The evidence suggests that students in grades 5 through 8 have difficulty relating isometric type drawings to the rectangular solids they represent. Errors made by students were analyzed and the effect of instruction in spatial visualization activities assessed. (MNS)

What two teachers found when they took a close look at the results of a sentence-solving test given in grades four and five is reported. Error patterns appeared less frequently after instruction but recurred on retention tests. How students can be helped is suggested. (MNS)

Ten examples of when the sequences of key presses given in calculator instruction booklets are either inefficient or lead to an incorrect answer are given. (MNS)

Examples of four interviews are presented to serve as sample evidence in support of more comprehensive diagnostic procedures in assessing reliably and validly the weaknessess and strengths of learners. The search for computational errors is seen to go beyond standard paper and pencil tests. (Author/MP)

This is a preliminary report on research into computational errors made by six- and seven-year-olds. (Author/MK)

A nine-step model is presented for diagnosing and correcting computation errors in arithmetic. The model, which lends itself to curriculum-based assessment and instruction, involves such steps as identifying error patterns, interviewing the student, and selecting the appropriate corrective strategy. (JDD)

This study investigated whether undergraduate students encode spurious correlations in memory and exhibit them during the learning process leading to ineffectual problem solving. Findings suggested that even experienced students relied on surface-structure feature-algorithm correlations for solving new problems. Findings pose implications for…

Following a pretest, 11 participants who were naive with regard to various algebraic and trigonometric transformations received an introductory lecture regarding the fundamentals of the rectangular coordinate system. Following the lecture, they took part in a computer-interactive matching-to-sample procedure in which they received training on…

Some possible reasons why remediation is needed in mathematics instruction are presented. The need to diagnose the problem and then provide appropriate, effective remediation is discussed. Four guiding principles for diagnosis are presented, followed by six questions covering hypotheses about the source of the difficulty. Suggestions are then…

The paper describes two experiments using the Computational Mathematics Monitoring System (CMMS) with mildly handicapped (educable mentally retarded-EMR and learning disabled-LD) students. In the first study, data is presented on the summative evaluation of the CMMS with 19 Ss. It is explained that evaluation results do not provide clear-cut…

Solving equations in elementary algebra requires knowledge of the permitted operations, and knowledge of what operation to use at a given point in the solution process. While just these kinds of knowledge would be adequate for an ideal solver, human solvers appear to need and use other kinds of knowledge. First, many errors seem to indicate that…

Evidence on learning problems due to dyscalculia is surveyed. Definitions, factors responsible for dyscalculia, split-brain research and hemispheric roles, mathematics learning problems and personality, materials for instruction, and levels of knowing mathematics are among the topics discussed with an extensive list of references. (MNS)

Four informal assessment techniques to detect student mistakes in math, increase motivation, and improve achievement include the following: building models and generating word problems, thinking aloud, building mathematical sentences, and making mathematical sentences to answer questions in word problems. (DB)

Results from a British study on Strategies and Errors in Secondary Mathematics are considered. Students' views of algebra and their difficulties are summarized, with some suggestions for teachers. (MNS)

Attention is called to the apparent widespread misunderstanding of algebraic notation by secondary school students, and how this may arise from some common approaches to teaching algebra to beginners is discussed. (MNS)