To build cognitive foundation for number, twenty-six low-performing, low-SES first graders did mathematical physical-knowledge activities, such as "bowling," during the first half of the year. As their arithmetic readiness developed, they tried more word problems and games. At the end of the year, these children did better in mental arithmetic and…

The influence of cognitive growth in working memory (WM) on mathematical problem solution accuracy was examined in elementary school children (N = 353) at risk and not at risk for serious math problem solving difficulties. A battery of tests was administered that assessed problem solving, achievement, and cognitive processing (WM, inhibition,…

This study investigated children's ability to interpret a natural social situation, depicted in a narrative story, and to use their understanding of that situation to generate and apply a mental model of debts and assets in solving problems including negative quantities. Fifty-one American students from a parochial school in a predominantly middle…

Learning activities and questioning skills that teachers in Tasmania can use to determine a child's mathematics understanding are presented. Covered topics include division, multiplication, subtraction, addition, sorting and classification, one-to-one correspondence, patterns, ordering, and counting. Included for each topic are the aim, needed…

Deciding how to approach a word problem for solution is a critical stage of problem solving, and is the stage which frequently presents considerable difficulty for novices. Do novices use the same information that experts do in deciding that two problems would be solved similarly? This set of four studies indicates that novices rely more on…

The focus of this report is children's construction and analogical transfer of mathematical knowledge during novel problem solving, as reflected in their strategies for dealing with isomorphic combinatorial problems presented in "hands-on" and written form. Case studies of 9-year-olds, one low and one high achieving in school…

Does conceptually oriented instruction jeopardize students' computational competence? If it does, then why are so many reform efforts continuing to emphasize the importance of teaching for conceptual understanding? If it does not, then why are the majority of teachers at all grade levels continuing to teach for computational competence without…

The first volume of the 29th annual conference of the International Group for the Psychology of Mathematics Education contains plenary lecture and research forum papers as listed below. Short oral communications papers, poster presentations, brief summaries of discussion groups, and working sessions are also included in the volume. The plenary…