A Comparison of Two Prominent Instructional Approaches to the Teaching and Learning of Multi-digit Computation.

Abstract

This dissertation compares two approaches commonly used to teach multi-digit computation in second through fifth grades. The two instructional approaches under investigation differ in their emphasis on aspects of mathematical proficiency, often referred to as procedural and conceptual knowledge. The question––of which approach should be preferred–– has been the center of debates in mathematics instruction for over 20 years. Instruction that differs in its emphasis on procedural and conceptual knowledge is thought to differ in cognitive demand on students. Instruction in U.S. schools has historically placed a high emphasis on procedural knowledge, the emphasis that is thought to be less cognitively demanding. I call this the common instructional approach. Research suggests that a more balanced and intertwined emphasis on procedural and conceptual knowledge, referred to as the blended instructional approach, will better support students’ learning. Other research suggests emphasis depends on who is being taught. Given new analytic methodologies, I investigated these theories using data from a daily teacher log and second through fifth grade student achievement measures collected by the Study of Instructional Improvement. I used four log items to define the instructional approach used in classrooms. Further, I use existing items and an IRT 2-parameter model to measure student’s knowledge of multi-digit computation. Limitations for linking levels without linking items or linking group were unsolved. I applied hierarchical linear models, Rubin’s causal framework, and propensity score causal inference techniques for studying causation. I found very few covariates systematically predict who receives the approaches. In the lower grades, school characteristics influence the instructional approach in use, but class characteristics influence the approach in use in the upper grades. From the causal analysis, students in classes receiving the blended instructional approach achieved the same as students in classes receiving the common instructional approach. Overall, this investigation found no support for the instructional approaches supported by the Standards. Furthermore, regarding analytic methods, this research concluded that future investigations comparing instructional treatments might benefit from using statistical methods that model treatments as they are received by students within and across academic years.