Discusses the debate concerning the teaching of calculus. States that some consider calculus reform urgent because of the course's position in undergraduate studies. Considers the quality of mathematics instruction in the computer era. Cites examples of institutional experiments with new course designs. (CW)

The authors discuss the question, "What is mathematics education research at the university level?" They go on to consider "Making progress in tertiary mathematics education research: pushing the field forward." This includes a discussion of basic concepts and theoretical frameworks used. Further, they consider who does such research and how one…

This quantitative study compared two groups of community college students who were studying elementary statistics. The control group consisted of 38 students in two classes during the fall of 1998, and the treatment group contained 40 students in two classes during the spring of 1999. The treatment group participated in ten data collection and…

I present a theoretical distinction that may prove useful in conceptualizing mathematics teacher education (and graduate education) and research on mathematics teacher education. Further, the distinction can contribute to developing frameworks on the design of mathematics curricula. The distinction between empirical activity and…

Explores how research on how people think, learn, and remember can be used as a guide in redesigning higher education, especially science, technology, engineering, and math (STEM) fields. Asserts that such research suggests against lectures, "canned" laboratory work, and frequent testing. (EV)

Contrasted are two review lessons of two secondary mathematics student teachers with those of their high school cooperating teachers. Differences between the review lessons were analyzed by interpreting teaching as a complex cognitive skill and as improvisational performance. Expert-novice distinctions are discussed. (KR)

Research of expert-novice differences is reviewed seeking to show experts possess a large body of domain specific knowledge. It was postulated that experts possess schemas enabling them to classify problems, call up the appropriate automated rules, then apply these to obtain the solution. (DC)

Offers calculus students and teachers the opportunity to motivate and discover the first Fundamental Theorem of Calculus (FTC) in an experimental, experiential, inductive, intuitive, vernacular-based manner. Starting from the observation that a distance traveled at a constant speed corresponds to the area inside a rectangle, the FTC is discovered,…

This article, which is organized around a single, well-known algorithm for root extraction, presents a way of incorporating dynamical systems into the teaching of mathematics. Included are sample exercises using complex numbers and the computer where students have the opportunity to do some analysis on this algorithm. (KR)

Various ways in which computers can be used in the classroom depending on the subject, students' background, and individual teaching style are discussed. A way to evaluate professional software packages for use in the classroom is included. (KR)

The programing language PROLOG is compared to LOGO in terms of its ability to handle mathematical ideas. This is demonstrated by using PROLOG in solving a geometric theorem and two lemmas. The listings of the computer programs used to solve the problems are included. (KR)

Discusses the surprising result that the expected number of marbles of one color drawn from a set of marbles of two colors after two draws without replacement is the same as the expected number of that color marble after two draws with replacement. Presents mathematical models to help explain this phenomenon. (MDH)

Discusses a pedagogical approach to calculus based on the question: What kinds of problems should students be able to solve? Includes a discussion of types of problems and curriculum threads for such a course. Describes a projects-based calculus with examples of projects and classroom activities. (Author/MDH)

Problem-solving strategies which use reflective thinking and inference in mathematics are discussed. Examples are provided with discussions of the learning process. The advantages of this approach are stressed. (CW)

New information technologies can act as a Trojan horse offering activities that will require major changes in the teaching-learning process. Computer aided learning applications are able to offer advanced students the opportunity to improve their skills and to maintain their motivation. In the spirit of "learning by doing", they are…