We present an investigation of the infinite sequences of numbers formed by calculating the pairwise averages of three given numbers. The problem has an interesting geometric interpretation related to the sequence of triangles with equal perimeters which tend to an equilateral triangle. Investigative activities of the problem are carried out in…

A bachelor's degree program in chemistry typically starts with basic concepts in mathematics, physics, and chemistry. Those principles are very important because they pave the ground for future advanced studies and, therefore, one needs to present them in a clear but rigorous way. One example is provided by the mathematical notion of an iterative…

This article is written to share teaching ideas about using commonly available computer applications--a spreadsheet, "The Geometer's Sketchpad", and "Wolfram Alpha"--to explore three classic and historically significant problems from the probability theory. These ideas stem from the authors' work with prospective economists,…

Mathematics educators frequently extol the virtues of inquiry-based instruction to classroom teachers. Although research suggests that inquiry benefits learners by allowing them to make sense of the mathematics they encounter, particularly through discourse with peers, to assume that all (or even most) teachers successfully create and implement…

This collection of 58 articles from the recently-published third edition of the International Encyclopedia of Education focuses on learning, memory, attention, problem solving, concept formation, and language. Learning and cognition is the foundation of cognitive psychology and encompasses many topics including attention, memory, categorization,…

The requirement for a method of capturing problem solving on a whiteboard for later replay stems from my teaching load, which includes two classes of first-year university general physics, each with relatively large class sizes of approximately 80-100 students. Most university-level teachers value one-to-one interaction with the students and find…

The current generation of students coming into food science and engineering programs is very visually oriented from their early experiences. To increase their interest in learning, new and visually appealing teaching materials need to be developed. Two diverse groups of students may be identified based on their math skills. Food science students…

We consider two different algebra topics that can be taught in a typical college class. With each topic, we demonstrate how a teacher can delve deeper using a computer algebra system.

Science centers can engage students; accommodate different learning styles and individual interests; help students become independent and confident learners; and encourage social skills among students. In this article, the author worked with third-grade students as they completed activities at learning centers during a week-long unit on simple…

Four- and 5-year-olds' understanding of basic turtle graphics commands was examined before and after a hands-on, interactive problem-solving experience. Children (n=32) saw display screen events consisting of an initial turtle state, a command transformation, and the resulting turtle state. They were asked to give the command executed in each…

Since LOGO was introduced at a 1981 National Council of Teachers of Mathematics conference, this computer language has spread through the schools and spawned Young People's LOGO Association groups throughout the United States and Canada. Teaching LOGO like other languages might alienate youngsters already at home with computer technology. (MLH)

Outlines a problem-solving method for beginning chemistry students that utilizes specific, concrete steps as well as computer-assisted tutorials. The method involves an approach referred to as the Factor-Unit Method coupled with a graphical "road map" which allows students to trace problems from start to finish. (JN)

Describes the current status and limitations of expert systems, and explores the possible applications of such systems in education and training. The use of expert systems as tutors, as job aids, and as a vehicle for students to develop their own expert systems on specific topics are discussed. (40 references) (CLB)

Described is an experience in assigning mathematics problems that have been purposefully selected from professional journals to assist upper level college mathematics students in developing confidence in their ability to contribute published solutions. Several examples are included. (JJK)

Five ways the computer can be used in psychology courses to teach thinking are described: using the computer to replace things that already work (e.g., a tachistoscope); programing the computer; simulating specialized procedures and situations; providing behavior to be observed and described; and posing problems for analysis and solution. (RM)