In three experiments, children aged between 3 and 5 years (N = 38, 52, 94; mean ages 3-7 to 5-2) indicated their confidence in their knowledge of the identity of a hidden toy. With the exception of some 3-year-olds, children revealed working understanding of their knowledge source by showing high confidence when they had seen or felt the toy, and…

Children's understanding of the inversion concept in multiplication and division problems (i.e., that on problems of the form "d multiplied by e/e" no calculations are required) was investigated. Children in Grades 6, 7, and 8 completed an inversion problem-solving task, an assessment of procedures task, and a factual knowledge task of simple…

339 children aged 6 and 7 at Oxford primary schools took part in a study of arithmetic. 204 of the children had been selected by their teachers as having mathematical difficulties and the other 135 children were unselected. They were assigned to an Addition Performance Level on the basis of a calculation pretest, and then given Dowker's (1998)…

Children sometimes solve problems incorrectly because they fail to represent key features of the problems. One potential source of improvements in children's problem representations is learning new problem-solving strategies. Ninety-one 3rd- and 4th-grade students solved mathematical equivalence problems (e.g., 3+4+6=3+__) and completed a…

Investigated strategies used by preschoolers to accomplish a repeatedly requested practical task. Participants satisfied customer requests for vegetables in a play store, with the number of moves and strategy type recorded and coded. Arithmetic pre- and posttests were also administered. Found that with repeated exposure, the children became…

Distinguishes the values of quantitative increments and qualitative shifts with regard to problem solving. Subjects were 136 children ranging from 6 through 8 years and were presented with the standard 3-disc problem to resolve in 3 minutes. Results indicated that qualitative shifts in children's representation of problem space are a crucial…

Examined precursors of knowledge change in college students' developing understanding of gear movement. Found that only some participants changed their problem-solving approach after instruction. Results suggest that having multiple approaches available and using instructional information to build on not-well-developed conceptions may contribute…

Studied development of procedural knowledge in 14 adults, aged 18 to 35 years, engaged in a novel task using a toy tractor-trailer rig. Results revealed three phases of development in subjects' knowledge of steering procedures and the rig's movement patterns, and their use of feedback information. Subjects also manifested different levels of…

Kindergartners and second graders listened to stories about problem solving that had similar or dissimilar protagonists, themes, and goal objects to those in target problems they were asked to solve. Kindergartners, but not second graders, were likely to transfer a solution associated with the same goal object from the story problem to the target…

Thirty-two middle class and 32 lower class southern Brazilian pre-adolescent (M=12.8 years) and adolescent (M=15.7 years) participants were individually interviewed regarding their perceptions of who (adolescent or parent) should determine the adolescent's actions in cases where the parents and adolescent disagree over the action choice.…

Relations among patterns of conceptual and procedural knowledge and grade were examined in 90 six- to eight-year-olds in order to explore addition and subtraction development. Conceptual knowledge was assessed by examining children's responses to pairs of problems reflecting various part-whole relations. Children solved related problems as part of…

Studied semantic and cognitive development of Korean-speaking and English-speaking children. Found that categorization and a naming spurt emerged later in Korean speakers than in English speakers, while means-ends abilities and success/failure words emerged earlier in Korean speakers than in English speakers. Also, Korean-speaking mothers…