An operational definition of careless errors was provided and used in an investigation of 50 children attending an international primary school in Lae, Papua New Guinea. Results indicated that mathematically competent and confident children tend to make a greater proportion of errors than other children. (MP)

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…

Sixty-four adults were tested on simple addition and multiplication problems presented in Arabic digit or English number-word format. Overall, response times and error rates were much higher with the word format, but more important, presentation format interacted with arithmetic operation and problem size. (DR)

This article describes activities that promote students' understanding of equation solving through analyzing and correcting student work. (Contains 5 figures.)

To learn more about the specific nature of the teaching and learning problems involved, researchers conducted a clinical study of 20 high school students enrolled a BASIC course. Investigators presented each student with a sequence of eight programming problems, ranging from easy to difficult. They asked questions to track student thinking and…

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…

Reports results obtained when 24 14-year-old students were presented with algebra tasks by a computer-based modeling system and, four months later, comparable paper and pencil tests together with detailed interviews. Comparison of the results revealed profound misunderstandings of algebraic notation and identified classes of strategies used by…

In this paper, we will discuss the way various features of consciousness interact with each other and with cognition, specifically, the cognition of mathematical reasoning and problem solving. Thus we are interested in how consciousness and cognition "work," in a somewhat mechanistic way, rather than in larger philosophical questions about…

This experiment investigated performance on a reasoning task in which the subjects had to say which of four half-hidden cards they needed to see fully in order to determine the truth or falsity of a conditional sentence. (Authors)

Theories--based on concretizing, assimilation, and structuring--of the use of metaphors in learning are assessed. Each is shown to predict different patterns of inferences and errors in problem solving. An experiment with 43 undergraduates involving college lectures indicated that structuring may provide the most important function of metaphors in…

This study investigated whether undergraduate students encode spurious correlations in memory and exhibit them during the learning process leading to ineffectual problem solving. Findings suggested that even experienced students relied on surface-structure feature-algorithm correlations for solving new problems. Findings pose implications for…