Many students view mathematics as a collection of theorems and facts that were discovered by intelligent mathematicians and all they have left to do is to study them carefully. Some believe it is important to help students change this view (Lavy & Shriki, 2003). One possible way is to enable students to modify the attributes of a given situation,…

Here we give an example of a problem that could be beneficially investigated by AS/A level students. It is a geometry problem that they can profitably tackle by geometric (especially geometry software) and algebraic means. Such problems naturally lead students to the need for proof--an essential part of mathematics that is often lacking in current…

In this article, the author describes two Powerpoint presentations designed to help visual learners calculate the circumference and the area of a circle. In particular, the author describes how these presentations can be used to establish mental images that can help pupils to understand, and so recall, the principles that underlie the formulae for…

This paper discusses the use of geometry and proportional reasoning techniques used at the United States Department of Agriculture by two of its branches: the Farm Service Agency and the Natural Resources Conservation Service. This paper discusses the agricultural agency and two branches involved, details a seven-lesson geometry module for high…

Todd Lee and colleagues share some of the common technology "pranks" and peculiarities from the three most common technology tools used in our classrooms: Microsoft Excel, graphing calculators, and The Geometer's Sketchpad. The "Surfing Note" includes a link to a collection of funny math cartoons from the Carolina Biological Supply Company.

This note considers the four classes of orthogonal polynomials--Chebyshev, Hermite, Laguerre, Legendre--and investigates the Gibbs phenomenon at a jump discontinuity for the corresponding orthogonal polynomial series expansions. The perhaps unexpected thing is that the Gibbs constant that arises for each class of polynomials appears to be the same…

A 3-by-5 card is used to represent two or more sets of parallel lines, four right angles, opposite sides congruent and to investigate the Pythagorean theorem, similar triangles, and the tangent ratio before the introduction of computers. Students were asked to draw two parallel lines, cross them with a transversal and label the angles, which…

Graphic tips for using the Geometer's Sketchpad (GSP) are described. The methods to import an image into GSP, define a coordinate system, plot points and curve fit the function using a graphical calculator are demonstrated where the graphic features of GSP allow teachers to expand the use of the technology application beyond the classroom.

In this article we describe a hands-on activity for a liberal arts mathematics course that focuses on the beauty and unity of mathematics. The purpose of the activity is to tie together several topics in the context of a "real-world" situation. These topics include: fractals, non-Euclidean geometry, symmetry, and Platonic solids. This activity…

Jean Louis Nicolet is a Swiss teacher of mathematics who found his subject so fascinating that he was puzzled as to why so many pupils could not share this enjoyment in their studies. He came to a conclusion which is now supported by the results of psychological research into the learning process: he suggested that the mind does not spontaneously…

In this study of deaf high school students, imagery and familiarity were found to be the best predictors of geometry word recall, whereas neither concreteness nor signability of the terms was a significant predictor variable. Recall of high imagery terms was significantly better than for low imagery terms, and the same result was found for high-…

In this article, the author investigates effective teaching and learning of geometrical concepts using dynamic geometry software (DGS). Based from her students' reactions to her project, the author found that her students' understanding of the concepts was better than if they had learned geometry through paper-based tasks. However, mixing computer…

This paper sits within the research on the affordances of new technologies in the mathematics classroom and focuses on a specific feature that is available in dynamic geometry environments, i.e. measuring tools, within the context of conjecturing and proving in open geometry problems. We develop a classification of different modalities of…

The "Test Development Notebook" is a resource designed for the preparation of tests of literal comprehension for students in grades 1 through 12. This volume contains 200 multiple-choice cloze exercises taken from textbooks in mathematics, and the accompanying answer key. Each exercise carries the code letter of the section to which it belongs.…

Because of the pressure to increase test scores in reading and mathematics, content areas such as social studies are being eliminated from many elementary schools' curricula. It is critical that teachers find ways to integrate social studies into reading and mathematics. Social studies and mathematics may not immediately come to mind when…