The article reviews the development of mathematics error analysis as a means of diagnosing students' cognitive reasoning. Errors specific to addition, subtraction, multiplication, and division are described, and suggestions for remediation are provided. (CL)

It is seen as important that mathematics teachers encourage open, imaginative investigations that give students an opportunity to probe, find patterns and relations, and derive new patterns and relations. The article focuses on multiplication tables and classes, including questions for further exploration. (MP)

Three experiments were conducted to examine children's use of multiplying and proportionality rules in judgments of area. In the first two experiments, 7- through 8-year-olds were asked to judge the area of rectangles. In the third, 8- through 11-year-olds were tested on ratio of a rectangle compared to a horizontal line. Results indicated…

Drill activities for addition, subtraction, multiplication, and division that are derived from the history of mathematics are suggested. (MK)

Activities that can be used for maintenance of computational skills and can lead to the discovery of a pattern verifiable by an algebraic procedure are noted. The language of algebra is used in nonroutine settings, with several challenges for further exploration. (MP)

Five approaches for teaching multiplication of negative numbers are reviewed. A study comparing the effectiveness of rote, induction, deduction, and modeling approaches found no significant differences. (MP)

A new approach to teaching the division of common fractions is described. The approach is related to the multiplication operation and involves children working with concrete materials. (MK)

Reviews the author's research on students' conceptions of mathematics and suggests ways to overcome or prevent misconceptions. (MP)

Presents a study exploring the effectiveness and efficiency of constant Time Delay and Sequenced Count-By procedures in the teaching of multiplication facts using children (N=43) from grades 3-6 having parents as tutors. Concludes that both procedures were effective. Appendix includes the questionnaire administered to parents and students.…

Discusses examples of children's invented equal-sharing strategies that lay a foundation for reasoning about equivalence by connecting ideas from multiplication, division, and fractions. (KHR)

Identifies factors affecting problem solving strategies in the case of a multiplicative comparative situation involving three unknown quantities whose sum is known, and in which comparison relations between two pairs of the quantities are given. Proposes a model of the complexity of a word problem about such situation to analyze solution…

Explores the five multiplication techniques found in the 12th century Lilavati by Bhaskara, which appear again in the 1494 Summa by Pacioli. Includes a student worksheet. (KHR)

Discusses arithmetic during long-multiplications and long-division. Provides examples in decimal reciprocals for the numbers 1 through 20; connection with divisibility tests; repeating patterns; and a common fallacy on repeating decimals. (YP)

Describes how five-year-old children responded to the investigation of looking for patterns in a multiplication square. Provides a 10 x 10 multiplication square for the investigation. (YP)

Three experiments examined whether children, like adults, can surpress interference effects when retrieving from long-term memory to solve arithmetic problems. Found that the associations between a number pair and its sum or product are of sufficient strength during the elementary school years to produce interference effects, depending on the age…