The purpose of this study was to compare instruction in multiplication and division by means of manipulative materials and pupil discovery to instruction using abstract and semi-concrete materials combined with teacher explanation and exposition. The effect of the two methods on pupils' attitude and achievement also was compared. Ten classrooms…

How children perceive doubling and halving numbers is discussed, with many examples. The use of calculators is integrated. The tendency to avoid division if other ways of solving a problem can be found was noted. (MNS)

Directions are given for a game providing practice with multiplication combinations and for a game involving counting and number combinations. (DT)

The Cockcroft Report on English Schools recommends that all schools design their syllabuses and examinations on the assumption that all students will have access to calculators. How to use calculators sensibly to improve what is taught and how curriculum content may change are discussed. (MNS)

Key factors in mathematics remediation for high school students are examined. Levels of learning are discussed, and suggestions are given for working at different learning levels. Examples are given for remedial activities with area, multiplicain, and decimals and percent, and additional references are included. (MNS)

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)

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)

A parent intervention using the "Copy, Cover, and Compare" method of teaching multiplication facts to an 8-year-old with learning disabilities was examined. Results indicated that repeated use of the 16-minute procedure was successful in increasing percent correct for the targeted multiplication facts. (Author/DB)

This article explains how to use constant time delay to teach multiplication facts to students who have learning disabilities. Specific techniques for using time delay on an individual or small group basis are outlined, a sample student data sheet is presented, and the role of reinforcement is addressed. (Author/JDD)

This study compared the effects of two cover, copy, and compare interventions on the written multiplication performance of two elementary school students with behavioral disorders. The verbal response condition resulted in greater increases in written multiplication performance and occasioned more than twice the number of opportunities to respond…

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)

College students were exposed to two pairs of mathematics assignments. Assignment Pair A included a high-effort assignment containing 18 long three-digit ? two-digit (3?2) multiplication problems with all numerals in each problem being equal to or greater than four and a moderate-effort assignment that contained nine long problems and nine…

This article explores the mathematics involved in the NCAA basketball tournament including data analysis, basic probability, expected value, and the multiplication principle. A fun activity is presented that applies these concepts and involves students shooting Ping-Pong balls to discover a best strategy. (Contains 3 tables and 3 figures.)

Mathematics games are often used in the classroom as a reward or warm-up activity before the "real" learning takes place. Many teachers have witnessed how useful games are for tuning-in students to the impending mathematics lesson. However, have teachers considered playing games as the central part of the lesson? This article explores…

Chapters 5 through 10 of a 14-chapter, three-volume work on arithmetical applications are contained in this document. Each chapter details the "use classes" of one broad arithmetical concept. (A "use class" of a concept is a set of examples of real world uses of the concept which share a common structure). Each chapter…