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,…

Discussed are possible lessons for teaching the algebraic concepts of variables, rational expressions, and functions. (CT)

This paper asserts that the key to algebra reform is to integrate algebraic reasoning across all grades and all topics, to "algebrafy" school mathematics. The distinction is made between algebra "the institution" and algebra "the web of knowledge and skill," which is also clarified. Finally, suggestions are made as to how the educational community…

This report examines and summarizes the needs in mathematics of the Fresno City school system. The study is one in a series of needs assessment reports for PROJECT DESIGN, an ESEA Title III project administered by the Fresno City Unified School District. Theoretical concepts, rather than computational drill, would be emphasized in the proposed…

REPORTED ARE THE TENTATIVE VIEWS OF A GROUP OF MATHEMATICIANS ON THE CONTENT OF A PRE-COLLEGE MATHEMATICS CURRICULUM THAT MIGHT CONCEIVABLY REPRESENT THE TYPE OF PROGRAM WHICH WILL BE OPERATING IN A FEW DECADES. THE COMMITTEE PRESENTS ITS VIEWS, NOT AS A CURRICULUM GUIDE FOR ADMINISTRATORS AND MATHEMATICS EDUCATORS, BUT AS A BASIS FOR DISCUSSION,…

Based on the assumption that each student learns in a unique way, this paper outlines the factors to be considered before selecting the methods of instruction for particular mathematics courses and their students. The advantages and disadvantages of the lecture/textbook and question/answer method, individualized instruction, self-pacing,…