In this article, pre-service teachers' mathematics content knowledge is explored through the analysis of two items about ratio from a Mathematical Competency, Skills and Knowledge Test. Pre-service teachers' thinking strategies, common errors and misconceptions in their responses are presented and discussed. Of particular interest was the range…

To find out whether the education community shares a collective understanding about how students should be evaluated, we surveyed 202 educators (from all grade levels) and scientists attending assessment workshops (Pennsylvania, California, and Massachusetts) or judging a national student competition (Washington, DC). The educators and scientists…

The 11th International Conference on Educational Data Mining (EDM 2018) is held under the auspices of the International Educational Data Mining Society at the Templeton Landing in Buffalo, New York. This year's EDM conference was highly competitive, with 145 long and short paper submissions. Of these, 23 were accepted as full papers and 37…

The purpose of the study was to determine whether students had knowledge of the extension rule (the conjunction of two or more events cannot be greater than the probability of any one of those events) and understanding of conjunction by giving a test of multiplicative probabilities. Involved were 598 students enrolled in introductory psychology…

Investigated relationships among different types of errors occurring during probability problem solving by 50 graduate students without mathematical sophistication. Categorized errors as text comprehension, conceptual, procedural, and arithmetic/computation errors. Discusses implications for the teaching and learning of probability problem…

Results indicate that for the task of generating counterexamples to invalid syllogisms, a primary source of difficulty is the first step of forming the negation of the conclusion, especially if the conclusion is a "Some are not" statement. When this step is done for the subject, most of the errors disappear. (Author/BJG)

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…

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…

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…

This paper encourages the use of Total Quality Management (TQM) tactics and other strategies as a practical means of fostering a quality culture in institutional research offices of higher education institutions. In particular, four approaches are advocated for understanding and minimizing errors: (1) use of TQM tactical tools to enhance work…

Describes a study which analyzed problem solvers' error detection processes by instructing subjects to think aloud when solving statistical problems. Effects of evaluative episodes on error detection, detection of different error types, error detection processes per se, and relationship of error detection behavior to problem-solving proficiency…

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…