We present a project for a differential equations class: an analysis of an H. G. Wells story in which is given a submersible's descent time, its ascent time, and its eruption from the surface before splashdown. (Contains 5 figures.)

The note discusses ways in which technology can be used in the calculus learning process. In particular, five MATLAB programs are detailed for use by instructors or students that demonstrate important concepts in introductory calculus: Newton's method, differentiation and integration. Two of the programs are animated. The programs and the…

A sequence of number pairs can be used to generate many interesting examples in teaching mathematics subjects at various levels. It is often used in elementary or middle school mathematics classes to illustrate the concept of "patterns." In this paper the authors present a few interesting ways of using this sequence to form examples for high…

The voices of African American students reveal sociocultural factors that influence their achievement in science and mathematics classes. Using a sociocultural theoretical framework (Mercer & Covey, 1980), this ethnographic study interpreted the perspectives of five African American students as they discussed their learning experiences in science…

A randomized trial of 265 consenting students was conducted within an introductory biostatistics course: 69 received eight small group cooperative learning sessions; 97 accessed internet learning sessions; 96 received no intervention. Effect on examination score (95% CI) was assessed by intent-to-treat analysis and by incorporating reported…

In this paper we report on some patterns of reasoning, which emerged during an activity of proving a mathematical statement performed by nine grade and university mathematics students. The statement in question involves drawing figures, working in arithmetic and in algebra. As for secondary students we detected fluency, flexibility and ability of…

Large lecture classes can often be quite impersonal. Creating a teaching team, consisting of the instructor, graduate assistants, and a few undergraduates, is one of the ways the University of Arizona has adopted in order to make the large lecture class more personal. As members of the Department of Mathematics we train the undergraduates, who are…

We apply a research-based analytical framework (MALA, for motivation, activity, learning and attribution) to better understand two student-centered college mathematics classes. We demonstrate ways in which the framework can be used to systematically identify problems with classroom management, to generate meaningful suggestions for improvement of…

This article advances a view of Computer Algebra Systems (CAS) as powerful inquiry-based learning tools. Through an in-depth exploration of the "Emptying the Bowl" activity, upper level mathematics students test their own mathematical hypotheses, thoughtfully analyse and manipulate computer-generated output, and answer questions…

In a previous paper, we showed the importance of using low-level commands of a CAS in order to enhance the students' conceptual insight into mathematics. In this paper, we wish to emphasise a different use of a CAS, which makes possible the exploration of new topics, when the necessary theoretical results have still not been acquired, and avoids…

Students sometimes have difficulty in mathematics because they solve problems mechanically, without understanding the ideas represented by their equations. This brief note provides mathematics instructors with ideas for rectifying this fundamental flaw in students' paradigm of problem solving. (Contains 1 footnote.)

We developed, piloted, and evaluated a successful model for integrating other disciplinary perspectives while learning a specific discipline. Faculty who taught first-year biology and mathematics courses produced examples of how these disciplines complement each other. These faculty presented students with the connecting threads that integrate…

The continuous technological progress of the past few decades affords a different orientation to the teaching-learning process, which is useful and advantageous when mathematical concepts are transmitted. This article pursues two different aims. The first one is to examine the present state of the traditional process in relation to the concepts of…

In this report we explore the role of reviewer agreement in judgments about alignment between tests and standards. Specifically, we consider approaches to describing alignment that incorporate reviewer agreement information in different ways. The essential questions were whether and how taking into account reviewer agreement changes the picture of…

NCES (1996) reported that almost one-third of all students entering colleges and universities are unprepared for college coursework and therefore required to enroll in developmental courses. This study focused on developmental and regular mathematics courses at the University of Arkansas at Monticello. Using final mathematics grades from the…