Examines ways in which students can learn about computational discrepancies that arise as a result of a calculator's limited ability to store numbers accurately. Suggests ways in which such discrepancies can be avoided. (Author/NB)

Provides classroom suggestions for combining numerical, algebraic, and geometric techniques with the understanding of a simple method for computing square roots. Historical origins of the method illustrate the debt owed to ancient minds living in what are now India, Pakistan, Iraq, and Egypt. (Author/NB)

Describes how the concept of similar triangles was taught using an optical method of estimating large distances as a corresponding activity. Includes the derivation of a formula to calculate one source of measurement error and is a nice exercise in the use of the properties of similar triangles. (Author/NB)

Describes the entire process involved when an untried problem was presented to a group of teachers. The lessons learned from their struggles are helpful reminders that open-ended problems should be presented to high school students. (Author/NB)

Poses the question, How can one find a polynomial function that agrees with a given input-output table? Describes one method that leads to some interesting mathematics. (Author/NB)

Concludes that writing about the executive processes of problem solving, difficulties encountered, alternative strategies that might have been used, and the problem solving process in general helped students in the treatment group learn to use executive processes more quickly and more effectively than students in the control group. (Author/NB)

Explores the use of a study group as a form of professional development for high school mathematics teachers. (Author/NB)

Explains how conic sections can be approximated by paper-folding activities and proves why they work. (Author/NB)

Uses cryptography to demonstrate the importance of algebra and the use of technology as an effective real application of mathematics. Explains simple encoding and decoding of messages for student learning of modular arithmetic. This elementary encounter with cryptography along with its historical and modern background serves to motivate student…

Ever since the first mariners sailed off the east coast of Scotland the Bell Rock has claimed many vessels and countless lives. Also known as the Inch Cape Rocks they lie 18 km off the coast at Arbroath. Located near the mouth of the Firth of Forth and its important shipping ports these dangerous rocks cover an area some 440 m long and 90 m wide.…

For many years I have been advocating the use of hands-on materials to assist students in the understanding and application of mathematical concepts. Some of the methods have been introduced as small parts of earlier Discovery articles, (de Mestre, 1994, 1996, 1998, 1999a, 1999b, 1999c, 2000a, 2000b, 2001), but here I propose to devote the whole…

This document shows a different way of adding lists of numbers to find a way of getting general formulae for figurate numbers and use Gauss?s method to check it.

This article describes sound waves, their basis in the sine curve, Fourier's theorem of infinite series, the fractal equation and its application to the composition of music, together with algorithms (such as those employed by meteorologist Edward Lorenz in his discovery of chaos theory) that are now being used to compose fractal music on…

The focus of this article is on Australian teachers' and pre-service teachers' gendered beliefs about their students and about computer use for mathematics learning. To illustrate what is happening in these areas, I will draw on results from two studies in which I have been engaged in recent years. I will also present the findings from other…

According to Kilpatrick (1987), in the mathematics classrooms problem posing can be applied as a "goal" or as a means of instruction. Using problem posing as a goal of instruction involves asking students to respond to a range of problem-posing prompts. The main goal of this article is a classification of mathematics questions created by Years 8…