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)

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)

Guidelines for effective ecological assessment are put forth in the form of a list of diagnostic questions and a checklist of variables in the child's environment that may be contributing to behavior problems. Physical, psychosocial, and physiological factors are listed for consideration in analyzing the totality of influences on the child. (PB)

Present composition teaching and testing techniques do not formally capture student improvement across essays. Contract learning, a procedure in which student essays are error-analyzed for repeated mistakes, can do so. Correction of those repetitions becomes a set of goals on a written contract signed by the teacher and student, and the student…

Students of English as a second language (ESL) often come to the classroom with little or no experience in writing in any language and with inaccurate assumptions about writing. Rather than correct these assumptions, teachers often seem to unwittingly reinforce them, actually inducing errors into their students' work. Teacher-induced errors occur…

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…

Notes that the basic elements of the English article system are best taught to foreign technical writing students over an extended period of time. Outlines a teaching method that emphasizes reducing errors that native English speakers perceive as wrong rather than teaching the nuances by which native writers fine tune their relationship with their…

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)

Numerical inaccuracies, which occur in many ordinary computations, can create serious problems and render answers meaningless. Cancellation and accumulation errors are described, and suggestions for experimentation are discussed. (MNS)

Four different conceptions of error-making from a pedagogical perspective are developed. Using errors as springboards for learning is advocated, so that better understanding of content and of the nature of mathematics results. (MNS)

This is a report of an application of the interpretation of errors and springboards in a real-life situation. If and why we need to reduce fractions is considered. (MNS)

A common mistake in adding fractions involves the confusion betwen the concepts of fraction and ratio. A coherent system to operate with ratios is developed. (MNS)

Areas of contradiction and controversy over error analysis are discussed, and an interference error analysis project is described, giving a detailed definition of interference error. Several practical approaches to teaching out interference errors are outlined. (MSE)

Helping students understand the round-off error is the focus. A computer program for Fibonacci numbers illustrates the point, which is then described mathematically. (MNS)