The purpose of this article is to offer teaching ideas in the treatment of the definite integral concept and the Riemann sums in a technology-supported environment. Specifically, the article offers teaching ideas and activities for classroom for the numerical methods of approximating a definite integral via left- and right-hand Riemann sums, along…

This study addresses the embodied approach of convergence of numerical sequences using the GeoGebra software. We discuss activities that were applied in regular calculus classes, as a part of a research which used a qualitative methodology and aimed to identify contributions of the development of activities based on the embodiment of concepts,…

We introduce a new open source (free) software package that provides a simple, highly interactive interface for carrying out certain mathematical tasks that are commonly encountered in physics. These tasks include plotting and animating functions, solving systems of coupled algebraic equations, and basic calculus (differentiating and integrating…

This study investigates 3 preservice secondary mathematics teachers' understandings of limits of sequences and their changing conceptions of limit during and after instruction involving interactive, dynamic sketches embodying the formal definition of the limit of a sequence. Manipulating a coherent visual representation of the formal definition in…

A summer bridge program for incoming engineering and computer science freshmen has been used at the University of Wisconsin-Milwaukee from 2007 to 2010. The primary purpose of this program has been to improve the mathematics course placement for incoming students who initially place into a course below Calculus I on the math placement examination.…

In 1999, Richard Lee Colvin published an article in "The School Administrator" titled "Math Wars: Tradition vs. Real-World Applications" that described the pendulum swing of mathematics education reform. On one side are those who advocate for computational fluency, with a step-by-step emphasis on numbers and skills and the…

The study of a real function of two real variables can be supported by visualisation using a Computer Algebra System (CAS). One type of constraint of the system is due to the algorithms implemented, yielding continuous approximations of the given function by interpolation. This often masks discontinuities of the given function and can provide very…

A program that can reduce difficult integration problems to simpler approximations using the trapezoidal rule to approximate the area under a curve is presented. (MP)

In this paper, a didactical proposal is presented to introduce the variational methods for solving boundary value problems to engineering students. Starting from a couple of simple models arising in linear elasticity and heat diffusion, the concept of weak solution for these models is motivated and the existence, uniqueness and continuous…

Presented are reviews of several microcomputer software programs. Included are reviews of: (1) Microstat (Zenith); (2) MathCAD (MathSoft); (3) Discrete Mathematics (True Basic); (4) CALCULUS (True Basic); (5) Linear-Kit (John Wiley); and (6) Geometry Sensei (Broderbund). (RH)

This correlation study examined the relationship between gender and the students' attitude and prior knowledge of using one of the mathematical software programs (MATLAB). Participants were selected from one community college, one state university and one private college. Students were volunteers from three Calculus I classrooms (one class from…

Investigates using computer spreadsheets in math classes. Describes current spreadsheets on the market. Summarizes how the spreadsheets work and provides information to build a template to find function maximums and minimums. Lists step by step instructions. (MVL)

Illustrates three examples usually delayed until sufficient terminology, concepts, and methods have been developed unless using calculators or computers. The three examples are on exponential growth, triangle construction, and end behavior of certain function. Discusses the advantages of technology-enhanced mathematics teaching. (YP)

Illustrates how muMATH can be used for manipulating abstract differentiation rules, optimization, implicit differentiation, related rules, and verifying the chain rule. (MVL)

Notes muMATH is a powerful computer algebra systems assistant for performing symbol manipulation in algebra and calculus. Provides several examples and program listings for calculus tutoring, differentiation drill problems, and integration drill problems. (MVL)