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…

The premise of this article is that the study of representation is valuable and important for mathematics and science students. Learning about representation should go beyond learning specific, sanctioned representations emphasized in standard curricula (graphs, tables, etc.) to include principles and design strategies that apply to any scientific…

This article describes how children build increasingly abstract knowledge of linear measurement, emphasizing ways they relate space and number. Assessments indicate children struggle to understand measurement, especially concepts related to complex paths as in perimeter tasks. This article draws on developmental accounts of children's knowledge of…

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 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…

Examined a conversation among high school physics teachers concerning a classroom discussion and teacher-written essays about their first- and second-graders' early reasoning about triangles. The examination sought to: (1) gain insight into the inquiry of teaching; (2) explore similarities and differences between inquiry in teaching and in…

Analyzed a corpus of videotapes in which university students solved physics problems to determine how students learn to understand a physics equation. Found that students learn to understand physics equations in terms of a vocabulary of elements called symbolic forms, each associating a simple conceptual schema with a pattern of symbols. Findings…

Evaluated the PREG conceptual model of human question asking. Found the model was sufficient as it accounted for nearly all of the questions produced by students, and was discriminating in that it could identify the conditions in which particular classes of questions are or are not generated. (Author/SD)

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…