We studied the acquisition of the ordinal meaning of number words and examined its development relative to the acquisition of the cardinal meaning. Three groups of 3-, 4-, and 5-year-old children were tested in two tasks requiring the use of number words in both cardinal and ordinal contexts. Understanding of the counting principles was also…

A 3-week problem-solving practice phase was used to investigate concept-procedure interactions in children's addition and subtraction. A total of 72 7- and 8-year-olds completed a pretest and posttest in which their accuracy and procedures on randomly ordered problems were recorded along with their reports of using concept-based relations in…

This study investigated whether instruction that involves comparing the equal sign with other relational symbols is more effective at imparting a relational interpretation of the equal sign than instruction about the equal sign alone. Third- and fourth-grade students in a comparing symbols group learned about the greater than, less than, and equal…

After the onset of formal schooling, little is known about the development of children's understanding of the arithmetic concepts of inversion and associativity. On problems of the form a+b-b (e.g., 3+26-26), if children understand the inversion concept (i.e., that addition and subtraction are inverse operations), then no calculations are needed…

Experiments were conducted to determine the influence upon task difficulty of these factors: age; percentage of redundancy between relevant and irrelevant cues; saliency of reinforcement, discriminability of relevant nonpreferred dimension, and learning set pretraining to reject preferred irrelevant dimensions. (Author/AJ)

Presented preschoolers and first graders with 3-term inversion problems such as 3 + 2 - 2 and similar standard problems to examine whether children used the inversion principle and if use was based on qualitative identity, length, or quantity. Found that both age groups showed evidence of using inversion in a fully quantitative manner, indicating…

Previous studies have shown that even preschoolers can solve inversion problems of the form a + b - b by using the knowledge that addition and subtraction are inverse operations. In this study, a new type of inversion problem of the form d x e [divided by] e was also examined. Grade 6 and 8 students solved inversion problems of both types as well…

Taken together, these five studies using structurally different kinds of conceptual problems provide evidence for qualitative developmental and cultural differences in classificatory behavior. (Authors/CB)

Evaluated the possibility that three-year-olds solve small-number conservation problems by an empirical procedure whereby the sets are quantified each time presented. Children chose the more numerous of two arrays, one containing two elements and the other three elements. Results disconfirmed claims that three-year-olds can conserve small numbers.…

In a reviewed series of spontaneous and learning-set studies of adults and children, adults solved problems even if they attended to four dimensions; young children failed when attending so broadly, but solved when attending to a single dimension. (Author/HS)