This paper reports on a collaboration between three authors; two mathematicians in a Swedish university and a UK-based mathematics educator. The focus of the enquiry was the evaluation of the experience of Swedish first-year undergraduate engineers required, in their mathematics class, to learn to use the programming language "Matlab". Students…

As students are first learning to construct mathematical proofs, it is often helpful for them to have the opportunity to see and evaluate proofs that others have written. In fact, several textbooks designed for use in a transition or bridge course include a few exercises in which students are given a proposed proof and asked to determine if it…

Many undergraduate students have difficulty with the transition to proof-based courses in mathematics. This paper discusses students' beliefs about proof and justification in mathematics just prior to entry into such courses. The paper is based on in-depth interviews with students. The data suggests that some students have beliefs that may in part…

Many of us are concerned about newly imposed demands coming from accrediting organizations or administrations to assess our mathematics departments and ourselves as individual instructors. To be sure, cynicism about assessment abounds on campuses. This article attempts to take on some generic objections and to unravel the complexities which lie…

This paper describes a sequence of lessons from two Calculus I classes for teaching the epsilon-delta definition of a limit. In these lessons, the author elicited students' misconceptions and perceptions of this definition through a reading/writing lesson and then used these student ideas to design a lesson aimed at addressing these misconceptions…

This article is a discussion of some geographical problems related to geographic and population centers of the U.S. The focus is on modeling, using concepts from calculus.

This article conceptualises a real-like model of a mathematical model as an inverse model. The inverse model draws on the un-complexity of concrete real life operations in order to help students to add concrete meaning to mathematical algorithms. The inverse model is described in the context of a pedagogical perception, which grants students in…

We find that students in the big mathematics service courses at the Johns Hopkins University who were encouraged to use calculators in K-12 have somewhat lower grades than those who weren't.

In this note we consider a type of integral that is usually presented as an example in any textbook discussion of integration by parts. Invariably this integral is determined by integrating by parts twice and solving. We will present an alternate approach to this integral which makes use of the linearity of the integral, i.e., the fact that…

If larger and larger samples are successively drawn from a population and a running average calculated after each sample has been drawn, the sequence of averages will converge to the mean, [mu], of the population. This remarkable fact, known as the law of large numbers, holds true if samples are drawn from a population of discrete or continuous…

The purpose of this study is to compare vocational school students' success at basic mathematics subjects with regard to their entrance to the university. The data were obtained by administering a "Personnel Information Form" and "the Mathematics Test" prepared by the researcher to 617 vocational school students and 26 two-year…

Much of modern mathematical research requires a serious level of commitment and ability on the part of the researcher and, as a natural consequence, precludes any real involvement by undergraduate mathematicians. However, to put it crudely, Computer Algebra Systems, can make experts of us all. With the use of such systems even the average…

This study investigated the effectiveness of collaboration between college lecturers and student peers in assessing the instructional practice of in-service student teachers (ISTs). The study was inspired by criticisms that college lecturers' assessments were not producing valid critiques of ISTs' mathematical and pedagogical competencies to…

This article describes an activity that involves the use of simulation for decision-making. It is useful for demonstrating concepts in probability and statistics. (Contains 4 figures and 2 tables.)

In this article, we discuss the importance, specifically for developmental educators, of understanding diverse students' use and perceptions of learning centers. Among the results of a survey of students' perceptions of the mathematics program in the General College, University of Minnesota, we found statistically significant differences in how…