The Evolution of Finger Counting Strategies in Addition: A Three-Year Longitudinal Study in Young Children.

In this study, the developmental trajectory of children's finger-based strategies for addition is described for the first time using a longitudinal design involving 207 children aged 4 ½ at the first testing point. Children were observed individually twice a year over a three-year period. The trajectory typically followed by children corresponds to the one theoretically described in the literature as supporting the gradual internalization of finger strategies and leading to the complete mentalization of the solving process. More precisely, children progressed from a modeling strategy in which each operand of an addition is represented on the fingers of each hand, through a concrete counting-on strategy, in which both operands are still represented but enumerated in a single continuous process, to a counting-on strategy, in which only one operand is kept in mind while the other is tracked on fingers. The frequent use of the concrete counting-on strategy between modeling and counting-on strategies supports Baroody's proposition that it serves as a transitional step between concrete and more abstract forms of numerical representation. However, the concrete counting-on strategy was associated with poor addition performance, suggesting that it corresponds to a reconstructive stage in which children gain new insights about numbers but lack the cognitive resources to fully capitalize on them. Overall, this study provides the first detailed description of the evolution of finger-based strategies toward the internalization of the addition solving process.