The goals of this dissertation were as follows: (1) application of quantitative methods to large-scale databases, (2) investigation of relationships between student mathematics achievement and student motivational attitudes for learning mathematics at the macro level (i.e., national level) and at the micro level (i.e., student level), (3) examination of the pattern of the cultural factors (i.e., student motivational attitudes for learning mathematics) among nations, (4) examination of the percentage of the school level in explaining total student mathematics achievement variance within the country, and (5) investigation of the relationships of student- and school-level factors associated with student mathematics achievement within the country.
In order to conduct this quantitative and international education study, the Trends in Mathematics and Science Study 2007 eighth-grade student and school datasets from 49 countries were used. Exploratory factor analysis, confirmatory factor analysis, and item response theory were used to examine the twelve items measuring motivational attitudes for learning mathematics. Descriptive statistics and correlation analysis were conducted to examine the relationship between student motivational attitudes and mathematics achievement at the individual and national level. To reduce this study to a manageable scale for conducting hierarchical linear modeling (HLM) analyses, Mahalanobis distance was computed to select countries based on their similarity for the three motivational variables. Finally, several HLM analyses were used to explain the relationships between student mathematics achievement and variables at the student and school level within the country.
The results indicated that the twelve items can form three motivational factors: intrinsic motivation, extrinsic motivation, and self-efficacy. The three factors have satisfactory psychometrical properties as variables for future research. However, it should be noted that the three motivational factors can measure student motivational attitudes well for students of average motivation better than students who are more extreme on motivation. The relationships between student mathematics achievement and student intrinsic motivation, extrinsic motivation, and self-efficacy are positive at the individual level. In contrast, these relationships at the national level are negative. Furthermore, based on these three student motivational factors, the 49 participating countries can be formed into six groups. Countries within a cluster tend to have geographical proximity or shared cultural and educational backgrounds.
In order to understand the relationships between these three motivational factors and other important predictors and student mathematics achievement from an organizational perspective, HLM was used to investigate these educational phenomena. The results showed that the school level accounts for a significant amount of variability of student mathematics achievement in the selected seven countries. Self-efficacy is the most consistent and important predictor of student mathematics achievement in all of the HLM analyses. Although proposed school-level variables do not consistently show significant relationships with student mathematics achievement, these variables account for much variability of student achievement at the school level. Finally, future research on methodological issues for analyzing multilevel and international large-scale databases, as well as potential research questions that could arise from conducting educational research using international large-scale databases are also proposed.