The association between relational reasoning and mathematics achievement : exploring the role of representational systems, underlying mechanisms, and causality

Abstract

Higher-order reasoning skills have been proposed to contribute to academic learning and achievement. Relational reasoning (RR), defined as the ability to discern meaningful regularities from seemingly unrelated streams of information, is an exemplar. While emerging evidence demonstrated the close association between RR and mathematical performance, most prior investigations measured RR with nonverbal tests. The role of verbal RR was rarely investigated. Plus, the underlying mechanism and potential causality between RR and mathematics achievement remained unexplored. The present thesis aimed to provide clarifications to these issues in three studies. With a newly developed verbal test of RR, Study 1 attempted to examine the relative contribution of nonverbal and verbal RR to mathematics achievement. A sample of 235 sixth graders were assessed on their nonverbal and verbal RR, computational skills, and mathematical problem solving. The new verbal test of RR showed satisfactory psychometric properties. Linear hierarchical regression analyses showed that controlling for cognitive abilities and literacy skills (working memory, spatial skills, and reading comprehension), both nonverbal and verbal RR significantly predicted computational skills and mathematical problem solving. The results provided support to the close association between RR and mathematics achievement. Study 2 further explored the association by adopting a longitudinal design and examining the mediation mechanisms. The same group of participants was tracked one year later (195 were retained). In addition to mathematics achievement, potential mediating variables (word problem representation, arithmetic fluency, and arithmetic principle understanding) were tested. Linear hierarchical regression analyses revealed that nonverbal RR significantly predicted future mathematics achievement, but verbal RR did not. Plus, overall mathematics achievement significantly contributed to future RR in both representations. A subsequent path analysis indicated that arithmetic principle understanding significantly mediated the relation between nonverbal RR and computational skills, and word problem representation mediated the prediction from both nonverbal and verbal RR to mathematical problem solving. These findings suggested potential causality from RR to mathematics achievement. In Study 3, this possibility was investigated with a randomized controlled trial. Another sample of 222 seventh graders were assigned to the intervention (component processes of RR) and active control (Cantonese phonetics) conditions. Both groups received pretests and posttests on RR, domain-specific skills, and mathematics achievement. Contrary to the hypotheses, 2 (Time) x 2 (Condition) ANOVAs showed that the intervention did not produce the expected near-transfer effect on RR, nor the far-transfer effects on domain-specific skills and mathematics achievement. The hypothesized causality between RR and mathematics achievement awaits further examinations with a more effective RR intervention. Exploratory analyses showed that the intervention group had significantly greater improvement in anomalous reasoning than the active control group, but not in the other forms. It implied that the intervention may have differential effects on individual forms of RR. Potential improvements on future RR intervention were discussed. These three studies not only unraveled the role of representational systems in RR and the mechanisms underlying its association with mathematics achievement, but also served as an empirical attempt to clarify the causal relation between the two constructs.