Discusses an attempt to promote the development of prospective elementary teachers' own subject-matter knowledge of the division of fractions as well as their awareness of nature and likely sources of related common misconceptions held by children. Indicates that before the described mathematics methods course, most participants knew how to divide…

This book is for boys and girls who know the numbers from one to thirty thoroughly, who can count to one thousand, who know something of the multiplication tables of two, three, four, five, six, ten, and twelve, and who understand the simplest facts about fractions. This book is both to be read and to be studied. It calls for oral recitation and…

This teacher guide is part of the materials prepared for an individualized program for ninth-grade algebra and basic mathematics students. Materials written for the program are to be used with audiovisual lessons recorded on tape cassettes. For an evaluation of the program, see ED 086 545. In this guide, the teacher is provided with objectives for…

Magic squares are used to generate number games similar to tic-tac-toe. Skills that are reinforced include addition of negative numbers and addition and multiplication of fractions. (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)

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)

This research focused on preservice elementary teachers' understanding and reconstruction of understanding about multiplication in the domain of fractions. At the start of the study, 44% of the 50 preservice teachers studied reported that they had a method for reasoning about multiplication with fractions, and 28% were able to describe a situation…

A case is given against teaching division of fractional numbers. Types of problems usually solved by division are solved by methods involving only multiplication. (JP)

Three different models with continuous materials, discontinuous materials, and number lines were used to study the operation concept in six investigations on multiplication with fractions with pupils aged 11-12 in a Penang International School. All approaches could be understood by pupils, but they preferred the area and fractional models. (MNS)

It is not complex to teach the algorithm for multiplying fractions so that children can multiply numerators and denominators to arrive at correct answers. However, it is a challenge to teach so that students build understanding of multiplication of fractions, extending what they have already learned about fractions and about multiplication of…

Examples of student-developed methods for dividing fractions and dividing and multiplying whole numbers are presented. Both are selected to show mathematical creativity in general mathematics students which would often be overlooked. (MP)

Discusses the generalization of the meaning of multiplication for whole numbers. Presents an example for multiplication of fractions. Provides several diagrams to help improve understanding. (YP)

Simple experiences with probability can extend third graders' understanding of the need for fractions. Three activities are given which build on language-arts experiences and incorporate concepts in multiplication, graphs, and fractions. (MNS)

The performance of 13 and 17-year-olds on National Assessment items involving computation with fractions is reviewed, together with findings from related research. Recommendations for improving instruction are offered. (SD) Aspect of National Assessment (NAEP) dealt with in this document: Results (Interpretation).