Children display an early sensitivity to implicit proportions (e.g., 1 of 5 apples vs. 3 of 4 apples), but have considerable difficulty in learning the explicit, symbolic proportions denoted by fractions (e.g., "1/5" vs. "3/4"). Theoretically, reducing the gap between representations of implicit versus explicit proportions…

Children's ability to place fractions on a number line strongly correlates with math achievement. But does the number line play a causal role in fraction learning or does it simply index more advanced fraction knowledge? The number line may be a particularly effective representation for fraction learning because its properties align with the…

Children's understanding of numbers is often assessed using a number-line task, where the child is shown a line labeled with 0 at one end and a higher number (e.g., 100) at the other end. The child is then asked where on the line some intermediate number (e.g., 70) should go. Performance on this task changes predictably during childhood, and this…

Accurate monitoring and control are essential for effective self-regulated learning. These metacognitive abilities may be particularly important for developing math skills, such as when children are deciding whether a math task is difficult or whether they made a mistake on a particular item. The present experiments investigate children's ability…

Children's sense of numbers before formal education is thought to rely on an approximate number system based on logarithmically compressed analog magnitudes that increases in resolution throughout childhood. School-age children performing a numerical estimation task have been shown to increasingly rely on a formally appropriate, linear…

Compares the Genevan and Cattell-Horn theories of intelligence and describes both similarities and differences. Describes a study investigating the relation of the Piagetian operative level to the child's ability to use crystallized solution procedures (aids) in making elementary numerical comparisons. (HOD)

Compared children's cognitive abilities at four years and their prenatal amniotic fluid testosterone levels. For girls, prenatal testosterone levels were related in a curvilinear manner to language comprehension and classification abilities, and inversely related to counting and knowledge of number facts. For boys, no relationships were found. (BC)

Investigates preschoolers' knowledge of counting principles by examining their ability to discriminate between features essential for correct counting and features typically present but unessential. Skill in executing the standard counting procedure was found to precede knowledge of the underlying principle. (Author/AS)