This article explores how a focus on understanding divisibility rules can be used to help deepen students' understanding of multiplication and division with whole numbers. It is based on research with seven Year 7-8 teachers who were observed teaching a group of students a rule for divisibility by nine. As part of the lesson, students were shown a…

Ten years ago, the author wrote a short piece entitled "Mathematics and numeracy--Is there a difference?". In mathematics, many put an emphasis on the content concepts and skills contained typically in strands such as Algebra, Number, Geometry, etc. Others argued that "mathematics" was about the "search for pattern" and that the key elements of…

Almost every adult in Australia has played Noughts and Crosses at some time in their life--it is that sort of game, a universal classic. Very few Australian adults play Noughts and Crosses, adult against adult, unless they are bored, witless and cannot think of anything better to do. Adults stop playing this game. Many will say it is boring, while…

This article presents a hands-on experiment that covers many areas of high school mathematics. Included are the notions of patterns, proof, triangular numbers and various aspects of problem solving. The problem involves the arrangements of a school of fish using split peas or buttons to represent the fish. (Contains 4 figures.)

This article traces the history of the number [Pi] from 3000 BC (the construction of the Egyptian pyramids) to 2005 (the calculation of the first 200 million digits of Pi).

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.)

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…

For mathematics teachers who are continually looking for ways in which to engage their students in the learning process, the capabilities offered by technology answer the call. Whether the technology comprises computer based applications or graphics calculators, often boring aspects can be bypassed so that students can work on the "good bits" and…

In the Western Gregorian Calendar, the date of Easter Sunday is defined as the Sunday following the ecclesiastical Full Moon that falls on or next after March 21. While the pattern of dates so defined usually repeats each 19 years, there is a 0.08 day difference between the cycles. More accurately, the system has a period of 70 499 183 lunations…

Mathematics is like a language, although technically it is not a natural or informal human language, but a formal, that is, artificially constructed language. Importantly, educators use their natural everyday language to teach the formal language of mathematics. At times, however, instructors encounter problems when the technical words they use,…

This article describes the Australian Informatics Competition (AIC), a non-programming competition aimed at identifying students with potential in programming and algorithmic design. It is the first step in identifying students to represent Australia at the International Olympiad in Informatics. The main aim of the AIC is to increase awareness of…

Ever since the first mariners sailed off the east coast of Scotland the Bell Rock has claimed many vessels and countless lives. Also known as the Inch Cape Rocks they lie 18 km off the coast at Arbroath. Located near the mouth of the Firth of Forth and its important shipping ports these dangerous rocks cover an area some 440 m long and 90 m wide.…

This document shows a different way of adding lists of numbers to find a way of getting general formulae for figurate numbers and use Gauss?s method to check it.