Dynamic/interactive graphing applets can be used to supplement standard computer algebra systems such as Maple, Mathematica, Derive, or TI calculators, in courses such as Calculus, Differential Equations, and Dynamical Systems. The addition of this type of software can lead to discovery learning, with students developing their own conjectures, and…

The author and his first-year algebra students explored the quadratic behavior behind the parabolic shape of fountains at the local family splash park. This hands-on discovery project has three main parts: (1) gathering data by experimenting with and photographing the fountains; (2) analyzing the photographs to obtain numerical data; and (3)…

Illustrates exploration of composition of functions, translations, and inverse functions on a graphing calculator. Includes reproducible student worksheets. (MKR)

Calculators are seen to shift the student focus in problem-solving situations from "how to do it" to "what to do," by keeping computation from standing in the way when pupils write or solve problems. (MP)

Worksheets designed to help students explore factoring integers are presented. (MP)

Using De Moivre's theorem and a parametric graphing utility, examines powers and roots of complex numbers and allows students to establish connections between the visual and numerical representations of complex numbers. Provides a program to numerically verify the roots of complex numbers. (MDH)

A sample problem shows some pitfalls in approximating square roots when working with calculators or computers. (MP)

The calculator is used to help students discover the Rule of 72 which is, in turn, used to investigate problems involving population, inflation, and energy reserves. (MP)

An exploration approach with calculators that promotes student investigation and development of mathematical processes and concepts is highlighted. The presentation helps to highlight the enormous potential of calculators to facilitate new and imaginative approaches to certain areas of number work, and shows how student interest is promoted. (MP)

Some functions on digits of positive integers are presented as possible sources for useful investigations by students, particularly through the use of calculators and computers or in the writing of small proofs. The material is designed to encourage students to conduct their own investigations. (MP)

An example of a lesson involving calculators that focused on calculator use is given. An examination of the traditional algorithm by the students led to student-directed investigations. (MP)

Three examples are given illustrating the use of the calculator in problems where determining patterns and making conjectures are stressed. (MP)

These exercises are designed to expose students to the nature and effects of inflation and consumption rates. Pupils are expected to see how long it takes for costs to increase to certain levels, and how quickly various growth rates can deplete a finite resource. Worksheets suitable for duplication are provided. (MP)

This discussion of cyclic patterns that appear in repeating decimals includes the use of the calculator in discovering the patterns. (MP)

Calculators that have the constant arithmetic feature are promoted, and examples of ways this feature can be used in lessons are presented. (MP)