Through the historical analysis of Dienes' works and through the suggestions of activities, the objective of this text is to understand the movement of systematization of knowledge for teaching and to teach classification, ranking, and ordination through the use of logical blocks during the Modern Mathematics Movement (1960-1980), a time of…

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,…

At grade 7, Common Core's content standards call for the use of long division to find the decimal representation of a rational number. With an eye to reconciling this requirement with Common Core's call for "a balanced combination of procedure and understanding," a more transparent form of long division is developed. This leads to the…

The first goal of this article to show the profound difference between how equality and similarity are understood in Greek geometry and how they are presented in modern mathematics classes. It highlights that the formula "equal-and-similar" reflects the distinct character of "equal" and "similar" as signs in Greek…

The purpose of this Executive Position Paper is to examine the ways in which teachers learn to implement a new mathematics curriculum. The four case study teachers described in this paper were in their first and second year of teaching the "Investigations" curriculum. In the course of learning to teach with "Investigations," the teachers were…

AN INTERIM UNIT HAS BEEN DEVELOPED TO ASSIST TEACHERS AND PUPILS IN MAKING THE TRANSITION TO A CONTEMPORARY MATHEMATICS PROGRAM. EXPERIENCE HAS SHOWN THAT ANY INTRODUCTORY WORK DURING THE YEAR PRECEDING THE INTRODUCTION OF A NEW PROGRAM HAS MADE THE FIRST YEAR CONSIDERABLY EASIER AND MORE PROFITABLE FOR BOTH TEACHERS AND PUPILS. EACH CONCEPT…

The current approach to mathematics instruction in the elementary schools combines elements of the new math with the traditional emphasis on computational skills. (IRT)

Demonstrated are binary operations on whole numbers which are commutative but not associative, or associative but not cummutative. Also presented are sets of numbers within which the Unique Factorization Theorem does not hold true. (JP)

An instructor taught one group of college freshmen using a modified form of traditional mathematics by including most of the concepts in modern texts, but also assigning a large number of problems for homework; the second group used a modern textbook with less problems for practice. The modified traditional group performed significantly better in…

The relationship between mathematics and chemistry has been changing rapidly in recent years. Some chemistry teachers have experienced difficulties in their teaching with the introduction of modern mathematics in the schools. Some suggestions for reinforcing the concepts and language of modern mathematics are put forth. (Author/MA)

Why calculus is taught in secondary schools is discussed, as well as how "modern mathematics" affected calculus, is calculus so difficult, and how calculus should be taught. (MNS)

The writer reminds readers that the polemics of reform frequently portray the realm of teaching and learning in more extreme terms than is really necessary. Likening calls for educational reform to scientific revolutions sparked by Kuhn, Darwin and Copernicus, that jettison completely the assumptions and premises of the theories they replace, Bond…

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