Students who can compute mathematical problems in their heads have learned a skill that is important for estimating and for understanding the number system. Practice activities that can help students master mental computation skills are described. (PP)

Analogies between topics in algebra and in arithmetic are noted. It is suggested that algebra teachers should consider how to take advantage of student backgrounds in arithmetic by exploiting these analogies. (MP)

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)

This article offers specific strategies to diagnose and remediate difficulties students may have in learning multiplication facts. Analyzes strategies students use to go from a known fact to an unknown fact. The point is made that, for many students, the order of interpretation of a number fact may affect accuracy. (DB)

Discussed are the background and implementation of a method of teaching fractions to primary children referred to as "The Visual Concept of Fractions." The advantages and criticisms of the use of this method are stressed. (CW)

Learning at a distance from the source of instruction through textbooks and other media is distance learning. Robert Record wrote mathematics textbooks for the home learner of the sixteenth century. He used dialogue between Master and Scholar to present concepts and correct possible mistakes and misconceptions. (DC)

A description of De Morgan's life and work is followed with quotations of his thoughts and insights on the teaching and learning of mathematics. The purpose is to illustrate the sharpness of his ideas, his creative insights, and his wit for the enjoyment of the reader. (DC)

Presented is an activity which examines an arithmetic concept from a geometric point of view. Objectives, prerequisite learning, and procedures are discussed. Four worksheets are provided with answers. (CW)

Activities that illustrate a problem-solving approach to teaching grouping symbols, such as parentheses and brackets, are described. Suggested exercises, answers to those exercises, and variations of this activity are included. (KR)

This article offers multiplication fact memorization training techniques that have been successfully used with students with learning disabilities in resource room and clinical settings. Techniques include organizing the facts, using finger multiplication, visual mnemonic flashcards, and musical reinforcement. (DB)

Six elementary-age children with learning disabilities were found to learn subtraction facts more rapidly when a rule teaching and correction strategy was employed, compared to learning facts by rote. A study of generalization of rule usage found that the two children studied did generalize the strategy to an additional problem. (Author/JDD)

An analysis of the 1990 National Assessment of Educational Progress (NAEP) found that only 46 percent of all high school seniors demonstrated success with a grasp of decimals, percentages, fractions and simple algebra. This article investigates error patterns that emerge as students attempt to answer questions involving the ability to apply…

Cross-cultural studies on mathematical cognition and education have suggested that curriculum and teaching have contributed to U.S. versus Asian differences in student performance; however, previous discussions of curriculum and teaching practices have been very general and have not focused on a detailed analysis of how mathematics concepts are…

In this article, the author describes a week of "timely" open-ended lessons with a high ability Y9 group of boys. He gives lessons that would give the students some sense of purpose, as they try to generate a mathematical entity to represent something they used regularly. He states that understanding metric time is something his students…