This article is concerned with cognitive aspects of students' struggles in situations in which familiar concepts are reconsidered in a new mathematical domain. Examples of such cross-curricular concepts are divisibility in the domain of integers and in the domain of polynomials, multiplication in the domain of numbers and in the domain of vectors,…

Concern about students' math achievement is nothing new, and debates about the mathematical training of the nation's youth date back a century or more. In the early 20th century, American high-school students were starkly divided, with rigorous math courses restricted to a college-bound elite. At midcentury, the "new math" movement sought,…

It was hypothesized that a supplemental unit in mathematical proof would increase students' chances of success in linear algebra. (Authors/JA)

Reported are three studies which have been completed since the inception of a collaboration between the Inglewood Schools and UICSM. These include a comparison by a matched-pairs design, a total group comparison in which covariance analysis provided statistical control, and an item analysis of the tests which obtained difficulty indices for the…

This is the first of a two-part paper; the conclusion appears in volume 27, number 3 (SE 506 350). (JM)

The author shows that the set of all sequences in which each term is the sum of the two previous terms forms a vector space of dimension two. He uses this result to obtain the formula for the Fibonacci sequence and applies the same technique to other linear recursive relations. (MM)

Ten recent results in pure mathematics are described, covering the continuum hypothesis, Diophantine equations, simple groups, resolution of singularities, Weil conjectures, Lie groups, Poincare conjecture, exotic spheres, differential equations, and the index theorem. Proofs are omitted, but references are provided. (DT)

Four periods of history are reviewed in an effort to build an informative background on the evolution of mathematics as a serious study in the schools. These four periods are (1) 300 B.C., (2) the second quarter of the 17th century, (3) the second quarter of the 19th century, and (4) the four decades of the 20th century from 1925 to 1965. (RP)