When the author first started teaching twenty years ago, he thought that as long as he was using dynamic geometry software (DGS) for students to "discover" conjectures instead of them learning the conjectures from a lecture or the textbook, he was maximizing their learning potential because they were using technology. Over the years, he…

Twenty-five years of teaching grades 8-12 mathematics has shown the author that students learn best when they can construct their own knowledge (constructivism) and that students, given appropriate guidance, can and will take on responsibility for their own learning (self-regulation theory). This article describes some classroom tools that she has…

In this article, the author presents one instructional strategy--scribing--tailored to the Tablet PC. He illustrates the role of the scribe during discussion through two classroom examples: (1) generalizing the polygon sum theorem; and (2) proving the third angle theorem. Then he analyzes scribing as an instructional strategy as well as students'…

This article describes the A, E, I, O, U technique, designed to help teachers ensure that teaching and learning are not mutually exclusive in the classroom. Most teachers would agree that motivating average teenagers to communicate how they got an answer or justify their problem-solving strategies can be as difficult as teaching a dog to whistle.…

Discusses how to help students avoid some pervasive reasoning errors in solving cumulative percent problems. Discusses the meaning of ."%+b%." the additive inverse of ."%." and other useful applications. Emphasizes the operational aspect of the cumulative percent concept. (KHR)

The students of a Mathematical Modeling and Problem Solving class investigate and explore the mathematics involved in fitting a box spring mattress up a stairwell by solving various optimization problems and by using The Geometer's Sketchpad. The results show that a very small fraction of the class was actually able to solve the problem without…

Illustrates the contrasting thinking processes of two beginning calculus students' geometric and analytic schemes for the derivative function. Suggests that teachers can enhance students' understanding by continuing to demonstrate how different representations of the same mathematical concept provide additional information. (KHR)

Describes a teaching experience through student-centered activities in a second year algebra class with gifted and talented students. Concludes that students learned more mathematics than the teacher originally planned to teach. (KHR)

Examines a root-approximation method using fixed points as a pedagogical tool for reinforcing and expanding students' conception of functions. (KHR)

Presents two examples of using the limitations of calculators to help students understand important mathematical ideas. The first example shows how a simple algebraic calculation can make a recursive model work long enough to perform the job at hand while the second shows how the limitations of a calculator can be used to introduce the need for…

Uses a probability tree to predict the most likely wild card team for a National League Championship. (KHR)

Describes a way of using the extended metaphor of an imaginary airline that bridges the gap between students' work with logic and their creation of proofs. (KHR)

Describes a method for teaching Euler's line, the co-linearity of the circumcenter, centroid, and orthocenter of a triangle. Discusses teaching results. (KHR)

Introduces human graphing by having students standing on certain coordinates instead of points plotted in ink. Includes teacher tips for success and possible graphing explorations. (KHR)

Illustrates ways of using algebra tiles to give students a visual model of competing squares that appear in algebra as well as in higher mathematics. Such visual representations give substance to the symbolic manipulation and give students who do not learn symbolically a way of understanding the underlying concepts of completing the square. (KHR)