A problem involving the search for an equivalence class of triangles is viewed to provide several exciting and satisfying moments of insight. After solving the original problem, there is a brief discussion of a slight variation and several notes regarding related theorems and ideas. References for additional exploration are provided. (MP)

Several activities that can be used to give children more experience with triangles are submitted. By handling triangular shapes and building triangles with strips, pupils can experience a diversity of triangles in a very concrete way. Examination of triangles and nontriangles can help develop understandings of some inequalities. (MP)

Presents a five lesson unit at the fifth grade level to teach the geometric concept of similarity using manipulative materials and multiple representations. The summary presents rationale for teaching and classroom management decisions. (MDH)

This submission contains the Proceedings of the 2011 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at Memorial University of Newfoundland in St. John's, Newfoundland. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning.…

Achievement in mathematics is an issue of great concern not only to students and parents but also to employers and researchers in Kenya. This is because the Kenya National Examination Council (KNEC) has continuously reported dismal results in this area, and especially in geometry. Also, KNEC indicates that it presents difficulties to both the…

In this article, I model how a problem-posing framework can be used to enhance our abilities to systematically generate mathematical problems by modifying the attributes of a given problem. The problem-posing model calls for the application of the following fundamental mathematical processes: proving, reversing, specializing, generalizing, and…

This paper, the second of a two part article, expands on an idea that appeared in literature in the 1950s to show that by restricting the domain to those complex numbers that map onto real numbers, representations of functions other than the ones in the real plane are obtained. In other words, the well-known curves in the real plane only depict…

Assuming that dynamic features of Dynamic Geometry Software may provide a basic representation of both variation and functional dependency, and taking the Vygotskian perspective of semiotic mediation, a teaching experiment was designed with the aim of introducing students to the idea of function. This paper focuses on the use of the Trace tool and…

Proof is a fundamental aspect of mathematics. Without the notion of proof, mathematics would not exist as a separate subject, as it would be essentially indistinguishable from science. Yet proof is often reserved for "high ability" students in schools or those studying mathematics in further education. The author's own memories of…

This article presents a rich geometry problem and discusses its solution. A variety of mathematically correct justifications for this answer are provided. (Contains 2 figures.)

The general factor of mental ability ("g") may reflect general biological fitness. If so, "g"-loaded measures such as Raven's progressive matrices should be related to morphological measures of fitness such as fluctuating asymmetry (FA: left-right asymmetry of a set of typically left-right symmetrical body traits such as finger…

This paper provides students with many interesting observations regarding the nature of magic squares, magic rectangles, and quasi-magic squares and provides tools for teachers to group students into ability-balanced cooperative learning groups.

The Math Forum is an online resource center for pre-algebra, algebra, geometry and pre-calculus. Its Virtual Math Teams (VMT) service provides an integrated web-based environment for small teams of people to discuss math and to work collaboratively on math problems or explore interesting mathematical micro-worlds together. The VMT Project studies…

How can the secondary Geometry course serve as an opportunity for students to learn to "be like" a mathematician--that is, to acquire a mathematical sensibility? In the first part of this dissertation, I investigate what might be meant by "mathematical sensibility". By analyzing narratives of mathematicians and their work, I identify a collection…

A teacher narrates from activities and discussions that arose among undergraduates and herself while doing critical explorations of mirrors. Surprised by light's behaviors, the students responded with curiosity, losing their dependence on answers as the format of school knowledge. Inadequacies in how participants supposed light works emerged in…