Background/purpose: In modern mathematical education, it is important to develop students' ability to understand the fundamental properties of geometric objects deeply. This makes it relevant to study the additivity of the area of triangles as a property inherent in various kinds of quantities and ways of representing it methodologically in the…

This article uses dynamic software in Excel to demonstrate several ways in which graphical and numerical approaches can be introduced both to enhance student understanding of l'Hopital's Rule and to explain why the Rule actually works to give the "right" answers. One of the approaches used is to visualize what is happening by examining…

Dynamic geometry software (DGS), such as Geometer's Sketchpad[TM], Cabri Geometry[TM], and GeoGebra[TM] has become a widely used classroom technology. The broad availability of DGS has given students the opportunity to engage in many aspects of reasoning and proof, including exploration, conjecture development, and proof, in its many roles. By…

Formal requests were recently introduced for integration of ICT in secondary school mathematics. As the main issue, students must develop competence to decide when and how it is appropriate to use available ICT tools and to use them. These new requests put demands on those teachers who have not developed corresponding competencies themselves.…

MATLAB is a powerful package for numerical computation. MATLAB contains a rich pool of mathematical functions and provides flexible plotting functions for illustrating mathematical solutions. The course of calculus-based business mathematics consists of two major topics: 1) derivative and its applications in business; and 2) integration and its…

This note takes up the issue of parallel curves while illustrating the utility of "Mathematica" in computations. This work complements results presented earlier. The presented treatment, considering the more general case of parametric curves, provides an analysis of the appearance of cusp singularities, and emphasizes the utility of symbolic…

This note describes a method for evaluating the sums of the m -th powers of n consecutive terms of a general arithmetic sequence: { S[subscript m] = 0, 1, 2,...}. The method is based on the use of a differential operator that is repeatedly applied to a generating function. A known linear recurrence is then obtained and the m-th sum, S[subscript…

This computer software program helps to make classroom worksheets, take home assignments, and school mathematics tests easy to design and manufacture. The accompanying printed teaching guide provides technical information for setting up and using the program, along with sample worksheets and instructions on how to create them using the software.…

This article discusses the impact of symbolic-manipulation systems on secondary school mathematics curriculum. Characteristics and possible roles for the symbolic systems are explored. Four references are listed. (YP)

"Learning by doing" in pursuit of real-world goals has received much attention from education researchers but has been unevenly supported by mathematics education software at the elementary level, particularly as it involves arithmetic word problems. In this article, we give examples of doing-oriented tools that might promote children's ability to…

Compares two methods of approaching problem solving in quantitative disciplines. The danger of looking at answers too quickly is discussed. (YP)

Discusses a student project visualizing the surface of a function using computer graphics. Describes topics to complete the project, function and its domain, scaling, coordinate axes, projection of the surface, sketching the graph, plotting, changing the viewpoint, and rotating the axes. Provides a BASIC program using the rotation of the axes and…

This article illustrates that mathematical theory can be incorporated into the process to solve differential equations by a computer algebra system, muMATH. After an introduction to functions of muMATH, several short programs for enhancing the capabilities of the system are discussed. Listed are six references. (YP)

Described is a computer algebra system that can be used to help students understand the calculus. Provides several examples of solving calculus problems using muMATH. Lists eight references. (YP)