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)

Ninety students in an introductory chemistry class were divided into three groups to test the power of algorithms to increase logical thinking abilities. The experimental group received approximately 10 hours of laboratory instruction based on the use of procedural algorithms. Experiment and control groups were tested for logical thinking…

Abstracts of 28 research reports are provided. The reports were prepared by investigators for presentation at the 54th annual meeting of the National Council of Teachers of Mathematics. A broad range of topics related to mathematics education are covered. Three reports concern the effects of differing presentations of mathematics, four are related…

The concept of an algorithm derives from the physical sciences, but it has often been misunderstood and misapplied in the social sciences and in education. The theoretical and practical significance of algorithms stems from their applicability to problems of learning, instruction, and instructional design, and they may potentially provide the…

The purpose of this study was to compare the repeated subtraction method of long division of a partitioning distributive method, both taught by recording manipulation of popsicle sticks. Two instructional units were prepared. Twelve fourth grade classes were used, with six being taught one approach and six using the other. Tests consisting of…

The author describes a technique for teaching various aspects of the subtraction algorithm (e.g., regrouping, borrowing) by relating them to the use of money. (SD)

An algorithm is given for the addition and subtraction of fractions based on dividing the sum of diagonal numerator and denominator products by the product of the denominators. As an explanation of the teaching method, activities used in teaching are demonstrated. (MN)

Helping teachers to build a strong bridge from concrete experiences to algorithms is the focus. A detailed sequence of activities is described. (MN)

Instructional sequences are presented for teaching two-digit multiplication and division with one- and two-digit divisors using a base-oriented approach. (MN)

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

The authors attempt to determine the effects of the use of direct and "combinations of tens" methods of two column-addition, ability, and grade level as factors in column addition efficiency. (MN)

Provides a metric area model which may be used to explain the square root algorithm. (CP)

Ideas on the long-term effects of using microcomputers in mathematics are presented. The changing perception of mathematics, the role of algorithms, the use of short computer programs, the effects on mathematical understanding, implications for teaching methods, logistic problems, examinations and assessment, and planning for the future are…

Two mental algorithms, one for addition and one for subtraction, are described. It is felt such algorithms should be taught explicitly. The usual process taught for paper and pencil is seen to inhibit mental arithmetic, and a need to include mental algorithms in the regular mathematics curriculum is promoted. (MP)