A nonconventional graphical way to represent functions (the Parallel Axes Representation) is discussed. A computerized environment designed to support the exploration of the representation of linear functions is described. The didactical potential of this representation is illustrated. (CW)

Presents an example of a proof to the mathematical problem of the sum of the cubes of the digits. Provides a Pascal program to search for these results. (MVL)

Discusses using the computer to promote versatile learning of higher order concepts in algebra and calculus. Generic organizers, generic difficulties, and differences between mathematical and cognitive approaches are considered. (YP)

Describes several phenomena in which interesting properties of numbers are demonstrated. Includes discussions of amicable, perfect, and sociable numbers. Presents computer programs for conducting a number chain search. (RT)

Shows that graphs can reveal much about feedback systems that formula conceal, especially as microcomputers can provide complex graphs presented as animations and allow students to interact easily with them. Describes feedback systems, evolution of the system, and phase diagram. (YP)

Use of probes and data-logging software to introduce dynamic line graphs to young children in the context of science investigations found this approach facilitated effective use of line graphs as models of relationships between variables. (Author/MKR)

Proposes the use of conceptualization, exploration, and higher-level problem solving in differential equations courses as a replacement for some of the traditional material that can now be delegated to the computer. (MKR)

Describes an experimental course in which the programming language ISETL served as a tool for exploring concepts in abstract algebra, and identifies instructional strategies that facilitate the successful use of ISETL. Offers informal observations regarding the effectiveness of this approach. (13 references) (Author/MKR)

Describes the use of simulation to introduce the bootstrapping technique of creating confidence intervals for the mean, median, and variance. These bootstrap confidence intervals are compared to the traditional confidence intervals for the purpose of analyzing accuracy of the technique. A Minitab program to produce confidence intervals is…

Discusses the vital place of proofs in geometry classes. Argues that, although inductive geometry with computer software certainly makes theorems come alive, proofs lead to insight and understanding that allow students to extend the concepts that they see in examples. Presents a theorem, its proof, and a computer exercise. (ASK)

Describes how to customize standard computer-software programs for use with elementary school students. Explains language-arts projects, especially the use of word processing; discusses children's procedures and attitudes; and describes the use of a draw program to create customized learning processes, particularly with mathematics. (LRW)

Argues that basic components of discrete mathematics can be introduced to students through gradual elaboration of experiences with iconic spreadsheet-based simulations of concrete materials. Suggests that the study of homogeneous and heterogeneous patterns of manipulative spreadsheet templates allows for appreciation of the development of…

Presents activities on problem solving, mathematical induction, proof by induction, and use of the phrase "without loss of generality." Provides a computer application illustrating recursive and iterative functions using C language. (ASK)

A series of computer tutorials provide opportunities for education students in an elementary-mathematics-methods course to explore a topic in depth. Tutorials cover content discussed in class and offer classroom situations for student response and reflection. At the end of each tutorial, students have a choice of assignments to complete in…

Provides a conceptual framework that can be used by teachers to analyze student responses that incorporates learning technologies. Introduces an assessment task on exponential functions that illustrates how the rubric can be used to identify an individual's level of performance. (ASK)