This study involved 179 9-year-olds and 352 13-year-olds in New Zealand. Four addition and four subtraction tasks were set to ascertain students' ability to use the number line. Comparison of these data with results from the national assessment in the United States are given. (MNS)

The informal subtraction strategies that children develop are discussed in detail, with the role of the counting-down strategy described. Problems and remedies for difficulties caused by counting backward and the double count are also presented. (MNS)

Mathematics departments rarely require students to study very much logic before working with proofs. Normally, the most they will offer is contained in a small portion of a "bridge" course designed to help students move from more procedurally-based lower-division courses (e.g., abstract algebra and real analysis). What accounts for this seeming…

Interviews were used to find the frequency of different types of errors made by 95 sixth-year Papua New Guinea students on a mathematics test. The general trend was the same as for western students, but the Papua New Guinea students made far fewer careless errors. (MNS)

This experiment involved 176 London children aged six and seven. Their levels of attainment on subtraction were quickly and accurately established by two questions. Then teaching programs were used to help them attain prerequisite skills. To symbolize too soon is a danger to be avoided. (MNS)

Several common errors reflecting difficulties in probabilistic reasoning are identified, relating to ambiguity, previous outcomes, sampling, unusual events, and estimating. Knowledge of these mistakes and interpretations may help mathematics teachers understand the thought processes of their students. (MNS)

Data indicate that relatively advanced science-oriented college students can experience serious difficulties in symbolizing certain meaningful relationships with algebraic equations. Reversal errors in formulating equations were seen to stem from two main sources: (1) a syntactic word order matching process and (2) a semantic static comparison…

This report discusses students' understanding of the algebraic concepts of gradient and intercept with respect to simple graphs. A pilot study is described which attempts to identify the difficulties students encounter and determine the number of students who have these difficulties. (MK)

The author has discovered that errors in grades often occur when scores are combined for final marks. These errors are not related to the grading individual assignments. Rather, they occur when teachers at all grade levels bring individual test and assignment scores together for the students' final grades. Unfortunately, professors of mathematics…

The goal of this study was to find a way to quantify three criteria of representational quality, described by Greeno, so that it would be possible to examine statistically the relationship between representational quality and other variables related to problem solution. The sample consisted of 18 college students, 84 percent of whom had…

This document contains 15 research papers presented at the Fourth and Fifth Annual Conferences of the Research Council for Diagnostic and Prescriptive Mathematics. The papers are organized into four sections. In part I, four position papers by Romberg, Engelhardt, Ashlock, and Heddens reflect research ideas which underlie the Council. Part II…

Diagnostic evaluation is a major way to help students overcome errors. How such evaluation can be done is discussed, with comments on what should be checked and recorded by the teacher. (MNS)

Three theorems for Pythagorean triples are presented, with discussion of how students can amend their ideas about such numbers. (MNS)

Some limitations of computing with calculators and computers are described, with particular reference to typical computations which might be performed by senior secondary school students. Types of errors, the laws of number, and intermediate round-offs are each illustrated, with conclusions and implications. (MNS)

A content-oriented analysis of written solutions to test items in Israeli high school graduation examinations in mathematics yielded six error categories: misused data; misinterpreted language; logically invalid inference; distorted theorem or definition; unverified solution; and technical error. (Authors/MNS)