A unique aspect of the implementation of a computer algebra system (CAS) at a comprehensive university in the U.S. allowed us to compare the student success and failure rates to the traditional method of teaching college algebra. Due to space limitations, the university offered sections of both CAS and traditional simultaneously and, upon…

To argue for the importance of an integrative approach to learning in introductory STEM (Science, Technology, Engineering and Mathematics) and other courses, we present a case study of a project incorporating cross-curricular skills in a college algebra course. We analyze student work on the project and responses to surveys, and find the…

This article confronts the issue of why secondary and post-secondary students resist accepting the equality of 0.999... and 1, even after they have seen and understood logical arguments for the equality. In some sense, we might say that the equality holds by definition of 0.999..., but this definition depends upon accepting properties of the real…

The number of incoming college students who require development mathematics coursework is a national problem. This is an enormous area of concern for a number of reasons--such as the monetary cost to students who must take courses for which they are not granted credit, and colleges and universities who must pay instructors to teach such courses.…

The article contains general information about the use of specialized mathematics software in the preparation of math teachers. The authors indicate the reasons to study the mathematics software. In particular, they analyze the possibility of presenting basic mathematical courses using mathematical computer tools from both a teacher and a student,…

When playing pool or billiards, a player often has the opportunity to make a "straight-in" shot, that is, one in which the cue ball, the object ball, and the target (e.g., a pocket) are collinear. With the distance from the cue ball to the target assumed fixed, the relative difficulty is here explored of shots taken at varying positions of the…

The purpose of this article is to elaborate Cottrill et al.'s (1996) conceptual framework of limit, an explanatory model of how students might come to understand the limit concept. Drawing on a retrospective analysis of 2 teaching experiments, we propose 2 theoretical constructs to account for the students' success in formulating and understanding…

In this paper, we explore the development of two grounded theories. One theory is mathematical and grounded in the work of university calculus students' collaborative development of mathematical methods for finding the volume of a solid of revolution, in response to mathematical necessity in problem solving, without prior instruction on solution…

Data from the ALEKS-based placement program at the University of Illinois is presented visually in several ways. The placement exam (an ALEKS assessment) contains precise item-specific information and the data show many interesting properties of the student populations of the placement courses, which include Precalculus, Calculus, and Business…

Large numbers of students in California's 112 community colleges are struggling to pass college-level math classes, including courses they need to complete a degree or transfer to a four-year institution. Community college students' success in rigorous math is crucial to their futures and to any effort to improve college completion rates in…

Much research and many papers on mathematics pedagogy have discussed assessment and, in particular, the need to provide a varied diet of methods by which students are assessed for the award of their degree. In this article, we explore the mix of assessment methods provided across a range of UK university mathematics departments. We examine the…

In this paper, after a brief discussion of historical background of the bilingual teaching in college mathematics, we analyze the difficulties in bilingual teaching of college mathematics firstly. Various approaches and methods that have been put into our bilingual teaching practice to overcome those difficulties are explored in detail. Finally,…

Completing a PhD on time is a complex process, influenced by many interacting factors. In this paper we take a Bayesian Network approach to analyzing the factors perceived to be important in achieving this aim. Focusing on a single research group in Mathematical Sciences, we develop a conceptual model to describe the factors considered to be…

This article describes how technology has been used to motivate the learning of mathematics for students of Sports Technology at Loughborough University. Sports applications are introduced whenever appropriate and Matlab is taught to enable the students to solve realistic problems. The mathematical background of the students is varied and the…

We present an analysis of several characteristics of examples in 10 college algebra textbooks used in community colleges or 4-year institutions. We analyzed the examples along four dimensions: cognitive demand, the responses expected, the use of representations, and the strategies available for verifying the correctness of the solutions. We found…