There are diverse ways to construct instructional activities that teachers can use to foster their students' development of mathematical thinking. It is argued that the use of computational tools offers teachers the possibility of designing and exploring mathematical tasks from distinct perspectives that might lead their students to the…

The concept of symmetry is fundamental to mathematics. Arguments and proofs based on symmetry are often aesthetically pleasing because they are subtle and succinct and non-standard. This article uses notions of symmetry to approach the solutions to a broad range of mathematical problems. It responds to Krutetskii's criteria for mathematical…

Presents a cooperative-learning lesson in which high school students visit stations equipped with different tools to establish the midpoint of a Pixy Stix, a brand of candy-filled straw. Provides solutions for two potential stations, suggestions to extend the activity, and two activity worksheets. (MDH)

The author has always been fascinated by the title identity. It's charming and simple, as well as easy to believe after pressing a few calculator keys. Several fine proofs have appeared in the literature, including several proofs without words. His own earlier proof is trigonometric, and he has often been dissatisfied with not being able to…

Building on their knowledge of the three possible outcomes of solving 2x2 systems of equations, students use three-dimensional geometric figures to investigate the eight possible outcomes for solving 3x3 systems of equations.

The current mantra in education is "technology, technology, technology." Many teachers and prospective teachers become frustrated with their lack of knowledge regarding the "appropriate" use of technology in the classroom. Prospective teachers need training in their education to understand how technology can be used "appropriately" in the…

Presents content and approaches for teaching geometry at the K-6 level. By use of the discovery technique, the author demonstrates how various topics can be taught beginning in three-dimensionalspace with the study of solid shapes. The sequence begins with the sorting of solid shapes, is followed by the ordering of solids by size and leads to the…

Examples are given of problems which can be solved pictorially, thus aiding in the general development of geometric intuition and in developing some of the basic ideas of probability. (MP)

Two problem-solving strategies involved in finding the area of a particular square formed on a geoboard are described in detail. (MP)

An example is given of a problem-solving approach by outlining the development of a generalization of the Pythagorean Theorem as applied to points on a unit circle. (MP)

Explores trapezoidal numbers, which are the result of subtracting two triangular numbers. Includes classroom activities involving trapezoidal numbers to help students develop their problem-solving skills. Includes reproducible student worksheets. (MKR)

Defines tessellations as closed geometric shapes that completely cover a surface without gaps or overlaps. Suggests how they can be used in technology class activities. (JOW)

A dynamic program for geometry called Cabri Geometry II is used to examine properties of figures like triangles and make connections with other mathematical ideas like ellipse. The technology tip includes directions for creating such a problem with technology and suggestions for exploring it.

There are four Euclidean centres of a triangle--the circumcentre, the centroid, the incentre and the orthocentre. In this article, the authors prove the following: if the centre is the incentre (resp. orthocentre) then there exists a triangle with given distances of its vertices from its incentre (resp. orthocentre). They also consider uniqueness…

Technology is a powerful tool in assisting students in problem solving by allowing for multiple representations. The vignette offered in this article provides insight into ways to solve open-ended problems using multiple technologies.