Two difficulties that students have in computing with fractions are idenfitied. Then a procedure is described, stressing the identity element, that resolves these difficulties and increases students' understanding and retention. (MNS)

Illustrates how upper elementary grade students can develop an understanding of the invert-and-multiply algorithm. (CCM)

A procedure is described that enables students to perform operations on fractions with a calculator, expressing the answer as a fraction. Patterns using paper-and-pencil procedures for each operation with fractions are presented. A microcomputer software program illustrates how the answer can be found using integer values of the numerators and…

The author feels teaching division of fractions is worthwhile because it will help students understand other algorithms. (MK)

The early use of the distributive law can aid students in learning addition of fractions and provide rapid approaches to computation involving other operations. (SD)

An algorithm and sequence which utilizes arrays of entities is proposed for explaining the division of two fractions. (MN)

A process of teaching fractions is detailed that respects pupil ideas and concept images and builds on these in a way that helps children to develop personal algorithms. This approach is an attempt to get away from perceived one-sided views found in most textbooks. (MP)

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)

A teaching sequence provides a guide to instruction on initial concepts of fractions, equivalent fractions, and addition with fractions. (MN)

Use of low-stress algorithms to reduce the cognitive load on students is advocated. The low-stress algorithm for addition developed by Hutchings is detailed first. Then a variation on the usual algorithm is proposed: adding from left to right, writing the partial sum for each stage. Next, a "quick addition" method for adding fractions proposed by…

Children's difficulties remembering correct algorithms for operations with fractions are traced to difficulties in the instructional sequence. Many teachers "teach mistakes" by failing to provide sufficient referents for their pupils. (MP)

Describes an attempt to encourage fifth- and sixth-graders to invent their own ways of solving problems involving division with fractions. Emphasizes the importance of social interaction in Piaget's constructivism and explains why debate and verification are important for children's construction of logico-mathematical knowledge. (22 references)…

This manual is a dictionary of some 150 errors made by students in their work in mathematics. A precise definition and examples are given for each of these errors and these, combined with a description of common causes of the error, form a background for diagnosis of student problems with arithmetic. Teaching strategies and ideas, each linked to a…

This book provides a comprehensive collection of 66 teaching strategies and ideas to help overcome problems with number, each linked to a specific kind of error described in the related manual. Most of these strategies are classroom-ready and easily implemented. Some are notes for the teacher to read and then plan activities accordingly, and many…

These are some of the individual materials needed by students using the Comprehensive School Mathematics Program for the Intermediate Grades, Part VI. The book of "Worksheets" contains materials that are labeled with the same letter and number as the lessons with which they are to be used. The six "Collage of Problems" booklets…