### Project Description

## Project Brief

The purpose of the study is to develop and test a model, based on Self-Determination Theory (SDT), describing the effects of motivational resources on mathematics performance. The model incorporates the assumption that intrinsic motivation positively affects mathematics performance, whereas external regulation negatively affects mathematics performance. Furthermore, it is assumed that mathematics self-concept affects mathematics performance both directly and indirectly through the mediating variable of intrinsic motivation. Finally, autonomy support can affect mathematics performance both directly and indirectly through the mediator of mathematics self-concept. The model was tested using data from the Third International Mathematics and Science Study-Revised (1999), or TIMSS-R (1999), on the mathematics performance of eighth-grade students in the USA. The conclusions drawn from the study were consistent with the predictions of SDT. Both structural equation modeling and multilevel path modeling analyses confirmed that intrinsic motivation positively influenced mathematics performance, whereas external regulation negatively influenced mathematics performance. A positive mathematics self-concept significantly affected mathematics performance both directly and indirectly through the mediator of intrinsic motivation. Finally, autonomy support in the classroom significantly affected mathematics performance both directly and indirectly through the mediator of mathematics self-concept.

## Conceptual Design

## Skills Needed

Structural equation modeling (SEM) analysis was performed, using the statistical program Mplus (Muthen & Muthen, 1998). SEM is a set of statistical techniques that include confirmatory factor analysis (CFA) and path modeling (Ulman, 2001). We conducted a series of SEM analyses. Several indices were used to assess model fit: the chi-square statistic, the *comparative fit index* (CFI), the *non-normed fit index* (NNFI), the *root-mean-square error of approximation* (RMSEA), the* standardized root mean-square residual* (SRMR) (Hu & Bentler, 1999), the Akaike information criterion (AIC), and the Bayesian information criterion (BIC).

### Initial Concept Planning

This study used data from the TIMSS-R 1999. The methodology used in the TIMSS-R (1999) study is presented in this section. TIMSS participants and procedures are described. Measures were developed of autonomy support, intrinsic motivation, external regulation, introjected regulation, and math self-concept.

### Drafts & Revisions

The model-fitting process suggested that Model 2 best fit the data (χ^{2} (13) = 92.170, CFI=0.953, TLI=0.951, RMSEA=0.049, SRMR=0.044). The model with the lowest AIC is preferred (Kline, 1998). Model 2 had the lowest AIC. On this basis, we selected Model 2 as the best model of all the models and based further analyses on that model. Model 2 is called the trimmed full model.

### Final Delivery

The path diagram that shows the fully-unstandardized parameter estimates for Model 2 appears in Figure 5. These findings support the model. First, intrinsic motivation positively affected math performance (β=7.865), whereas external regulation negatively affected math performance (β= -15.196), consistent with the first hypothesis (*H1*). Math self-concept positively affected math performance (β=11.399), consistent with the second hypothesis (*H2*). Autonomy support positively affected math self-concept (β=0.072) and math performance (β=1.474), consistent with the third hypothesis (*H3*). Math self-concept significantly affected math performance through the mediator of intrinsic motivation, consistent with the fourth hypothesis (*H4*). Finally, autonomy support in the classroom significantly affected math performance through the mediator of math self-concept, consistent with the fifth hypothesis (*H5*).

## Conclusion

Our findings have practical implications. SDT argues that self-perceptions of autonomy and competence should interact to increase well-being (Deci & Ruan, 1985, 2000; Fisher, 1978; Ryan, 1982). Past research (Grolnick, Ryan, and Deci, 1991; Williams & Deci, 1996; Williams, Freedman, & Deci, 1998) showed that autonomously motivated people show greater competence, and that autonomous motivation and self-perceived competence both affect school performance. Consistent with the predictions of SDT, when teachers support autonomy of students in the classroom, they provide a classroom climate that fosters math achievement. As teachers try to support students’ competencies, they are more likely to foster students’ self-perceptions of competence, which, in turn, promotes math achievement.

## Excellent Results

The path diagram that shows the fully-unstandardized parameter estimates for Model 2 appears in Figure 5. These findings support the model. First, intrinsic motivation positively affected math performance (β=7.865), whereas external regulation negatively affected math performance (β= -15.196), consistent with the first hypothesis (*H1*). Math self-concept positively affected math performance (β=11.399), consistent with the second hypothesis (*H2*). Autonomy support positively affected math self-concept (β=0.072) and math performance (β=1.474), consistent with the third hypothesis (*H3*). Math self-concept significantly affected math performance through the mediator of intrinsic motivation, consistent with the fourth hypothesis (*H4*). Finally, autonomy support in the classroom significantly affected math performance through the mediator of math self-concept, consistent with the fifth hypothesis (*H5*).

# We’re Here To Help Your Business Blast Off!

Through Creative Ideas, Innovation & Sheer Determination