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,…

Why do schools teach mathematics, and why do they teach the mathematics that they do? In this three-part dissertation, I argue that the justifications offered by national education systems are not convincing, and that students are tested on content whose purpose neither they nor their teachers clearly understand. In the first part of the…

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 Montessori Observer" is mailed four times each year, in March, May, September and November, to Society members throughout the world. The purpose is to provide news and information about the Society's work in Montessori education, and to extend awareness of Montessori principles throughout the world. This issue contains a feature…

This article, by the author of "Why Johnny Can't Add," finds the New Math to be a failure as an instructional method since it is based on a reliance on artificial, complicated axioms that were invented to satisfy the needs of professional mathematicians, not students. (JA)

Prime numbers play an extremely important role in modern mathematics. Apart from still being the object of intense research activity, their applications in banking and security underline a key phenomenon: in the modern world, useful applications of mathematics often come from very "pure" abstract theories. Curiously, despite their…

Reviews some major tenets of the new math as it was originally intended and then examines what went wrong with the new math revolution. (MP)

We analyze probability content within middle grades (6, 7, and 8) mathematics textbooks from a historical perspective. Two series, one popular and the other alternative, from four recent eras of mathematics education (New Math, Back to Basics, Problem Solving, and Standards) were analyzed using the Mathematical Tasks Framework (Stein, Smith,…

Discusses the Entebbe Modern Mathematics Project and relates it to the change in curriculum in Lagos. It also discusses problems attendant on curriculum changes in a developing country like Nigeria. (Author)

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)