Introduces a toy, the Educated Monkey, developed to help students learn multiplication tables and associated division, factoring, and addition tables and associated subtraction. Explains why the monkey works and reviews geometric, algebraic, and arithmetic concepts. (KHR)

Analyzes discussions with teachers (n=26) of Key Stage 2 classes (ages 7-11) during interviews on mathematical tasks based on use of pattern. Finds that pattern was used frequently, but that some teachers had a wider and more sophisticated view of pattern than others. Includes references and an appendix. (CMK)

Reanalyzes data obtained in 1987 on mental calculation strategies used by 11-year-olds in England, Wales, and Northern Ireland. Classifies mental strategies developed in the past decade in international research. Compares frequency and effectiveness of the strategies used by pupils of different levels of attainment. Discusses basic arithmetic…

Investigates the development of understanding of multiplication from the early school years through to the top primary age group. Identifies the children's difficulties and analyzes their solution strategies. Reports that progressive abstraction is related to the children's developing understanding of number and to their procedures for addition.…

Classifies children's solution strategies by degree of abstraction and by use of physical objects. Children in grades one, two, and three were given two multiplication and four division word problems that differed in semantic structure. (Author/YP)

Gives a multi-lesson project exploring multiplication arrays. Students are given opportunities to model multiplication tables with rectangular arrays, develop and extend ideas about patterns, organize and present visual patterns symbolically in tables, and represent visual patterns graphically. (MKR)

Described are the strategies of 44 academic mathematicians on a set of computational estimation problems involving elementary multiplication and division. Discussion centers on the theoretical implications evident from pretest/posttest results in terms of the variety of strategies used and how the choice of strategy changed across the two tests.…

The purpose of this study was to compare the achievement for the operations of multiplication and division on whole numbers of elementary grade students who were taught functional diagnostic strategies with a randomly selected group who were not taught the informal diagnostic strategies. Included are the methodology, results, and discussion. (KR)

Number sequences are useful complements to traditional drill and practice. Described is an activity in which the basic rule, add the tens digit to five times the ones digit, is used to generate a sequence of numbers. The dialogue between teacher and student discussing characteristics of emerging patterns is given. (MDH)

Compared effects of peer-delivered (PDF) and self-delivered (SDF) immediate corrective feedback intervention on multiplication performance of six second grade students. SDF resulted in greater multiplication performance for four of six students, suggesting that SDF interventions may be more efficient and less obtrusive than PDF interventions and…

Design details, operation, and initial field test results are reported for DynaMath, a computer-based dynamic assessment system that provides individually tailored, instructionally useful assessment of students with disabilities. DynaMath organizes and outputs student performance data, graphically shows the "zone of proximal…

Describes the use of graphic area models of multiplication to provide visual, concrete representations for students learning two-digit multiplication. (MKR)

It is difficult for students to unlearn misconceptions that have been unknowingly reinforced by teachers. The examples "multiplication makes bigger,""pi equals 22/7," and the use of counter examples to demonstrate the numerical property of closure are discussed as potential areas where misconceptions are fostered. (MDH)

Structure of mathematical concept of multiplication and its integration into conceptual system, with respect to formal and informal aspects of understanding for 10 university students, are investigated through linear scale assessment of examples for prototypical effects and through follow-up interview which included direct explanations of…

Presented is the ancient Egyptian algorithm for the operations of multiplication and division of integers and fractions. Theorems involving unit fractions, proved by Fibonacci, justifying and extending the Egyptian or Ahmes' methods into the Hindu-Arabic numeric representational system are given. (MDH)