Like many commodities, the price of gasoline continues to rise, and these price changes are readily observed in gas stations' signage. Moreover, algebraic methods are well suited to model price change and answer the student's question. Over the course of one ninety-minute block or two forty-five-minute classes, students build functions…

Graphing polar curves typically involves a combination of three traditional techniques, all of which can be time-consuming and tedious. However, an alternative method--graphing the polar function on a rectangular plane--simplifies graphing, increases student understanding of the polar coordinate system, and reinforces graphing techniques learned…

Using technology to explore the coefficients of a quadratic equation can lead to an unexpected result. This article describes an investigation that involves sliders and dynamically linked representations. It guides students to notice the effect that the parameter "a" has on the graphical representation of a quadratic function in the form…

For many the phrase "teaching math online" evokes a vision of teaching and learning that is not based in physical classrooms. Perhaps teachers and students are even interacting asynchronously. In math classrooms in the United States, the increasing availability of devices (e.g. laptops, Chromebooks™, smartphones, and tablets) and…

Inclusion and differentiation--hallmarks of the current educational system--require a paradigm shift in the way that educators run their classrooms. This article enumerates the need for techno-kinesthetic, visually based activities and offers an example of a calculator-based programming activity that addresses that need. After discussing the use…

Card sorting has the potential to provide opportunities for exploration of a variety of topics and levels. In a card-sorting task, each participant is presented with a set of cards--each of which depicts a relationship--and is asked to sort the cards into categories that make sense to him or her. The concept of function is critical to…

When teaching mathematics with technology, the author does so in the belief that technology enables students to experience mathematical ideas in a way that might not otherwise be possible. However, teachers must be careful: Sometimes technology does not produce results in the way that they or their students expect. Rather than allowing unexpected…

Simulation is an important learning tool that allows students to grasp probability concepts, especially when the actual scenario does not need to be replicated entirely. In the cases of tossing coins and rolling dice, gathering the data before analyzing them can be laborious and might be a waste of precious class time--time that might be better…

Students are more likely to develop a deep conceptual understanding of mathematics when they interact with and discuss their thoughts with others. The National Council of Teachers of Mathematics (NCTM) (1989, 2000) has recommended that students be active learners--communicating with one another, conjecturing, exploring, and justifying claims by…

In this article, the authors discuss the importance of unexpected graphs as a vehicle for encouraging critical classroom dialogue. By examining such graphs more critically, teachers and their students can reexamine beliefs about the authority of technology in their classrooms. (Contains 15 figures.)

Constant feature is the calculator's feature to add subtract, multiply or divide the same number more than once without entering it each time. Application of the power of the constant feature to consumer mathematics, probability and iterative processes with problem solving implications are discussed.

This article illustrates the fact that unless tempered by algebraic reasoning, a graphing calculator can lead one to erroneous conclusions. It also demonstrates that some problems can be solved by combining technology with algebra.

Describes the results of a teacher's exploration of the effects of using graphing calculators in calculus instruction in sections other than those that are experimental. Two experimental and two traditional sections of Calculus I and II participated in the study. (DDR)

Discusses the behavior of functions under reciprocal mappings, focusing on the horizontal reciprocal transformation. Offers suggestions for using the graphing calculator, for extending the concepts, and for teaching about reciprocal mappings. (JRH)

Some tips that combine knowledge of mathematics history and technology for adapting Ferrar's method to factor quintics with a TI-83 graphing calculator are presented. A demonstration on the use of the root finder and regression capabilities of the graphing calculator are presented, so that the tips can be easily adapted for any graphing calculator…