To explain children's difficulties learning fraction arithmetic, Braithwaite et al. (2017) proposed FARRA, a theory of fraction arithmetic implemented as a computational model. The present study tested predictions of the theory in a new domain, decimal arithmetic, and investigated children's use of conceptual knowledge in that domain. Sixth and…

Understanding fractions is critical to mathematical development, yet many children struggle with fractions even after years of instruction. Fraction arithmetic is particularly challenging. The present study employed a computational model of fraction arithmetic learning, FARRA (Fraction Arithmetic Reflects Rules and Associations; Braithwaite, Pyke,…

We examined, on a trial-by-trial basis, fraction magnitude comparison strategies of adults with more and less mathematical knowledge. College students with high mathematical proficiency used a large variety of strategies that were well tailored to the characteristics of the problems and that were guaranteed to yield correct performance if executed…

This study examined how toddlers gain insights from source video displays and use the insights to solve analogous problems. Two- to 2.5-year-olds viewed a source video illustrating a problem-solving strategy and then attempted to solve analogous problems. Older but not younger toddlers extracted the problem-solving strategy depicted in the video…

An eight-session microgenetic study of acquisition of an insightful problem-solving strategy was conducted. A total of 35 second graders who did not use this insightful strategy initially were assigned to two groups that differed in the frequency of problems likely to facilitate discovery and generalization of the strategy. Children in the…

The present study focused on two main goals. One was to test the "representational mapping hypothesis": The greater the transparency of the mapping between physical materials and desired internal representations, the greater the learning of the desired internal representation. The implication of the representational mapping hypothesis in the…

Considers how preceding articles by Jansen and van der Maas, and Halford et al., contribute to understanding of how rule use can be best assessed, how systematic rule use can be reconciled with variable rule use, when children begin to use rules, and how children generate new rules. Summarizes current understanding of development of knowledge…

The field of children's learning was thriving when the Merrill-Palmer Quarterly was launched; the field later went into eclipse and now is in the midst of a resurgence. This commentary examines reasons for these trends, and describes the emerging field of children's learning. In particular, the new field is seen as differing from the old in its…

Discusses metacognitive and associative models of children's strategy discovery and use. Contends that models based on only one type of mechanism cannot entirely account for observed variability and constraint revealed by microgenetic studies of children's strategy change. Proposes a new model of children's strategy development in which…

Employed a trial-by-trial analysis of spelling-strategy use to examine whether the overlapping-waves model could account for strategy choices in spelling for children tested in first and second grade. Found that the model was useful for understanding the development of spelling, despite the fact that explicit use of backup strategies had a minimal…

A new field of children's learning is emerging. This new field differs from the old in recognizing that children's learning includes active as well as passive mechanisms and qualitative as well as quantitative changes. Children's learning involves substantial variability of representations and strategies within individual children as well as…

Experiments with 23 kindergarten and 24 third-grade students show that children can use conceptual understanding to accurately evaluate strategies that they not only do not yet use but that are more conceptually advanced than strategies they use. Results demonstrate commonalities in functioning of constraints in privileged and nonprivileged…

This study tested three hypothesized mechanisms through which explanations might facilitate problem-solving strategy generalization in kindergarteners through second graders. Results suggested that explanations facilitated generalization through the creation of novel goal structures that enabled children to persist in use of the new strategy…

Maintains that recent theoretical and methodological advances have sparked renewed interest in studying children's learning. Describes consistent and interesting findings regarding how children learn and intriguing proposals regarding mechanisms underlying learning. Argues that increasing the focus on children's learning promises practical…

Investigated the serial recall strategies of 96 children aged 5-8 years by applying a theoretical and methodological approach originally developed to investigate preschoolers' arithmetic strategies. Results indicated the use of multiple approaches for serial recall and adaptive strategy choices. (RJC)