Investigating the Generalizability of Schema-Based Instruction Focused on Proportional Reasoning: A Multi-State Study

Abstract

This study used integrative data analysis (Curran & Hussong, 2009), which allows combining data from different studies, to examine the generalizability of a research-based mathematics program, schema-based instruction (SBI), with a focus on proportional reasoning. Data were pooled from existing SBI studies spanning three U.S. states in which teachers and their classrooms were randomly assigned to either a SBI or control condition. Results of a series of multilevel (i.e., two-level, students within teachers) models indicated the effectiveness of SBI in improving students’ mathematical problem-solving performance. The pooled data findings clarify that SBI improves students’ mathematical problem solving more so for proximal than distal measures. These findings also show Black and Hispanic students continue to lag behind White students, that teachers with more experience tend to be associated with higher performing classrooms, and that increasing concentrations of students eligible for free or reduced price lunch and students receiving special education services are generally associated with weaker performances. Implications of these findings are discussed.

KEYWORDS:

• Proportional reasoning
• schema-based instruction
• integrative data analysis
• middle school

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The research reported here was supported by the Institute of Education Sciences, U.S. Department of Education, through Grant #R305A110358. The opinions expressed are those of the authors and do not represent views of the Institute of Education Sciences or the U.S. Department of Education. The first author is the primary author of the schema-based instruction program, which was unpublished at the time these studies were conducted. However, to ensure objectivity of findings, all scoring, entry and data analysis were conducted by research assistants and the methodologist, who do not have any interests that might be interpreted as influencing the research. The research assistants and methodologist independently reviewed the manuscript to ensure data analysis, findings, discussion, and interpretations were appropriate, accurate, and objective.