Parameterizing Individual Differences in Fraction and Decimal Arithmetic

Abstract

Math problem solving frequently involves choices among alternative strategies. Strategy choices, and effects of problem features on strategy choices, both vary among individuals. We propose that individual differences in strategy choices can be well characterized in terms of parametric variation in three types of influence: global bias, relevant feature effects, and irrelevant feature effects. We test this framework by applying it to children's strategy choices in fraction and decimal arithmetic. We describe a simple mathematical model of strategy choice in this domain that is based on a recent theory of arithmetic development and includes parameters representing the three types of influence above. We estimate these parameters in a sample of 120 fifth to ninth graders and find that all of them vary substantially among children. Further, we find that different parameters relate differently to other domain-specific and domain-general abilities, supporting the utility of distinguishing among the parameters and estimating them separately for individuals. We discuss implications of the results regarding the nature and origins of individual differences in strategy choice in fraction and decimal arithmetic and math more broadly.