When public schooling was first introduced in the United States, early proponents emphasized the need for mathematics as critical for an informed citizenry in a democracy. Half a century later, this purpose of mathematics has been almost entirely overshadowed by the push for mathematics to maintain technological and economic advantages. The belief…

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…

One of the most salient arguments in favor of a semiotic approach, put forward on various occasions among others by Luis Radford, claims that semiotics is most appropriate to treat the interaction between socio-cultural and objective aspects of knowledge problems. But if we want to take such claims seriously, we have to undertake revisions of our…

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 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…

A new algorithm for computing roots of any order is presented, along with the historical roots of its development.

This article describes Everyday Mathematics, a new math education curriculum targeted to kindergarten, first grade, and second grade students in Holland. It will be introduced to third and fourth grades in 2008. The curriculum helps prepare pupils for standardized tests; allows for students to work at their own rate; involves parents in helping…

This paper provides a general overview of the forces that contributed to the rise and fall of the "new math" movement. It is noted that the movement developed as a response to certain problems in mathematics education; these problems remain to be solved. Some small-scale successes were achieved, from which we can learn. The answer to…

Explores differences between mathematical definitions and non-mathematical definitions by contrasting three approaches to mathematical reasoning. Examines the consequences of the use of those approaches in a first course in real analysis. Analyzes students' reasoning behavior during analysis and suggests reasons for students' difficulties with the…

Compares the origins, curricular and pedagogical content, and impact of the new math and standards-based reform movements, describing: events leading up to this new math era and characteristics of representative curriculums; the demise of the movement; the National Council of Teachers of Mathematics' standards-based reform movement; and reactions…

This paper reports on the conclusions drawn from an investigation of the modern mathematics reform movement in Brazil. The main focus is the dissemination of reform ideology to the Brazilian mathematics education community and the outcomes resulting from misinterpretations of the intended curriculum during the implementation process. (Author/JJK)

This paper discusses some findings of research studies developed in Italy on the approach to theoretical knowledge. Two examples are discussed in detail: (1) a classroom discussion concerning the shift from an empirical to a theoretical compass in primary school (fifth grade); and (2) the scheme of a teaching experiment on overcoming conceptual…

The media has criticized the American education system for being slow to implement technology in schools. To remedy that perception, the federal government and private corporations have planned additional funding for technology. This paper reflects on previous attempts to change, such as "New Math" or the "Follow Through" post-Head Start program,…

In 1964 the island of St. Lucia began the St. Lucia Mathematics Program, a five-year program designed to develop materials and a primary level program of modern mathematics for use in the English-speaking Caribbean territories. Representatives from the ministry of education, the teachers' college, and the University of the West Indies Institute of…