Gabriel's Horn is a solid of revolution commonly featured in calculus textbooks as a counter-intuitive example of a solid having finite volume but infinite surface area. Other examples of solids with surprising geometrical finitude relationships have also appeared in the literature. This article cites several intriguing examples (some of fractal…

The purpose of this qualitative case study was to examine the modeling of technology by mathematics professors in two universities in teaching required courses for secondary level pre-service mathematics teachers. Six professors participated in this case study. Their responses were documented in pre- and post-interviews and data were gathered from…

The implementation of online texts, videos, homework, and tests has changed the process of instruction in introductory college mathematics courses. With this change, more of the students' learning takes place outside of the traditional college classroom and in places such as tutoring centers and dorm rooms. A combination of chi-square tests--for…

Games are a useful and fun way to review material in class, and encourage students to actively participate in review sessions. In fact, researchers have concluded that playing games can be an effective learning tool, especially in mathematics, in situations where the goal is to reinforce specific ideas or concepts. Two places this type of…

Focuses on students showing a lack of conceptual insight while using computer algebra systems (CAS) in the setting of an elementary calculus and linear algebra course for first year university students in social sciences. The use of a computer algebra environment has been incorporated into a more traditional course but with special attention on…

Recently the Department of Mathematical Sciences at Middle Tennessee State University embarked upon the task of restructuring its undergraduate program. An important component of this restructuring was a recommendation for the use of technology to enhance the teaching and learning process. As a result, technology was rigorously used in the fall of…

Describes the experiences and conclusions of a long-range program to revitalize undergraduate instruction in mathematics utilizing state-of-the-art workstations and the computer algebra system, Maple, and includes two examples of this type of instructional improvement. Focuses on computer-intensive calculus. (MKR)

Investigates the impact of the TI-89 hand-held Computer Algebra System (CAS) on student achievement in a first year college core calculus course. Analyzes data from an experimental study conducted at the United States Military Academy at West Point from 1998-2000. Results indicate that the TI-89 hand-held CAS experimental group attained a higher…

Compiles observations from a multivariable calculus class in which computers were used extensively. Results show that visualization skills can be improved and that students use technology in very innovative ways. (Author/MM)

In this paper are described some features of the intensive use of math software, primarily DERIVE, in the context of modeling in an introductory university course in differential equations. Different aspects are detailed: changes in the curriculum that included not only course contents, but also the sequence of introduction to various topics and…

Presents a semiotic analysis of the potential of computer algebra systems (CAS) for enabling mathematical activity on a conceptual level higher than usual. Illustrates examples of theoretical points from a development project in the context of a first year university course in calculus. Discusses how CAS may be used in a didactical analysis and in…

Reports on the responses of students using a computer algebra system (CAS) called DERIVE in an introductory calculus course at undergraduate level. Indicates that the use of this technology was a catalyst for students to use three types of learning strategies: (1) regularly using multiple representations, (2) discussing meaning with peers and…

This paper describes a model for effective incorporation of technology into the learning experience of a large and diverse group of students in first-semester first-year tertiary mathematics. It describes the introduction of elementary use of MATLAB, in a course offered both on-campus and at a distance. The diversity of the student group is…

Compares student achievement based upon which calculus program--traditional calculus, Harvard Consortium Calculus, or Calculus Using Mathematica--the student completed. Finds some differences when students took different types of calculus during subsequent terms. Justifies teaching reformed calculus in place of traditional calculus. (Author/ASK)

Presents a study on calculus reform that examines how instructional approaches that place different emphases on the use of technology and multiple representations impact undergraduate calculus students' ability to use and understand connections between different representations of concepts. Compares three courses--traditional calculus, calculus…