In this paper we describe a number of types of errors and underlying misconceptions that arise in mathematical reasoning. Other types of mathematical reasoning errors, not associated with specific misconceptions, are also discussed. We hope the characterization and cataloging of common reasoning errors will be useful in studying the teaching of…

Results from testing long division with students from age 11 to Continuing Education were traced. A much higher percentage of wrong answers was given when there was an embedded zero in the answer. (MNS)

Dialogue from an interview with a child about division basic facts is presented. The facts are considered by groups, and specific errors are noted. Finally, remediation ideas are given. (MNS)

Considered are concept development and errors in using both Logo and BASIC made by 25 prospective teachers in a computer literacy course. Understanding errors that students exhibit in programing may affect the ways mathematics teachers understand the process of learning structured content like mathematics. (MNS)

Illustrates the schematic approach to analyzing children's (n=499) errors in solving mathematical problems using children's written solutions. Identifies five levels of errors: no solution, using irrelevant procedure, incomplete schema with no errors, incomplete schema with errors, and complete schema with errors. (24 references) (Author/MKR)

Discusses how student errors can be utilized to understand the nature of the conceptions that underlie students' mathematical activity. Looks at why errors are made in mathematics, how teachers and students perceive errors, and how to use errors in the classroom. (MDH)

This article recommends a holistic approach to student problems in mathematics. Teachers need to be aware of all paradigms (e.g., developmental, behaviorist, psychoanalytic) explaining causes of problems in mathematics. Examples of misunderstandings resulting from insufficient knowledge, insufficient mathematical vocabulary, and overgeneralization…

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…

The purpose of this study is to contribute to an understanding of how errors could be employed in mathematics instruction so that the students use them constructively in support of their learning of mathematics. A teaching experiment was designed to create an ideal context in which the pedagogical approach to errors as springboards could be…

It is the premise of this study that the performance of black students in math and science is crippled by the interference of their language patterns. It is argued that schoolwork of these students demonstrates how nonstandard English can lead to misunderstanding. The connection between students' misunderstandings of certain quantitative relations…

The contributions of acceptance of misconceptions about mathematics, mathematical self-concept, and arithmetic skills to mathematics anxiety and to statistics course performance were studied in 92 adult students aged 18 to 57 with a median age of 27, (16 males and 76 females). Results showed that acceptance of misconceptions and mathematical…

A brief overview is given of a research project funded to investigate the cause and cure of errors in ratio and proportion, algebra, and fractions. Choosing pertinent information, interviewing students, listing significant features, developing lessons, and testing the materials are considered. (MNS)

Many children with learning handicaps have difficulty learning to write numerals. The source of numeral-writing difficulties and some things which can be done to teach or remedy this skill are presented. (MNS)

A collection of student distortions, represented by student-invented variations of theorems, are presented. They were drawn from examination papers of 17-year-old students in Israel. (MNS)

Ten crucial mathematical concepts with which errors are made are listed, with methods used to teach them to high school students. The concepts concern order, place values, inverse operations, multiplication and division, remainders, identity elements, fractions, conversions, decimal points, and percentages. (MNS)