Background: Recent research showed that cross-notation magnitude knowledge of fractions and decimals was related to better performance in fraction arithmetic, but it remains unclear whether it made an independent contribution to fraction arithmetic longitudinally when other cognitive variables are considered. Aims: To examine the extent to which…

The present study investigated the development of fraction comparison strategies through a longitudinal analysis of children's responses to a fraction comparison task in 4th through 6th grades (N = 394). Participants were asked to choose the larger value for 24 fraction pairs blocked by fraction type. Latent class analysis of performance over item…

Discusses research findings that relate to teaching fractions for conceptual understanding. Gives teacher/student dialogues that illustrate the thought processes of students as they form part-whole and improper fraction concepts. (MDH)

Discussed is why students have the tendency to apply an "add the numerators and add the denominators" approach to adding fractions. Suggested is providing examples exemplifying this intuitive approach from ratio, concentration, and distance problems to demonstrate under what conditions it is applicable in contrast to the addition algorithm. (MDH)

This guide contains a collection of alternative techniques for teaching arithmetic that have proved useful in teaching both children and adults with various learning problems. Discussed first are several underlying principles of instructing individuals with learning disabilities, problems, and differences and special accommodations for…

Uses work on children's counting schemes and a radical constructivist orientation to describe the development of computer microworlds for the teaching of rational numbers. Suggests that the design of complex software systems needs a strong theoretical background to provide direction for the design. Suggests that computer environments are the…

Uses the constructivist principle of active learning to explore the possibly essential elements in transforming a cognitive play activity into mathematical activity. Suggests that for such transformation to occur, cognitive play activity must involve operations of intelligence that, yield situations of mathematical schemes. Illustrates the…

Comments on the Fractions Project presented in this same issue. Discusses two major ideas: the construction of mathematics of children and its basis and playful actions as a basis for mathematical actions. Highlights the understanding of children's mathematical concepts and schemes as they grow and are organized in the context of computer…

Comments on the Fraction Project presented in this same issue. Examines the choice of appropriate perspectives on the phenomena induced and observed and the generalizability of the results. Investigates the phenomena as involving student attunement to constraints built into the computer-based learning environments and in terms of explicit…

Comments on the Fraction Project presented in this same issue. Suggests that it has uncovered many implications for instruction. However, there are limitations as the proposed setting is restricted by the present school circumstances. Concludes that better learning will not come from finding better ways for teachers to instruct but from giving the…

Interprets and contrasts children's mathematical interaction from the points of view of radical constructivism and of Soviet activity theory. Proposes a superseding model based on the interrelations between the basic sequence of actions and perturbation and the interaction of constructs. Supports the model by describing how children used…

Proposes a new model of children's mathematics by composing aspects of the Fraction Project and critiques presented in the same issue. Argues that computer microworlds provide children with dynamic learning environments in which they are the primary actors and teachers with a medium for interact with children's mathematics while trying to maintain…

This guide presents math-focused learning projects and accompanying inquiry activities to help students pass the math portion of the GED 2002. It is Volume 2 of a proposed four-volume series; Volume 1 describing the concept of the GED as project is also available. Section 1 relates GED as project to the math portion of the GED and explains how…