By handling numbers in unexpected ways, computers and calculators create headaches for computer programers and set traps for unsuspecting users by sometimes producing wrong answers. Specific examples of such computer/calculator errors are discussed. (Author/JN)

Illustrates, categorizes, and analyzes typical mathematical errors in algebra and trigonometry made by high school and lower division college students. (16 references) (Author/MKR)

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…

Discusses two types of student writing problems: error characteristics (spelling, pronoun usage, subject-verb agreement, run-on sentences, and capitalization) and nonerror characteristics (density of ideas, variety of referents, and variety of expression). Suggests ways to diagnose and correct them. (HTH)

Attention is called to the apparent widespread misunderstanding of algebraic notation by secondary school students, and how this may arise from some common approaches to teaching algebra to beginners is discussed. (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)

Predictive validity of preadmissions measures may be understated because of correctable defects in freshman year and cumulative high school grade point averages (GPAs). A study used item response theory (IRT) to develop a more reliable measure of performance and test it using Stanford University data. Results showed increased predictability.…

Summarizes information processing models of the mind based on a literature review; describes a prototypical model of college learning; examines links between mental models and cognitive errors; reviews cognitive science students; and identifies six factors contributing to cognitive error production. (104 references) (Author/MBR)

Students were administered either conditional syllogism, biconditional syllogism, or conditional and biconditional syllogism tests. Analyses confirmed a tendency towards biconditionality. With conditional syllogisms, results indicated variations across forms of both major and second premises and a reversed developmental trend on problems which…

Reasoning patterns and learning difficulties of six students are illustrated in support of the contention that language and notation often disguise thought. (MN)

An overall schema of interpretation for programming instructors is given, so that the misconceptions students develop in programming can be determined more readily. Types of language-independent and -dependent bugs, how they can be identified, and how to help students overcome them are addressed. (MNS)

Advantages and disadvantages of joint maximum likelihood, marginal maximum likelihood, and Bayesian methods of parameter estimation in item response theory are discussed and compared. (Author)

Reports on a study to determine if having students write about the work required in doing three types of exercises from elementary algebraic fractions would affect the students' error patterns on quizzes. The study involved six developmental studies in elementary algebra classes. (PK)

Describes observations, written samples, and interviews of (n=24) high school teachers learning concepts of group, subgroup, coset, normality, and quotient group in an Abstract Algebra course. General observations are made about the role of errors and misconceptions in light of an action-process-schema framework. (32 references) (MKR)

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)