Several schemes use modular arithmetic to append a check digit to product identification numbers for error detection. Some schemes are discussed, including ones for money orders and library books. Then a foolproof method is presented. (MNS)

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…

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";…