Individual differences in addition strategy choice: A psychometric evaluation.

Abstract

The strategy choice model (SCM) is a highly influential theory of human problem-solving. One strength of this theory is the allowance for both item and person variance to contribute to problem-solving outcomes, but this central tenet of the model has not been empirically tested. Explanatory item response theory (EIRT) provides an ideal approach to testing this core feature of SCM, as it allows for simultaneous estimation of both item and person effects on problem-solving outcomes. We used EIRT to test and confirm this central tenet of the SCM for adolescents’ (n = 376) solving of addition problems. The approach also allowed us to identify the strategy choices of adolescents who still struggle with basic arithmetic. The synthesis of SCM theory and EIRT modeling has implications for more fully investigating the sources of individual differences in students’ problem solving, and for identifying problem-solving patterns associated with poor academic achievement.

Is counting hindering learning? An investigation into children’s proficiency with simple addition and their flexibility with mental computation strategies

“…Overall accuracy was high (95% correct). The frequency of min-counting for simple addition reported here for elementary school students was similar to that found by Rhodes et al (2019) for middle school students (20%). Whereas Rhodes et al modeled individual differences to investigate variations in aggregate measures, we clustered individuals into groups that displayed similar performance characteristics.…”

“…Cowan et al (2011) reported that many second and third grade children in the UK were not using retrieval when solving simple addition problems. Rhodes et al (2019) highlighted the frequent use of min-counting by adolescent students in the United States. In an Australian study involving 200 students in seventh grade, Hopkins and Bayliss (2017) found fewer than half the cohort relied on retrieval-based strategies for simple addition.…”

A unified model of arithmetic with whole numbers, fractions, and decimals.

“…Our analyses of UMA’s behavior focused on two aspects of individual differences. First, some individuals shift from backup strategies to memory retrieval more quickly than others (Geary et al, 2004; Hofman et al, 2018; Lemaire & Siegler, 1995; Rhodes et al, 2019). Second, although many students display either high accuracy and high reliance on retrieval or low accuracy and low reliance on retrieval, some students display high accuracy but low reliance on retrieval; Siegler (1988a) dubbed these three types “good students,” “not-so-good students,” and “perfectionists.”…”

“…Children differ not only with respect to how quickly or accurately they perform mathematical tasks, but also with respect to the strategies they use. In arithmetic, individual differences in strategy use have been observed with whole numbers (Rhodes et al, 2019; Siegler, 1988a), fractions (Braithwaite et al, 2019), and decimals (Braithwaite et al, 2021). Such differences in strategy use often affect performance more than individual differences in fluency with particular strategies do.…”