Predicting adaptive expertise with rational number arithmetic

Abstract

Background: Adaptive expertise is a highly valued outcome of mathematics curricula. One aspect of adaptive expertise with rational numbers is adaptive rational number knowledge, which refers to the ability to integrate knowledge of numerical characteristics and relations in solving novel tasks. Even among students with strong conceptual and procedural knowledge of rational numbers, there are substantial individual differences in adaptive rational number knowledge.

Aims: We aimed to examine how a wide range of domain-general and mathematically specific skills and knowledge predicted different aspects of rational number knowledge, including procedural, conceptual, and adaptive rational number knowledge.

Sample: 173 6^th and 7^th grade students from a school in the southeastern US (51% female) participated in the study.

Methods: At three time points across 1.5 years, we measured students' domain-general and domain-specific skills and knowledge. We used multiple hierarchal regression analysis to examine how these predictors related to rational number knowledge at the third time point.

Result: Prior knowledge of rational numbers, general mathematical calculation knowledge, and spontaneous focusing on multiplicative relations (SFOR) tendency uniquely predicted adaptive rational number knowledge, after taking into account domain-general and mathematically specific skills and knowledge. Although conceptual knowledge of rational numbers and general mathematical achievement also predicted later conceptual and procedural knowledge of rational numbers, SFOR tendency did not.

Conclusion: Results suggest expanding investigations of mathematical development to also explore different features of adaptive expertise as well as spontaneous mathematical focusing tendencies.

Keywords: adaptive expertise; flexibility; mathematical development; rational numbers; spontaneous mathematical focusing tendency.