & Hodell, 1989 ; Simmons & Blyth, 1987 ; Wigfield, Eccles, Mac Iver, Reuman, & Midgley, 1991). This disengagement which brings some students into a progressive drop out has interested researchers since about twenty years. Their studies have attended to explain this progressive shift and have showed that transition to middle high school is a crucial time when young adolescents are most likely to experience constraining teaching practices. So changes in school environment have often been associated with a decline in academic achievement, performance motivation, and self-perceptions particularly in mathematics (Eccles, Midgley & Alder, 1984 ; Eccles & Midgley, 1990 ; Feldlaufer, Midgley & Eccles, 1988). Feldlaufer et al. (1988), Midgley Anderman and Hicks (1995) have demonstrated that after moving into middle high school students have fewer opportunities to make decisions and to have interactions with their peers. In addition social comparison would be more present in the teaching practices damaging their sense of competence and affiliation. Students evolving in context that does not allows to satisfy these needs will lose interest in this environment and will not adapt themselves to it creating difficulties and progressive disengagement. Indeed, for these researchers conflicts that exist between school environment and these growing motivational needs are responsible for this motivation decline. But even if these studies give us important elements in understanding the evolution of motivation, they provide incomplete explanations. According to Bryk and Raudenbush (1987), “researches on individual change have been plagued by inadequacies in conceptualization, measurement and designs” (p.147). Current studies are based on transversal or semi-longitudinal designs which consequently do not allow capturing the changing nature of the motivation. To adequately report the dynamic nature of motivation it would be necessary to conduct real longitudinal studies. Unfortunately this kind of research is less frequent than cross sectional ones because of two main difficulties. First of all, collection of repeated data over time is a very difficult task which requires and important human and material investment. Second, beyond the possibility of following the population of interest, it is the analysis of longitudinal data that raises problems. Indeed the hierarchical structure of longitudinal data cannot be treated by classic statistical methods like Ordinary Least Squares (OLS). This method does not take into account the nested structure of data and impose to choose one unit of analysis which in turn generates biased estimates. The aim of this communication is to present, on the basis of an empirical work, the relevance and contribution of the multilevel growth models in the description and explanation of the motivation growth trajectory during transition to middle high school. By the present study we will try to answers two main questions: - How really does motivation change over the first year of middle high school or what are the characteristics of motivation growth trajectory? - Can we predict differences in these changes or what are the factors that explain the differences in motivation growth trajectory?

Study Overview Exploring change supposes a longitudinal design with repeated data. For this reason, we questioned at four occasions more than one thousand students (varying from 1067 to 1080 from the first to the last wave of data collection) during the 2006-2007 school year. These students were nested in 47 classrooms which were themselves nested in 15 middle high schools. The first data collection took place in October, the three others at the end of each academic quarter (December, Mars and June). The mathematics teachers (N=30) were also to complete a questionnaire in March and return it to the researcher. A booklet containing all the questionnaires needed for the study was distributed to each participant (students and teachers). They were informed that the responses provided on the questionnaire would remain strictly anonymous and that the data would be used solely for the purposes of this study Method Recent advances in statistical methods now allow empirical exploration of developmental change across life span. Specially elaborated for the analysis of nested data hierarchical linear growth models are now available for exploring longitudinal data. This method that allows describe and explain developmental change over time can be considered as an extension of hierarchical linear models (Aitkin & Longford, 1986 ; Goldstein, 1986 ; Mason, Wong & Entwisle, 1983 ; Raudenbush & Bryk, 1986). We adopted a multiple data collection design to describe how student’s motivation change but also how individual trajectories vary across students. Instruments Relative Autonomy Index (RAI) Self determinated motivation, which is the variable of interest in this study, was evaluated by a French translation of the Academic Self Regulated Questionnaire (Ryan and Connell, 1989). We use RAI which represents a combination of the different subscale scores proposed in this instrument. The more the RAI is, the more student’s motivation is self determinated (adopted in a voluntary way in the absence of any external contingency like reward or punishment). Student’s achievement goals The scale used to measure goals pursued by students is a French translation of Patterns of Adaptative Learning Scales (PALS, Midgley et al., 2000). Two sub-scales were retained; the pursuit of a mastery goal and the pursuit of performance goal. Mastery goal pursuit is an orientation in which students tend to develop new capacities and knowledges to improve their competences by using self-referenced criteria. Performance goal pursuit is an orientation in which students' sense of satisfaction is highly influenced by their grades and by other external indicators of success such as normative comparison. Implicit theories of intelligence We used an adapted version of Dweck scale (2001). Two dimensions were evaluated. The first one was relative to an incremental conception of intelligence the other one was relative to a stable conception of intelligence. Academic self concept in mathematics This variable was evaluated through a translation of Academic Self Description Questionnaire (Marsh, 1990). In a general way, items from this scale provide an estimation of perceptions students have on themselves in mathematics Perceived motivational climate Perceived motivational climate vas measured by the Learning Climate Questionnaire (LCQ, Self Determination Theory, unknown date). Items evaluate the degree students perceived their teachers as supporting their motivational needs of autonomy, competence and affiliation. Perceived goal orientation promoted within family To estimate the type of goal valued within family we used a French translation of PALS. Items were relative to the parents’ pursuit of performance or mastery goal for their children. Perceived classroom goal structure It was evaluated via three subscales extracted from the PALS. The first one aimed at evaluating teachers’ practices oriented toward a mastery goal within his class. The second one aimed at evaluating the way that mathematics teacher valued a performance approach orientation and then the last one were designed to assess teachers’ practices orientated toward an avoidance performance goal Motivational climate established by teacher The questionnaire administered here is an adaptation of the LCQ. We constituted a general score reflecting the motivational needs support reported by teacher Classroom goal structure established by teacher The scale used to measure the Classroom goal structure established by teacher is a French translation of PALS. Three dimensions were retained. The first one was relative to teaching practices valuing a mastery orientation. The second was relative to practices valuing an approach performance goal and the last was relative to an avoidance performance goal orientation. Teachers’ perception of pressures from the working climate The scale used to measure the perceived constraints at work was a French version of the Constraints at Work Scale developed by Pelletier, Legault and Séguin-Lévesque (2002). The first sentence of the questionnaire invited teachers to give their feeling about the climate in which they taught.

The first question we wanted to answer (How really change motivation over the first year of middle high school) is descriptive and asks us to characterize each student’s motivation pattern of change over time. Concretely it consisted of specifying the unconditional growth model and testing which type of function best represents intra-individual motivation change. Here we wanted to know if motivation evolution was linear, nonlinear, if it was positive or negative. The second one (Can we predict differences in these changes?) is relational and asks us to examine the association between predictors and pattern of motivation change. It aims at explaining the heterogeneity change over time for both initial status and rate of change. The relevance of such a question was to understand why some students are more motivated than others at the beginning of the year and why some show faster rate of change over time than other. We wanted to know if students with different characteristics or experiencing different types of contexts demonstrate different patterns of change. At the end of this model specification we can say that the initial level of RAI is of 0.84 point (theoretically it can vary from -12 to +12). In addition initial status and rate of change significantly vary at the same student over time but also from one student to another and from on class to another. A quadratic function indicates that motivation change over time is non linear. At the beginning of the first year of middle high school RAI score rises until wave 2 (Extremum= -.4038/2* (- 0.1013)) who corresponds at the end of the second quarters. Thus, we can affirm that from October until Mars motivation evolves positively and then decreases slightly from this period until the end of the year school. Impact of individual time varying predictors and environmental factors will be discussed.