Pascal's Triangle is, without question, the most well-known triangular array of numbers in all of mathematics. A well-known algorithm for constructing Pascal's Triangle is based on the following two observations. The outer edges of the triangle consist of all 1's. Each number not lying on the outer edges is the sum of the two numbers above it in…

Math can sometimes seem like a strange language from foreign land--one communicated in symbols, numbers, and geometric figures. When teachers talk about mathematical concepts, even familiar, garden variety words such as "parallel," "power," "even," "odd," "multiply," "difference," "product," "positive," and "negative" take on brand-new meanings.…

The author discusses the historical development of the thermometer with the view of helping children understand the role that mathematics plays in society. A model thermometer that is divided into three sections, each displaying one of the three temperature scales used today (Fahrenheit, Celsius and Kelvin) is highlighted as a project to allow…

Three activities are presented that are designed to develop an understanding of equivalence. Equivalent fractions have the same value, but may be expressed with a different denominator or different notation. "Decimal Fraction Dominoes" focuses on the equivalence of commonly occurring fractions, decimal fractions, percentages and their…

This article examines the mathematics underlying the construction of perspective images of three-dimensional objects. Through hands-on applications and the use of standard secondary content, the article presents perspective art in a away that is accessible to secondary teachers and their students.

This study reports on how students can be led to make meaningful connections between such structures on a set as a partition, the set of equivalence classes determined by an equivalence relation and the fiber structure of a function on that set (i.e., the set of preimages of all sets {b} for b in the range of the function). In this paper, I first…

This note introduces an interesting random walk on a straight path with cards of random numbers. The method of recurrent relations is used to obtain the convergent probability of the random walk with different initial positions.

A simple proof to some known results on the convergence of linear recursive sequences with nonnegative coefficients is given, using the technique of monotone convergence.

This article compares first-year university students' development of the concept of limits to mathematicians' historical development of the concept. The aim was to find out if students perceive the notion as mathematicians of the past did, as understandings of the concept evolved. The results imply that there are some similarities--for example,…

This submission contains the Proceedings of the 2009 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at York University in Toronto, Ontario. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims of the Study Group…

Conventional testing systems usually give students a score as their test result, but do not show them how to improve their learning performance. Researchers have indicated that students would benefit more if individual learning guidance could be provided. However, most of the existing learning diagnosis models ignore the fact that one concept…

Elementary school students often misinterpret the equal sign (=) as an operational rather than a relational symbol. Such misunderstanding is problematic because solving equations with missing numbers may be important for the development of higher order mathematics skills, including solving word problems. Research indicates equal-sign instruction…

This article focuses on the important role of applications in teaching mathematics to students with career paths other than mathematics. These include the fields as diverse as education, engineering, business, and life sciences. Particular attention is given to instructional computing as a means for concept development in mathematics education…

Many preservice teachers report having had little exposure on the use of technology in the teaching and learning of mathematics. Without guidance on the appropriate use of technology, prospective teachers are left to form their own beliefs about what is appropriate technology use. This study assessed preservice teacher beliefs and conceptions of…

This article examines 9-11 year olds' attempts to beat the computer at a game of strategy and asks how far and under what circumstances they developed a strategic approach to the game. Extracts from videotape transcripts are analysed to reveal the components of children's particular approaches, evident even amongst children who did not develop an…