The exploration of number patterns as a pedagogical approach to introducing algebra has been advocated by many mathematics educators. French (2002) comments that the introduction of algebra through what is potentially a wide range of pattern generalisation activities may be effective in assisting pupils to see algebra as both meaningful and…

Over the past four decades, gender differences in mathematics learning have continued to attract attention from both the research and broader communities, in Australia and internationally. In this article, the authors briefly summarise key and persistent findings. They argue that the findings warrant a further investigation of the performance in…

"Research studies show that when students discover mathematical ideas and invent mathematical procedures, they have a stronger conceptual understanding of connections between mathematical ideas." Flewelling and Higginson state that inquiry, investigations, and problem solving "give students the opportunity to use their imagination and to get into…

Teacher professionalism is a social construct which varies across time and place. In relation to the teaching of mathematics in the middle school, professionalism is a concept under siege; with the advent of national testing some teachers predict dire consequences for student learning. In this small research project several teachers depicted their…

Pattern generalising problems offer a very rich context for exploring relationships among quantities, expressing generality and representing the same relationship in different ways. Selecting appropriate tasks for students to work on in class is by no means a straightforward process, but there are ways to handle it. This article aims to explore…

Inquiries into the state of mathematics and science education in Australia express the need to make the curriculum more relevant and meaningful to students' lives. However, such a vision requires that teachers understand how relevance can enter mathematics and science classrooms in meaningful and appropriate ways. This paper uses snippets from…

According to this author, the solution to the "phonics versus whole language" debate over the teaching of reading is balance and a focus on the needs of all students. There is similarly a need, in developing numerate young people, to focus on the teaching and learning of mathematics and mathematics skills some of the time, and on application and…

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.…

For many years I have been advocating the use of hands-on materials to assist students in the understanding and application of mathematical concepts. Some of the methods have been introduced as small parts of earlier Discovery articles, (de Mestre, 1994, 1996, 1998, 1999a, 1999b, 1999c, 2000a, 2000b, 2001), but here I propose to devote the whole…

This paper investigates some aspects of number patterns that have been a subject of interest and engaged students of mathematics for many years. It is left for the teacher to select and fashion any aspects they feel suit their own students.

A renovation of school buildings at Rosetta High School, in the northern suburbs of Hobart, Tasmania, has provided an opportunity for students to use a real life context to develop and apply mathematical understanding. This has led to students achieving educational outcomes for the Essential Learnings (ELs) curriculum that affirm the role of…

In this article the author presents readers with some very useful activities, ideas and problems. He has used these at various times over the years and together they make a very interesting collection. These pieces have come together from different sources, but like a jigsaw, they complete the picture of understanding of the numbers inside the…

For the last three years the author of this paper has been teaching mathematics to a group of students at Year 9 level who have rarely had success in mathematics, particularly in the area of algebra. Most of these students struggle with algebraic concepts and processes and generally have poor retention of any acquired knowledge. For the two years…

The problem considered in this paper demonstrates that quite profound and inherently fascinating mathematics is accessible to students who have a sound number sense and deep conceptual understanding of very basic mathematics. This is one of many reasons why we should teach mathematics in ways that promote these attributes in students.

One section of this "scrapbook" section describes Pythagoras' belief in the connections between music and mathematics -- that everything in the universe was a series of harmonies and regulated by music. Another section explains why Phythagoras felt it important for women to be encouraged to learn mathematics. At least 28 women were involved in his…