The literature on proportional reasoning is reviewed. After methodology is discussed, strategies used to solve proportion problems, variables that influence performance, and training studies are each considered. (MNS)

Documented are major categories of errors that appear as children learn decimal fractions. Then the conceptual sources of these errors are established. Different curriculum sequences influence the probability that these classes of errors will appear. They can be used as diagnostic tools to detect children's understanding of mathematics topics.…

Describes observations, written samples, and interviews of (n=24) high school teachers learning concepts of group, subgroup, coset, normality, and quotient group in an Abstract Algebra course. General observations are made about the role of errors and misconceptions in light of an action-process-schema framework. (32 references) (MKR)

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…

This research is aimed at diagnosing the problem-solving skill of elementary school children and subsequently improving their competence in early mathematics. To reach this goal, a computer assisted instruction (CAI) program on open sentences, incorporating knowledge about students' problem solving strategies and misconceptions, was constructed.…

Suggests that student errors in mathematics be used as motivational devices and starting points for mathematical explorations, involving problem solving and problem posing activities. It is further suggested that errors can foster a deeper and more complete understanding of mathematical content and nature of mathematics itself. (PK)

Investigated was how easily pupils aged 12 and 13 who were initially unaware of the invariance of an operation (with decimals) modeling a situation could be led to such awareness. Results from clinical interviews are reviewed and a protocol presented. It appeared difficult to induce conservation. (MNS)

Presents a selection of solutions of the "Three Hungry Men" problem from grade three to college students with three different strategies used: backward, forward, and forward/backward strategies. Provides error patterns in each strategy. Discusses some implications for teaching of problem solving. (YP)

This article outlines the last step in a five-step process for preparing students to engage in a systematic mathematics problem-solving and decision-making process. The lesson plan teaches students to reread the problem, reexamine the question, check selection of operation, and recheck calculations and compare answers. (JDD)

Data from the Stanford Test of Academic Skills Level I, administered to 10,910 tenth graders in Hawaii in Fall, 1985, are analyzed. The purposes of this report are to provide information on the effectiveness of the mathematics program in the high school, including the identification of deficiency areas and recommendations for improving…

Brief articles are included on exploring mathematical patterns, with two computer programs listed for finding happy numbers; a simple periodic function in trigonometry; and comments on humorous student errors. (MNS)

The projection of shadows task developed by Inhelder and Piaget was used to identify error patterns and solution strategies used by diverse populations in a sequence of proportion tasks. In Study A, two group tests were administered to 607 students from science and mathematics classes in grades 9 and 10. A sub-sample of 69 students was involved in…

Most studies of children's solution processes on simple addition and subtraction word problems have used individual interviews or the analysis of error patterns on paper-and-pencil tests as the primary data-gathering techniques. The present paper reports an investigation in which the contribution of eye-movement data was explored for studying…

The nature of arithmetic disabilities in children is discussed first in this review. Then research studies are reported, classified by cognitive and neuropsychological studies and social competency studies. Finally, suggestions for remediation are provided. (MNS)

Describes mathematical problems which occur when using the computer as a calculator. Considers errors in BASIC calculation and the order of mathematical operations. Identifies errors in spreadsheet and calculator programs. Comments on sorting programs and provides a source for Mathemagical Black Holes. (MVL)