Even though there is a great temptation as teachers to share what is known, many are aware of an idea called "rules that expire" (RTE) and have realized the importance of avoiding them. There is evidence that students need to understand mathematical concepts and that merely presenting rules to carry out in a procedural and disconnected…

Arithmetic was the first mathematical subject to enter the school curriculum in the United States in a formalized manner. Until the first quarter of the nineteenth century, the prevailing pedagogy of this subject revolved around the tenets of mental discipline theory and the rules method of teaching, which valued memorization and repetitive drill…

This article explores the educational and philosophical contributions of Nikolai V. Bugaev, a prominent 19th-century Russian mathematician and founder of the Moscow philosophical-mathematical school. The study specifically focuses on Bugaev's textbook, "Arithmetic of Whole Numbers," analyzing Bugaev's pedagogical approaches within the…

The aim of the study reported in this paper was to explore and enhance experienced school mathematics teachers' knowledge of students'thinking, as it is manifested in practice. Data were collected from records of classroom observations, interviews with participating teachers, and weekly teacher-researcher meetings organized in the school. In this…

This chapter describes a promising new approach to teaching developmental arithmetic and prealgebra, and presents research findings that demonstrate how a faculty support network helped instructors adopt new teaching strategies and gain confidence in teaching the reformed course.

Pratham's "Read India" initiative is a large-scale intervention to improve basic learning and arithmetic among children in primary school. It was started almost 10 years ago and has evolved considerably over time. Currently, this initiative uses two strategies. The first strategy is to work directly with village communities and local…

This guidance report focuses on the teaching of mathematics to pupils in Key Stages 2 and 3. It is not intended to provide a comprehensive guide to mathematics teaching. We have made recommendations where there are research findings that schools can use to make a significant difference to pupils' learning, and have focused on the questions that…

With the introduction of arithmetic as a compulsory part of the elementary school curriculum in late eighteenth- and early nineteenth-century Germany, textbooks and pedagogical methods were wanted. Relying on the traditions of the Rechenbucher and informed by the demand for method found in Wolffian style advanced textbooks, the first generation of…

During the twentieth century, major changes occurred in conception of arithmetic as a school subject. These changes resulted from both the study of arithmetic itself and from influences from movements and developments outside the subject matter; and they have affected both the content of arithmetic and the methodology of presenting that content to…

Describes why a traditional arithmetic curriculum is no longer appropriate. Also presents the rationale behind some of the newer methods of mathematics instruction in the elementary schools. (BD)

Many people believe that the 1989 National Council for Teachers of Mathematics (NCTM) standards heralded the biggest mathematics reform of the 20th century. Despite all reform efforts, recent studies indicate that mathematics taught in primary and middle school mainly consists of basic arithmetic tasks that use memorization and repetition. Today…

This book sets out a constructivist, inquiry-based approach to instruction. The approach builds on clear understandings of children's current levels of knowledge, where their learning should progress to, and the means by which children learn early numeracy topics. The methods presented in this book have been used extensively by practitioners in…

This article is reprinted from the February 1954 issue of the "Arithmetic Teacher." It is a succinct and perceptive analysis of mathematics education for children during the first half of this century. (MNS)

"In Brief" focuses on K-12 mathematics and science research and implications for policymakers, educators, and researchers seeking to improve student learning and achievement This brief highlights the learning gains of 240 elementary students involved in a long-term study in Madison, Wisconsin and their remarkable ability to reason with arithmetic…

A range of estimation techniques are described, and a series of mental computation procedures based on concepts of measurement and real numbers are presented in detail. (MP)