Context is what makes mathematical modeling tasks different from more traditional textbook word problems. Math problems are sometimes stripped of context as they are worked on. For modeling problems, however, context is important for making sense of the mathematics. The task should be brought back to its real-world context as often as possible. In…

Although research shows that Computer Algebra Systems offer pedagogical opportunities, more than a decade later some teachers are reluctant to change established practices. In 2002, the University of Melbourne in Australia launched a research project to investigate implementation of a senior mathematics course in which students could use a…

Mathematics educators frequently extol the virtues of inquiry-based instruction to classroom teachers. Although research suggests that inquiry benefits learners by allowing them to make sense of the mathematics they encounter, particularly through discourse with peers, to assume that all (or even most) teachers successfully create and implement…

In January 2006 the Billings (Montana) Public Schools adopted a computer-assisted instruction (CAI) intervention aimed at helping students recover credits that they had attempted but had not attained. The author volunteered to teach the algebra component in his high school. Through the following seven semesters, he came to better understand the…

This article describes preparation and delivery of high school mathematics lessons that integrate mathematics and astronomy through The Geometer's Sketchpad models, traditional proof, and inquiry-based activities. The lessons were created by a University of Texas UTeach preservice teacher as part of a project-based field experience in which high…

This article describes explorations using The Geometer's Sketchpad for algebra and calculus content.

With the help of technology and a basic high school algebra method for finding the vertex of a quadratic polynomial, students can develop and prove the formula for least-squares lines. Students are exposed to the power of a computer algebra system to generalize processes they understand and to see deeper patterns in those processes. (Contains 4…

The use of laptops and other technology in teaching and learning of algebra 1 was found to add new dimensions to the way students studied the subject. But all its positives and negatives are still to emerge and students also need to be comfortable using the computer technology.

Describes computer or calculator-graphing technology to develop parametric representations which help students connect mathematical topics from algebra and trigonometry through algebraic, graphical, and numerical representations. Computer or calculator graphing utilities instantly transform algebraic expressions into visual and numerical displays…

Graphs equations in two variables using a BASIC screen-sweep program that generates solutions to equations by applying the intermediate value theorem. Provides suggestions for investigations that result in graphs of a butterfly, the Cheshire cat, the Trisectrix of Catalna, E. T. waving goodbye, a praying mantis, and others. (MDH)

Examples illustrate the use of APL for teaching selected topics from logic, set theory, algebra, number theory, and calculus using the glass box approach. (MP)

Two computer exercises involving the classification of geometric figures are given. The mathematics required is relatively simple but comes from several areas--synthetic geometry, analytic geometry, and linear algebra. (MN)