Children's Strategy Choices on Complex Subtraction Problems: Individual Differences and Developmental Changes

Abstract

We examined how children's strategy choices in solving complex subtraction problems are related to grade and to variations in problem complexity. In two studies, third- and fifth-grade children (N≈160 each study) solved multi-digit subtraction problems (e.g., 34–18) and described their solution strategies. In the first experiment, strategy selection was investigated by means of a free-choice paradigm, whereas in the second study a discrete-choice approach was implemented. In both experiments, analyses of strategy repertoire indicated that third-grade children were more likely to report less-efficient strategies (i.e., counting) and relied more on the right-to-left solution algorithm compared to fifth-grade children who more often used efficient memory-based retrieval and conceptually-based left-to-right (i.e., decomposition) strategies. Nevertheless, all strategies were reported or selected by both older and younger children and strategy use varied with problem complexity and presentation format for both age groups. These results supported the overlapping waves model of strategy development and provide detailed information about patterns of strategy choice on complex subtraction problems.

Working memory predictors of written mathematics in 7- to 8-year-old children

“…Consistently, evidence shows developmental differences indicating that different mathematical training is effective in different age groups (e.g., Caviola, Gerotto, & Mammarella, 2016). Finally, there is some evidence that younger children tend to use less reliable and less efficient strategies prior to a declarative shift in strategy use (see Schneider, 2008, for a review of this), which might have influenced the pattern of results we observed (e.g., Caviola, Mammarella, Pastore, & LeFevre, 2018). For all these reasons, the present findings should be replicated using a more diverse sample including children at different levels of the mathematical curriculum.…”

A distinction between working memory components as unique predictors of mathematical components in 7–8 year old children

“…Different predictors of mathematics performance have been identified butamong several othersworking memory, a system for the short-term storage and manipulation of information, has been repeatedly associated with several different mathematic skills. It has been shown that working memory predicts performance on tests of approximate mental addition (Caviola et al, 2012(Caviola et al, , 2016Kalaman & Le Fevre, 2007;, written subtractions (Caviola et al, 2016(Caviola et al, , 2018, number facts (Steel & Funnell, 2001), multi-digit operations (Heathcote, 1994), magnitude representation (Pelegrina et al, 2015), arithmetical problems (Passolunghi & Siegel, 2001;Passolunghi & Mammarella, 2010;Rasmussen & Bisanz, 2005), quantitative central conceptual structures (Morra et al, 2019), and geometrical achievement (Giofr e et al, 2013. Importantly, working memory is a generic term, for which we also see alternative models.…”

Early Engagement of Parietal Cortex for Subtraction Solving Predicts Longitudinal Gains in Behavioral Fluency in Children

“…Some behavioral studies interpret the response times patterns shown by children as young as 5 years old as evidence in favor of the retrieval strategy for solving the majority of subtraction problems (Siegler, 1987). Others, relying on self-report, found that 5th graders use more retrieval and less counting to solve subtraction problems as compared to 3rd graders, who reported using more procedures (Caviola et al, 2018). According to this hypothesis, educated adults have had enough experience with arithmetic to be able to retrieve single-digit subtractions directly from memory (Siegler, 1989;Geary et al, 1993).…”