This booklet is a catalog of error patterns found in basic arithmetic and algebra courses. It is intended to be used as a resource by instructors and tutors teaching these concepts. The material is divided into major concept headings with subheadings. The error patterns are named and given a brief general description followed by a specific example…

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)

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)

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)

Why students have difficulty with a proof (such as Cantor's) is discussed, with the focus on proof by contradiction. Methods may fail due to the difficulty of the concept and lack of understanding of how students are thinking. (MNS)

This manual is a dictionary of some 150 errors made by students in their work in mathematics. A precise definition and examples are given for each of these errors and these, combined with a description of common causes of the error, form a background for diagnosis of student problems with arithmetic. Teaching strategies and ideas, each linked to a…

Students make errors in mathematics for a variety of reasons. It is the job of the educator to identify the source of these errors and to assist students in correcting them. The purpose of this monograph is to help identify, analyze, and evaluate students' computational proficiency. This monograph is divided into four sections: "Whole Numbers";…

Illustrated first is the case in which a wrong procedure (with fractions) leads to a correct result. Trying to justify why it works in this case and looking for similar patterns involved interesting algebraic considerations as well as use of computers. (MNS)

A series of common misconceptions with regard to infinite sets is considered. Several notions of infinite numbers proposed by different mathematicians are compared. It is argued that so-called errors should rather be called alternative conceptions. (MNS)

Seventh-grade students were tested to uncover arithmetic errors. Answers and intermediate steps were analyzed and models to represent students' behavior were developed. Certain errors were common across students. Others were tied to the format of the test item. Some superficial understandings of mathematical concepts were exposed. (Author/DC)

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…

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)