Relationship between the Learning Hierarchy and Academic Achievement on Strategies Used by Third-Grade Students when Solving Multiplication Word Problems

Abstract

Distinguishing between sources of variability in mathematics performance may contribute to a more comprehensive theory of mathematics skills. Research has examined student differences based upon scores on achievement tests, which provide overall proficiency, but may not provide the detailed information for identifying and remediating difficulties. The Learning Hierarchy (Haring & Eaton, 1978) considers how students learn different academic skills as they progress through a learning sequence and has previous support as an intervention heuristic (Daly & Ardoin, 1997), but there is limited research for mathematics (Burns, Codding, Boice, & Lukito, 2010). The purpose of this study is to extend previous research by examining the Learning Hierarchy conceptual model as a framework based on performance on a fluency measure, as well as broaden the previous research base around the characteristics of problem solving for students by examining strategy use of students in specific phases in the Learning Hierarchy. Participants were 492 third grade students and were administered measures of computation fluency and application. Students were classified into four categorical phases based on accuracy and fluency scores (Burns, 2004; Burns, VanDerHeyden, & Jiban, 2006; VanDerHeyden & Burns, 2008). To examine strategy use, student responses were scored for overall accuracy and coded for strategy used to solve the problem (Zhang,Ding, Barrett,& Xin, 2014). The results support previous research findings in strategy development suggesting that mathematics achievement significantly predicts accuracy of strategy (Zhang et al., 2014). When student performance was compared based upon phases of the Learning Hierarchy, students in initial phases displayed more variation in strategy selection but, were less accurate and used lower quality strategies. The current findings are promising for consideration of the Learning Hierarchy as a potential conceptual heuristic model in mathematics. Current results were contextualized within previous research and potential implications for theory and future research supporting the validity of the Learning Hierarchy framework as well as the potential of understanding strategic development on intervention were discussed.