The article describes the harmonic mean and explores situations for using it. Activities that involve hands-on practice for students are provided. Students learn to recognize which mean, harmonic or arithmetic, is appropriate.

This article describes a way to use color to help students develop formulas for functions that describe growing patterns. (Contains 4 figures.)

The article discusses the use of L-systems, which provide students with a unique method to construct line fractals, including the Koch snowflake, the Sierpinski triangle, and the Harter-Heighway dragon. Applets that use L-system theory offer a graphics tool that promotes geometric reasoning, sparks enthusiasm, and connects to historical themes in…

The article deals with the area of polygons that are inscribed in a given circle. Naturally, the following question arises: Among all n-polygons that are inscribed in a given circle, which one has the biggest area? Intuitively, it may be guessed that is suitable for secondary students, and without any use id calculus, but only using very…

Available research supports a belief that a high-quality mathematics education for high school students cannot be accomplished unless a highly qualified mathematics teacher is in the classroom. This author primarily addresses the need for small, rural schools in Missouri to employ such highly-qualified mathematics teachers, although he also states…

In this article, the author discusses Sudoku--a logic puzzle that has appeared in many newspapers in recent years. In its introductory form it consists of a 9x9 grid in which the digits 1 to 9 inclusive are each to be placed nine times in the 81 separate cells of the grid. Each row and each column may not have any digit repeated. If these were the…

In this article, the author discusses the game of Hex, including its history, strategies and problems. Like all good games, the rules are very simple. Hex is played on a diamond shaped board made up of hexagons. It can be of any size, but an 11x11 board makes for a good game. Two opposite sides of the diamond are labelled "red," the other two…

Teachers all over the world are aware that students struggle with fractional concepts and with elementary algebra. Support for this assertion can be found in a variety of research reports. The National Assessment of Educational Progress (NAEP), a United States report, indicates that students have recurrently demonstrated a lack of proficiency in…

In 1854 the German scientist Zeising claimed that the ratio of a person's height to the height of their navel is in the same ratio as the Golden Ratio ([phi] = 1.62). There is so much hype about the Golden Ratio that it is worth reading an article at http://www.maa.org/devlin/devlin_06_04.html. It explains why some of the more far-fetched ideas…

Several researchers have noted how children's whole number schemes can interfere with their efforts to learn fractions. An Australian study found that children who were successful with the solution of rational number tasks exhibited greater whole number knowledge and more flexible solution strategies. Behr and Post (1988) indicated that children…

A solid understanding of equivalent fractions is considered a steppingstone towards a better understanding of operations with fractions. In this article, 55 rural Australian students' conceptions of equivalent fractions are presented. Data collected included students' responses to a short written test and follow-up interviews with three students…

In this article, the author presents a paper folding activity that can be used for teaching fractions. This activity can be used to describe areas of folded polygons in terms of a standard unit of measure. A paper folding fractions worksheet and its corresponding solutions are also presented in this article. (Contains 2 figures.)

Politicians have used the promise of "back to basics in our schools" as an educational platform for some time now, possibly in recognition that this is something the general population perceives as an issue they might just vote for. In the various positions the author has held, both professional and in community service, she has been required to…

For many children, mathematics is an inherently difficult subject to learn. Between 5 and 8 percent of children between the ages of 6 and 14 have a particular type of cognitive deficiency that limits their aptitude to acquire knowledge and understanding of fundamental ideas in numeracy. Increasingly, researchers in the cognitive sciences are…

Fractions and algebra are critically important components of the mathematics education of the youth. Unfortunately, however, students have typically struggled in these areas. For this reason, teachers and researchers have focused their attention on these topics for at least the past century. This article discusses what research shows regarding…