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)

Constant time delay procedures were used to teach 15 multiplication facts in 1 hour to a 10-year-old student with mild learning handicaps and behavioral disorders. Correct levels of responding were maintained and generalized across persons and settings up to 8 weeks after training. (DB)

Discusses the use and construction of "fact fans," fun and easy-to-make manipulatives that provide elementary school students with the opportunity to explore mathematics operations being studied in the classroom and to practice addition, subtraction, multiplication, and division facts. (BB)

This study evaluated the effectiveness of teaching multiplication facts and related word problems using the concrete-representational-abstract teaching sequence and strategy instruction to three middle school students with mental retardation. Evaluation of the 21 scripted lessons given each student found only four occurrences (out of 63 lessons)…

Describes a mathematics lesson using digital sums that allows teachers to assess third grade students' understanding of reasoning, arithmetic, and geometry. (ASK)

Third-graders showing negligible mastery of multiplication combinations were randomly assigned to two groups which practiced different subsets of combinations. Retest results were inconsistent with Siegler's (1988) proposal that item-specific computational practice is necessary to change error patterns and promote mastery. Results suggested that…

Basic fact acquisition is an important component for developing higher-order math skills. However, getting students with a history of academic noncompliance to engage in activities related to skills acquisition can be difficult. Prior research demonstrates that engagement increases when nonpreferred activities are preceded by a series of brief…