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…

This tutorial presents a geometric proof done by sketch to compose a square or equilateral triangle from four small boards. It then converts the procedure into a series of 12 drawing steps with Geometer's Sketchpad. The complete Geometer's Sketchpad file of this demonstration is located at: http://poncelet.math.nthu.edu.tw/chuan/dissect/2dud.html.…

The computer can be used as a tool to represent and communicate geometric knowledge. With the appropriate software, a geometric diagram can be manipulated through a series of animation that offers more than one particular snapshot as shown in a traditional mathematical text. Geometric constructions with the computer enable the learner to see and…

Shows how an empirical approach to geometry using computer-based dynamic geometry software can create didactic situations in which students require proofs. Reports classroom experiences that show where students felt the need for proof in order to explain phenomena or to convince themselves of counterintuitive results. (Author/MKR)

Describes the use of spreadsheets to discuss mathematical concepts without using algebraic notation. Presents examples using Fibonacci numbers and factorials. (MKR)

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)

Describes investigative choices made and strategies used by students to solve problems in classrooms that provided access to a computer algebra system (CAS). Reports that technology-neutral mathematics questions were attempted by approximately equal numbers of students using CAS and traditional paper and pencil. Reveals that students who used the…

Describes a cooperative effort using telecommunications. Utilizes a potential e-mail dialog between the authors and a secondary mathematics teacher from a rural Kansas community who had heard about the interclass Hexiety project, which allows students to develop a context for their mathematical knowledge, to present ideas about the project. (ASK)

Focuses on how to write clear programs with C++ that are easier to debug and modify. Student programs designed according to these outlined principles will tend to develop more quickly, have less bugs, and be much easier to debug. (ASK)

Discusses some aspects of learning to read the process of the variation in congruence and relate it to the original geometry of the sphere since it touches on more general questions about how models are appropriated and used. Presents a learning episode that implemented projective models for both spherical and hyperbolic geometry in Object Logo.…

Discusses the use of MAPLE, a computer algebra system, to find Chinese pseudoprimes. (MKR)

Illustrates two ways of exploring the properties of cubic polynomials. The first exploration uses a Computer Algebra System (CAS) to help students understand an important part of mathematical history, the discovery of an algorithm to find the roots of a cubic equation. The second exploration states some conditions required for a curve and finds a…

Computer algebra systems have great potential uses, but learning the basic concepts of algebra is itself a mathematical activity. Explores theoretical concepts that may be seen as essential enabling skills for computer algebra systems users. (Author/ASK)

Considers the idea of "intentional knowledge" and the difference in nature between "knowledge" as a construct of society, and 'knowing' as construct of an individual. Discusses how the theory of didactical situations differs from other constructivist theories with regard to the notion of "intentional knowledge." Uses two cases to illustrate the…

Computer animation-simulation models of complex processes and events, which are the method of instruction, can be an effective didactic device. Gaining deeper knowledge about objects modelled helps to plan simulation experiments oriented on processes and events researched. Animation experiments realized on multimedia computers can aid easier…