Phenomenon of mathematical fluency.

This study explored the longitudinal relationship between motivation and acquisition of a second modern foreign language (MFL). Participants were 11 to 12 year-old pupils attending the first year of secondary school. They constituted a naive population as formal MFL learning in the United Kingdom begins in secondary school. MFL achievement, assessed using national curriculum standards, and self-report measures of motivation were collected at four time points throughout the year. Previous motivation was found to be the only predictor of motivation at the end of the academic year. In the same way, previous achievement was the only predictor of final achievement. Results showed that the correlational relationship between motivation and achievement over time was stable, with modest effect size. Cross-lagged panel analysis was adopted in order to assess the causality of the observed relationship between motivation and achievement. However, no cross-lagged relationships were observed in this sample. Once accounting for the stability of the constructs and their cross-sectional (contemporaneous) relationship, no further variance was explained by cross-lagged relationships between motivation and achievement at different time points.