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…

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

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 article describes creative ways to interest children in mathematics. (CD)

This article traces changes in mathematics teaching, stresses the importance of mathematics in the lives of today's children, and gives some suggestions for new teaching methods. The applications and distortions of Piaget's learning theory as applied to mathematics instruction are also discussed. For journal availability, see SO 506 042. (JK)

This set of transparencies shows how the manipulation of combinatorial structures in the context of modern combinatorics can easily lead to interesting teaching and learning activities at every level of education from elementary school to university. The transparencies describe: (1) the importance and relations of combinatorics to science and…

Questionnaires administered to 3,500 math teachers explored professional background, learning objectives, classroom organization, teaching techniques, and textbook use. Apparently math teaching has changed little in 15 years; little impact of "new math" was seen. Moreover, teachers considered computational skills and algebraic manipulation as most…

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,…

Through a research grant funded by the Vocational Division of the Indiana State Department of Public Instruction, a developmental research project was undertaken to develop machine trades-related mathematics materials using the terminology, concepts, and methods of modern mathematics. The two volume set is designed to be utilized by first and…