Children's failure to reason often leads to their mathematical performance being shaped by spurious associations from problem input and overgeneralization of inapplicable procedures rather than by whether answers and procedures make sense. In particular, imbalanced distributions of problems, particularly in textbooks, lead children to create…

The integrated theory of numerical development posits that a central theme of numerical development from infancy to adulthood is progressive broadening of the types and ranges of numbers whose magnitudes are accurately represented. The process includes four overlapping trends: (1) representing increasingly precisely the magnitudes of non-symbolic…

The integrated theory of numerical development posits that a central theme of numerical development from infancy to adulthood is progressive broadening of the types and ranges of numbers whose magnitudes are accurately represented. The process includes four overlapping trends: 1) representing increasingly precisely the magnitudes of non-symbolic…

Longitudinal associations of domain-general and numerical competencies with individual differences in children's understanding of fractions were investigated. Children (n = 163) were assessed at 6 years of age on domain-general (nonverbal reasoning, language, attentive behavior, executive control, visual-spatial memory) and numerical (number…

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…

We tested whether adults can use integrated, analog, magnitude representations to compare the values of fractions. The only previous study on this question concluded that even college students cannot form such representations and instead compare fraction magnitudes by representing numerators and denominators as separate whole numbers. However,…

Developmental predictors of children's fraction concepts and procedures at the end of fourth grade were investigated in a 2-year longitudinal study. Participants were 357 children who started the study in third grade. Attentive behavior, language, nonverbal reasoning, number line estimation, calculation fluency, and reading fluency each…

Learning of class inclusion by 5-year-olds in response to empirical and logical explanations of an adult's answers was examined. Contrary to the view that young children possess an empirical bias, 5-year-olds learned more, and continued learning for longer, when given logical explanations of correct answers than when given empirical explanations.…

Five experiments were performed in the area of children's causal reasoning to validate a previously reported developmental difference, to examine the role of a possible mediating mechanism, and to test a number of competing theoretical interpretations. (GO)

Data suggest that young children can rapidly learn to classify transformations correctly that do and do not affect liquid quantity. (Authors)

Many preschoolers know that plants and animals share basic biological properties, but this knowledge does not usually lead them to conclude that plants, like animals, are living things. To resolve this seeming paradox, we hypothesized that preschoolers largely base their judgments of life status on a biological property, capacity for teleological…

This paper questions evidence for the thesis that causal reasoning of older children is more logical than that of younger ones, and describes two experiments which attempted to determine (1) whether there are true developmental differences in causal reasoning, and (2) what explanations for developmental differences can be supported. In the first…

This paper argues in favor of using interactional strategies in the study of formal operations reasoning. Interactional designs allow a convergent approach to specifying processes underlying the interaction of variables. In contrast, current methodologies contain two inherent disadvantages: they have limited utility in specifying the processes…

This study examined 6- to 8-year-old Slovenian children's acquisition of matrix completion proficiency and compared microgenetic and age-related changes on the task. Microgenetic analyses indicated that: variability of children's errors increased before they discovered the correct strategy, the correct strategy became dominant shortly after…

Interest in U-shaped development has itself undergone a U-shaped progression. Twenty-five years ago, interest in U-shaped development was high. This interest was evident at a 1978 conference in Tel Aviv on "U-shaped Behavioral Growth" that resulted in the publication of a book of the same title 4 years later (Strauss, 1982). The breadth…