This paper focuses on elementary school students' use of mathematically-based (MB) and practically-based (PB) explanations. The mathematical context used in this study is multiplication. Two issues are discussed. The first issue is a comparison between MB and PB explanations used by students before they are formally introduced to multiplication in…

Presents and criticizes current theories of multiplication in order to pave the way for an alternative foundation for the concept of multiplication. Formulates a uniform concept of multiplication that recognizes anew the importance of the roles of multiplier and multiplicand. (Contains 22 references.) (ASK)

This article presents an alternative to the traditional method of multiplying polynomials, FOIL. The method can be used with any size of polynomial.

The purpose of the present research is to compare the effects of a Direct Instruction flashcard procedure on the mastery of multiplication facts by two high school students with attention deficit hyper-activity disorder (ADHD) and oppositional defiant disorder (ODD). Both students were enrolled in a separate high school for students with behavior…

This programed mathematics textbook is for student use in vocational education courses. It was developed as part of a programed series covering 21 mathematical competencies which were identified by university researchers through task analysis of several occupational clusters. The development of a sequential content structure was also based on…

The purpose was to ascertain whether there existed differential achievement effects associated with the factors and levels of context, form, item-stem and item-response format, size of common number, and school grade, as they relate to two variations of distributivity. Twelve 9-item tests were constructed and given to intact 4th-, 5th-, 6th-, and…

The ARROW (Aural, Read, Respond, Oral, Written) Technique using students' self-voice echoing was the most effective method in helping 25 dyslexic adolescents learn their multiplication tables compared to tutor voice, read and say, and write and say methods. (CL)

The author discusses some unique and non-routine ways of developing the multiplication facts. (CT)

Outlines a pattern for multiplication of fractions which facilitates the solution of a large class of problems. Beginning with the rate pair motion, a sequence of interrelated ideas are suggested that should help develop ability in problem solving in both relatively common and in more technical situations. (BR)

Children (n=336) in grades 1-5 were interviewed individually using a Piagetian task to study development from additive to multiplicative thinking. Multiplicative thinking was found to appear early (in 45% of second graders) but to develop slowly (only 48% of fifth graders used consistently solid multiplicative thinking). (Author/MKR)

The present study contrasts mathematical knowledge that two sixth-grade teachers apparently used when teaching fraction multiplication with the Connected Mathematics Project materials. The analysis concentrated on those tasks from the materials that use drawings to represent fractions as length or area quantities. Examining the two teachers'…

Dividing by zero can be confusing for students at all levels. If teachers are to provide clear and understandable explanations of this topic, they must possess a strong conceptual understanding of it themselves. In this article, the authors present qualitative data on fourth- through eighth-grade teachers' perceptions of division by zero. They…