Rethinking the Role of "Quality Instruction" in Predicting Algebraic Learning within an Opportunity-Propensity Framework: An Exploratory Cross-Cultural Study

• Published in: Journal of educational psychology Vol. 115; no. 2; pp. 241 - 266
• Main Authors: Ding, Meixia, Byrnes, James, Ke, Xiaojuan
• Format: Journal Article
• Language: English
• Published: American Psychological Association 01.02.2023
• Subjects: Algebra; Comparative Education; Correlation; Cross Cultural Studies; Educational Quality; Elementary School Students; Foreign Countries; Instructional Effectiveness; Mathematics Achievement; Mathematics Instruction; Predictor Variables; Prior Learning; United States; China
• ISSN: 0022-0663
• DOI: 10.1037/edu0000767

This exploratory study examined whether instruction aligned with the Institute of Education Sciences recommendations (i.e., use of worked examples, representations, deep questions) predicts student learning of early algebra, particularly inverse relations, in elementary classrooms. Instructional quality was determined through an opportunity-propensity analysis of cross-cultural data (N = 569) from the United States and China, which showed that teaching played a stronger role in student learning than previously reported. Results from structural equation modeling indicated that teaching quality--especially teachers' use of deep questions--had both direct and indirect effects (through prior knowledge) on student learning, which together demonstrated greater predictive power than what was reported in previous studies. Specifically, direct path results showed that instructional quality, rather than teacher characteristics, played a more important role in predicting student learning. Indirect effects showed that instructional quality, mediated through students' prior knowledge, predicted the most about students' mathematics achievement. Taken together, the results of the analysis provided strong evidence that implementation of worked examples, representations, and deep questions were positively related to student learning in early algebra. Hierarchical linear regression confirmed these findings but indicated that teaching quality in the current data explained more additional variance in "correctness" than "inverse understanding" for student learning. These findings suggest that the kind of instruction examined in prior opportunity-propensity studies had a weaker effect because it did not align with the Institute of Education Sciences recommendations. Findings also shed light on the extent to which classroom instructions are better at developing students' algebraic readiness.