Discussion of information and information retrieval focuses on the connection between a calculus defined on channels and information retrieval, and proposes a model of an information retrieval system based on this calculus. Topics include conditionality, situation theory, the flow of information, channel theory, and four principles for an…

Reports on a study on the construction of examples and counter-examples in a college-level calculus course. Verbal and written productions of the students were classified as one of activity, expression, content, and correctness. Finds two types of strategies, global and local. Analysis also distinguishes between "winning" and…

Describes the five-year evolution of a multi-sectioned precalculus course for business and health professions majors at the University of Hartford. Concludes that students have benefited from the revised course that uses the graphing calculator, calculator-based laboratory (CBL), and group work. (ASK)

Explores the practice of one high school teacher who provided students with concrete examples from their physics class to give them a contextually rich environment in which to explore the abstractions of calculus. Indicates that students discovered connections between the physics concepts of position, velocity, and acceleration and the calculus…

Examines first-year university students' (n=630) understanding of fundamental calculus concepts at three South African universities. Identifies several misconceptions underlying students' understanding of calculus concepts. Addresses some of the common errors and misconceptions related to students' understanding of 'limit of a function' and…

To integrate technology into mathematics teaching and learning effectively, teachers could create a technology-based learning environment that provides students with opportunities to experience the process of mathematical investigation. These opportunities range from exploring using mathematical ideas to making and testing conjectures, as well as…

For over a decade mathematics instructors have been using graphing calculators in courses ranging from developmental mathematics (Beginning and Intermediate Algebra) to Calculus and Statistics. One of the key functions that make them so powerful in the teaching and learning process is their ability to find curves of best fit. Instructors may use…

Some of the graphing capabilities of The Geometer's Sketchpad (GSP) in the "Technology Tips" are introduced. The new graphing features of GSP allow teachers to implement the software not only in geometry classrooms but also into their algebra, precalculus and calculus classes.

An evaluation designed to test basic graphical-thinking skills to students entering calculus or applied calculus at American University was given to use the assessment to discover the underlying causes for student's inability to use graphs effectively. The study indicates that graphical representation is not emphasized properly in the curriculum…

Computer algebra systems are frequently used for research. In addition, some instructors have based entire advanced courses around these systems. One benefit is that they allow students to become familiar with the methods of calculus by individual experimentation. However, instructors have generally seen computer algebra systems as unsuitable for…

The authors give a rigorous treatment of the differentiability of the exponential function that uses only differentiable calculus. It can thus make "early transcendental" courses complete.

This paper examines the mathematical work of the French bishop, Nicole Oresme (c. 1323-1382), and his contributions towards the development of the concept of graphing functions and approaches to investigating infinite series. The historical importance and pedagogical value of his work will be considered in the context of an undergraduate course on…

We find infinite series in calculus to be one of the most confusing topics our students encounter. In this note, we look at some issues that our students find difficult or ambiguous involving the Ratio Test, the Root Test, and also the Alternating Series Test. We offer some suggestions and some examples, which could be a supplement to the set of…

The question of how a mathematics student at university-level makes sense of a new mathematical sign, presented to her or him in the form of a definition, is a fundamental problem in mathematics education. Using an analogy with Vygotsky's theory (1986, 1994) of how a child learns a new word, I argue that a learner uses a new mathematical sign both…

We provide a geometric proof of the formula for the sine of the sum of two positive angles whose measures sum to less than [pi]/2. (Contains 1 figure.)