This guide continues instruction of the three guides in SE 012 723 and of the two guides included in SE 012 724. Counting skills, appreciation of pattern and order, and understanding of place value are extended to numbers up to one million, and the associative, commutative and distributive laws are made explicit. Manipulation of equations is…

Grid paper activities are discussed as a way to help students conceptualize fractions. (MP)

This article shows how an inexpensive calculator can be used advantageously to determine repeating decimals. Even the decimal representations of numbers, such as one-seventeenth and one-nineteenth, can be easily computed. Many examples are given, and some theoretical discussion is included. (Author/MP)

Nine children were tested to determine the appropriateness of Piaget's part-whole fraction concept interpretation for both the discrete case and the continuous cases of length and area. (MP)

The author urges that subtraction be introduced by "taking away" rather than by equal addition; multiplication be first demonstrated in sets; division be understood as sharing; and unit fractions be denoted at first by using the written word for denominator. (MN)

Algorithms are developed and presented for the addition and multiplication of positive rational numbers using only their repeating decimal representation. (MN)

The concept of even and odd integers is explored through the use of fractions. (JT)

In this, the third article in a series on the author's teaching methods, the teaching of fractions is described. The author examines the types of errors which children commonly make. (SD)

How laser videodisc technology can be used to improve mathematics instruction is described, with note of the development of a videodisc curriculum on mastering fractions. Relevant research is reviewed, as well as how teachers can use the technology. The instructional design is described, and field-testing and revision reported. (MNS)

The conceptual difference between understanding and algorithmic performance is examined first. Then some dilemmas that flow from these distinctions are discussed. (MNS)

Four activities with window panes are described and illustrated as they extend children's knowledge of fractional numbers. (MNS)

Investigated effects of computer assisted instruction (CAI) on learning efficiency, defined as either higher passing percentage or less time on task. Subjects (N=24) were college mathematics students who either were lectured or had a CAI tutorial on the lowest common denominator. The CAI group took less time, but solved more problems incorrectly.…

Discussed the use of Cuisenaire rods in teaching the multiplication of fractions. Considers whole number times proper fraction, proper fraction multiplied by proper fraction, mixed number times proper fraction, and mixed fraction multiplied by mixed fractions. (JN)

Research findings on children's understanding of fractions, gleaned from interviews, are briefly noted. (MNS)

Twenty-nine students in grades four, six, and eight were asked to find solutions to fraction equivalence problems and to verify their solutions using discrete material. Discontinuities were observed between strategies students used for producing solutions and supporting knowledge grounded in physical reality. (Author/MNS)