We consider the effect on estimation of simultaneous variable centering and interaction effects in linear regression. We technically define, review, and amplify many of the statistical issues for interaction models with centering in order to create a useful and compact reference for teachers, students, and applied researchers. In addition, we…

Curriculum materials are among the most pervasive and powerful influences on school mathematics. In many mathematics classes, student assignments, the questions the teacher asks, the ways students are grouped, the forms of assessment, and much more originate in curriculum materials. At the same time, teachers have considerable latitude in how they…

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…

This paper proposes an hypothsis describing how some college students incorrectly view semantically laden letters and provides both clinical and written data that supports that hypothesis. Several word problems were given to nine college math students. These students were then interviewed as they attempted to solve these problems. In addition to…

Investigated long-term retention of mathematical concepts in a Keller plan course conducted without a final examination as compared to a conventional lecture course with a final examination. Results indicate greater long-term retention of concepts for students taking a traditional lecture course with final examination rather than the Keller plan…

Provides a brief summary of current research in mathematics education at the college level. Explores the current needs of college-level faculty. Suggests ways of coping with the apparent perception that some of the best contemporary research is useless or irrelevant from the practitioner's point of view. (22 references) (JJK)

The main features of the theoretical framework of French research in didactical mathematics are presented. An example is given that presents the rationale for the construction of a didactical situation and its analysis. (CW)

Investigated are three misconceptions of probability and the differential effect of two activity-based instructional units. Response categories (law of averages, law of small numbers, and availability) are identified. Treatment differences (evaluation or no evaluation) appear to influence subjects' interpretations of the information. (YP)

A structured system of visual features is seen to parallel the propositional hierarchy of operations usually associated with the parsing of algebraic expressions. Women more than men were found to depend on these visual cues. Possible causes and consequences are discussed. Subjects were secondary and college students. (Author/DC)

A study documented 10 college students' understanding of the limit concept and the factors affecting changes in that understanding. Encouragement by the researchers for the students to change their common informal models of limit to more formal conceptions were met with extreme resistance. (Author/JJK)

This paper describes the implications of constructivism both for what to teach and for how to teach. The first part discusses three approaches on what to teach: (1) relating mathematical knowledge to other knowledge; (2) checking for self-consistency; and (3) putting thinking before facts. The second part is on how to teach based on…

Through individual interviews with remedial and precalculus university students, five characteristics of the student were identified that influence whether a diagram is used in solving a problem and whether its use is successful. The interviews also suggested a set of subskills that contribute to the overall ability to draw effective diagrams.…

Results of the most recent administration of the National Assessment of Educational Progress (NAEP) suggest that the majority of secondary students believe in the independence of random events. In the study reported here, a high percentage of high school and college students answered similar problems correctly. However, about half of the students…

There has been much recent discussion concerning the content of the standard calculus course for students majoring in mathematics and the sciences. Some of this discussion has focused on the available textbooks. One weakness noted in some of these books involves the definitions of limit and continuity for functions of several variables. A…

This study investigated the effects of various levels of secondary school calculus experience on performance in first-year college calculus, with focus on student performance on conceptual and procedural exam items. Students who had a year of secondary school calculus differed significantly in performance from those who had either no experience or…