A distinction is made between estimation and checking, and an analysis of standard errors made on calculators when pupils are checking answers is given. (MP)

Discussed are the mathematical methods for detecting a variety of common error patterns within the bar-coded identification numbers utilized in conjunction with scanning devices. Schemes for the use of check digits are examined that ensure conditions for detecting errors of specific types, including single digit error, transposition error, twin…

The use of the microcomputer in an interactive graphics mode offers exciting possibilities for mathematics and science education. Errors made with graphs are used to introduce ideas of what should be taught. Both understanding equations and graphing utilities are stressed. (MNS)

A set of brief reflections about different aspects of mathematical errors and their roles in education is given. The nature and variety of errors and their positive use in learning mathematics are highlighted. (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)

Four basic types of student errors in computation are noted and described. These are: (1) mechanical, (2) careless, (3) conceptual, and (4) procedural. It is felt many teachers deal with all errors as if they were of the unhabituated procedural type, with not enough attention given to other possibilities. (MP)

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)

Presents an activity applicable at the beginning of the year to review necessary algebra concepts that are often misunderstood by students. Presents a true/false worksheet made up of examples illustrating common algebra and trigonometry errors made by students. (MDH)

Delineates and describes four types of questions which may help teachers learn more about student understanding, namely, silent questions, oral questions, written questions, and students' questions. (PK)

Suggests that student errors in mathematics be used as motivational devices and starting points for mathematical explorations, involving problem solving and problem posing activities. It is further suggested that errors can foster a deeper and more complete understanding of mathematical content and nature of mathematics itself. (PK)

This document was prepared to assist teachers in Virginia in three ways: (1) by assessing student achievement on the competencies adopted by the State Board of Education; (2) by diagnosing student errors in mathematics; and (3) by prescribing instructional activities designed to promote student mastery of skills assessed in the competency program.…