The 5-stage model of Ross was used to examine the role of instruction in facilitating children's acquisition of place value knowledge. Compares children from 2 samples on 10 tasks designed to reveal their thinking about place value. Discusses implications for theory and classroom. (YP)

This study illustrates the types of information microgenetic methods can yield. Ninety-seven 5-year olds who had not mastered number conservation were given training in conservation or in reasoning about conservation. Results elucidate how changes in thinking occur and demonstrate children's efforts to understand other people's reasoning. (SLD)

The teaching of negative numbers poses problems at the school level. A historical account of the intellectual difficulties in the evolution of negative numbers and a method of viewing negative numbers as an extension of the number system to help overcome these difficulties are presented. (MDH)

Explores relative developmental influences of age, number-sense, and context on primary school children's ability to estimate measures. Finds that, although number-sense improved with age, estimation did not; ability to perceive number relations influenced ability to estimate area; and estimation was more accurate in textbook exercises than in a…

Devises a new curriculum to introduce rational numbers by using developmental theory as a guide. Experiment concluded that students in the treatment group showed a deeper understanding of rational numbers than those in the control group, showed less reliance on whole-number strategies when solving novel problems, and made more frequent references…

As students translate number words into the language of mathematics they explore number composition, equivalent expressions, and patterns in numbers and words. (MKR)

In the present article, we argue that the conceptual change approach to learning can apply in the case of mathematics, taking into consideration the particular nature of mathematical knowledge and the neurobiological bases of mathematical cognition. In the empirical study that is reported in this article, we investigated ninth graders'…

The study examined the ability of preschool-age children to solve five format exemplars of number-numeral correspondence. Results indicated that some children were able to solve number-numeral correspondence problems in some formats and not in others. This deficiency was remediated by training in one, two, or (at most) three format exemplars.…

This article discusses the summability of some divergent series by Cesaro's method of successive arithmetic means. (MM)

Explores whether 5-month-old infants (N=56) develop numerical- or location-based expectations by using a violation of expectation paradigm with possible and impossible events. Reports that infants use a more abstract representation than object location, the numerical nature of which is discussed. Contains 25 references. (Author/ASK)