This article reconsiders Case's theory of central conceptual structures (CCS), examining the relation between working memory and the acquisition of quantitative CCS. The lead hypothesis is that the development of working memory capacity shapes the development of quantitative concepts (whole and rational numbers). Study I, with 779 children from…

In a 1-hour teaching interview, 20 children (aged 7 to 11) discovered how to tell whether objects might be made of the same material by using ratios of measures of weight and size. We examine progress in the children's reasoning about measurement and proportional relations, as well as design features of instruments, materials, and tasks crafted to…

To conceive the infinity of integers, one has to realize: (a) the unending possibility of increasing/decreasing numbers (potential infinity), (b) that the cardinality of the set of numbers is greater than that of any finite set (actual infinity), and (c) that the leap from a finite to an infinite set is itself infinite (immeasurable gap). Three…

Learning science includes learning to argue with "inscriptions": images used to symbolize information persuasively. This study examined sixth-graders learning to invest inscriptions with representational status, in a geographic information system (GIS)-based science investigation. Learning to reason with inscriptions was studied in emergent…

This article describes a detailed analysis of knowledge building in a problem-based learning group. Knowledge building involves increasing the collective knowledge of a group through social discourse. For knowledge building to occur in the classroom, the teacher needs to create opportunities for constructive discourse in order to support student…

The nature and evolution of intertextuality was studied in 2 urban primary-grade classrooms, focusing on read-alouds of an integrated science-literacy unit. The study provides evidence that both debunks deficit theories for urban children by highlighting funds of knowledge that these children bring to the classroom and the sense they make of them…

A schema based view of addition development is compared with Siegler's latest strategy-choice model, which includes an addition goal sketch (a basic understanding of "the goals and causal relations" of addition; Siegler & Crowley, 1994, p. 196). This metacognitive component in the latter model is presumed to develop as a child practices a basic…

Based on close observations of two 4-year-old children responding to their parents' requests for quantitative comparisons, we offer a "participationist" account of the origins and development of numerical thinking, one that portrays numbers as a product rather than a pregiven object of human communication. In parallel, we propose a…

Investigated the development among fourth-graders of two-dimensional space concepts within a mathematics unit on grids, coordinates, and rectangles. Found that students' knowledge of grid and coordinate systems related to levels of competence in number sense, spatial-geometric relationships, and the ability to discriminate and integrate the two…

This interview study gathered information about the prior knowledge and thinking of kindergarten to third- graders regarding the supply of water, heat, and light to modern homes. Findings indicated that students possessed only limited and spotty knowledge about utilities in modern homes. Within general trends, there was evidence of growth in…

Investigated effects of two instructional interventions on 5- to 9-year-olds who could perform a balance beam task but either could not explain the principle or had naive theories. Found that more students who had observed the experimenter model and were then encouraged to explain what they saw improved performance over the pretest than students…

Compared the rational quality of fourth-graders' discussion of literary texts with an ideal model and over the course of the academic year. Analyzed the collaborative reasoning capabilities of 6 three-student groups using a graphical coding system with an analysis of the literary content of the students' argumentation. Identified important…

Examined how elementary school students remember what they learn and how they learn in science and social studies. Found that students used long-term working memory for sorting, interpreting, and integrating representations of classroom experiences as they acquired knowledge and skills. Recollection 12 months later replaced details with inferences…

Investigated the cognitive gains of interacting pairs of Grade 10 students who show low levels of competence and fail to solve a task individually but who improve when working in peer interaction. Found that this phenomenon may occur when the two students disagree, have different strategies, and active hypothesis testing is made possible. (JPB)

Investigated intervention effects on mental models of multivariable causality in middle school students involved in inquiry learning. Found that inquiry learning promoted a correct mental model based on additive effects of individual features and a meta-strategic understanding of the need to control influences of other features. Also found…