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

Data indicate that relatively advanced science-oriented college students can experience serious difficulties in symbolizing certain meaningful relationships with algebraic equations. Reversal errors in formulating equations were seen to stem from two main sources: (1) a syntactic word order matching process and (2) a semantic static comparison…

The goal of this study was to find a way to quantify three criteria of representational quality, described by Greeno, so that it would be possible to examine statistically the relationship between representational quality and other variables related to problem solution. The sample consisted of 18 college students, 84 percent of whom had…

Verbal protocols were collected from math-anxious and math-comfortable college students while they solved algebra problems. These protocols were then examined for differences in problem-solving processes. Differences occurred in the use of two basic strategies: generating values and symbolic transformations. Math-anxious students generated more…

Solving equations in elementary algebra requires knowledge of the permitted operations, and knowledge of what operation to use at a given point in the solution process. While just these kinds of knowledge would be adequate for an ideal solver, human solvers appear to need and use other kinds of knowledge. First, many errors seem to indicate that…

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)

Nearly 48 percent of the students in Developmental Studies Mathematics courses at a major southern university during the fall of 1983 had taken college preparatory mathematics courses in high school. Some had even taken trigonometry, pre-calculus, or calculus. Yet, they were placed in university developmental studies mathematics courses because…

The investigation reported is primarily a description of how college students solve or fail to solve algebra equations. Protocols were collected from two groups of college students; one group was expected to be good solvers, the other group contained many poor solvers. The investigators sought to identify and classify the difficulties students…

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)

This exploratory study applied two new cognitively sensitive measurement models to constructed-response quantitative data. The models, intended to produce qualitative characteristics of examinee performance, were fitted to algebra word problem solutions produced by 285 examinees taking the Graduate Record Examinations (GRE) General Test. The two…

Research was conducted investigating properties of skill in learning, in the domain of elementary algebra. Thinking-aloud protocols indicate that early knowledge of the subjects studied was fragmentary, rather than involving systematically flawed procedures. Computational models, developed to simulate observed errors, focused on the role of…

This issue contains abstracts and critical comments on 11 articles, plus an editorial comment entitled "A Teacher Shortage?". Studies included concern solution processes on addition and subtraction examples; numerical rule induction; individual differences in performance on manipulative, pictorial, and symbolic tasks; the effect of a…