In a classroom environment in which continual access to graphing calculators is assumed, items that have been used to assess students' understanding of functions often are no longer appropriate. Describes strategies for modifying such items including requiring students to explain their reasoning, using calculator-active items, analyzing graphs and…

Past research has shown that many scientists, when asked to interpret unfamiliar graphs that have nevertheless been culled from introductory undergraduate courses in their own field, experience problems and cannot give the standard answer accepted in the field. Yet, these same scientists turn out to be highly competent when it comes to graphs from…

An activity which stresses on identifying features of functions like the rate of change, intercepts, local and global behavior, zeros and asymptotes is designed to increase the level of understanding of the students and also to clear any doubts that they might have. The students are then asked to make a summary of what was discussed in the class,…

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…

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…

This paper presents a visual representation of complex solutions of quadratic equations in the xy plane. Rather than moving to the complex plane, students are able to experience a geometric interpretation of the solutions in the xy plane. I am also working on these types of representations with higher order polynomials with some success.

Within statistics instruction, students are often requested to sketch the curve representing a normal distribution with a given mean and standard deviation. Unfortunately, these sketches are often notoriously imprecise. Poor sketches are usually the result of missing mathematical knowledge. This paper considers relationships which exist among…

An integral, either definite or improper, cannot always be computed by elementary methods, such as reversed usage of differentiation formulae. Graphical properties, in particular symmetries, can be useful to compute the integral, via an auxiliary computation. We present graded examples, then prove a general result. (Contains 4 figures.)

One of the units of in a standard differential equations course is a discussion of the oscillatory motion of a spring and the associated material on forcing functions and resonance. During the presentation on practical resonance, the instructor may tell students that it is similar to when they take their siblings to the playground and help them on…

It is shown that the well-known Lorentz formula for time dilation can be derived from a distance-time graph plotted for a spaceship communicating with Earth.

Inscriptions are central to the practice of science. Previous studies showed, however, that preservice teachers even those with undergraduate degrees in science, generally do not spontaneously produce inscriptions that economically summarize large amounts of data. This study was designed to investigate the production of inscription while a group…

Research findings show the difficulties younger students have in working with graphs. Higher mental operations are necessary for a skilled interpretation of abstract representations. We suggest connecting a concrete representation of the modeled problem with the related graph. The idea is to illustrate essential mental operations externally. This…

We describe a computer tutorial that introduces the concept of the steady state in enzyme kinetics. The tutorial allows students to produce graphs of the concentrations of free enzyme, enzyme-substrate complex, and product versus time in order to learn about the approach to steady state. By using a range of substrate concentrations and rate…

This booklet contains a representative sample of the efforts of colleagues at 11 institutions to use graphing calculators to enhance the teaching of calculus and precalculus. The first section contains examples of graphs for teachers to choose from for presentations, including: simple examples to illustrate some standard ideas in precalculus,…