Three elementary-school students were exposed to Fractions 1, an instructional program for fraction problem-solving skills based on "direct instruction" principles. Fraction performance increases could reasonably be attributed to the instructional program. Improvements were durable across a short follow-up period and transfer occurred to similiar…

Three proofs for the problem show there exist irrational numbers a and b such that a to the b power is rational'' are presented and discussed. (DT)

This study was supported by a grant from the Carnegie Corporation to Educational Testing Service. (MH)

Procedures for using an abacus to teach addition to learning disabled children are described. Considerations in choosing, constructing, and doing basic problems with an abacus are discussed. (CL)

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…

Simplicity in number naming in a language (e.g. "ten-two" in Chinese is simpler than the irregular "twelve" in English) has been used to explain cross-cultural disparities in children's computational competence. In contrast to previous research focusing only on whether children can provide the correct answers, in this study (N =117 and 92) we…

This article, reprinted from "Arithmetic Teacher" in 1979, as part of the "MT" 100 celebration, discusses the importance of fractions.

Usiskin takes another look at fractions, years after writing the article "The Future of Fractions" for "Arithmetic Teacher."