Using Measures of Mathematics to Predict Response to Supplemental Intervention

Abstract

The method for correctly identifying and intervening with students who are not meeting grade level expectations has varied. Historically, an approach relying on underlying cognitive characteristics or processing skills was used. This approach, referred to as an Aptitude-by-Treatment Interaction (ATI) was criticized for not fully capturing student needs or explaining intervention effectiveness (Cronbach & Snow, 1977; Kearns & Fuchs, 2013). Alternatively, a framework called a Skill-by-Treatment Interaction (STI) relies on matching interventions based on measurable and alterable skills (Burns, Codding, Boice, & Lukito, 2010). Preliminary research in the area of mathematics suggests that the STI approach may be useful in identifying specific subskill needs, such as conceptual understanding or computational fluency, for students (Burns, 2011). The purpose of the current study was to better understand the relationship between mathematics assessment and intervention design. Specifically, the study examined the link between specific skill assessments of conceptual understanding, computational fluency, and application and word problem solving with a conceptually-based or computation-based intervention. Participants were 46 third and fourth grade students attending a suburban elementary school in the upper Midwestern United States. All participating students received a conceptually-based and computation-based intervention, the order of which was counterbalanced, for two weeks, respectively. Students were assessed using measures of conceptual understanding, computational fluency, and application and word problem solving. Results indicated that gains in computation and application and word problem solving were best predicted by students’ pretest performance on the same measure, regardless of intervention. Interestingly, gains in computational fluency following a computation-based intervention were predicted by students’ prior conceptual understanding. Pretest performance on the conceptual understanding and computational fluency measures were used post hoc to analyze groups of students based on identified need. Students’ identified need did not account for a significant proportion of the variance following intervention. The current results were contextualized within previous research and potential implications for practice were discussed. Specifically, the results of the study were discussed in terms of their contribution to (1) the role of and relationships between essential knowledge bases comprising mathematical proficiency, and (2) how the current study might inform frameworks for matching assessment data to intervention. Lastly, limitations to the study and future directions for research were outlined.