Not so long ago, the common response of teachers to high school use of computer algebra systems (CAS) was invariably along the lines of, "What will be left to teach if our students have access to devices which solve, factorise, do calculus and more?" and "If students use such tools, then they will never learn how to do their mathematics, and their…

Implementing best practices like cooperative learning, using concrete manipulatives, problem solving, technology, active learning, multi-age grouping, and team teaching have shown benefits for students when learning mathematics concepts within the curriculum (Zemelman, Daniels & Hyde, 1998; NCTM, 2000). What started as a professional development…

The history of mathematics is full of rich examples that can help students to see the place of the discipline within our cultural heritage. Valuable as this can be, it also has the unfortunate side-effect of making students think that all the math has already been done and they do not get a sense that the subject is dynamic and growing.…

John Napier was born in 1550 in the Tower of Merchiston, near Edinburgh, Scotland. Napier's work on logarithms greatly influenced the work that was to be done in the future. The logarithm's ability to simplify calculations meant that Kepler and many others were able to find the relationships and formulas for motion of bodies. In turn, Kepler's…

Calculus is a mathematical concept that is fundamental to how we understand the world around us. Whether it is in the world of technology, finance, astronomy, sociology, medicine, calculus in one form or another can be found. This brief article describes the origins of calculus in Greece, further developments by Newton and Leibniz, and the…

In this paper, the author compares the two games played most frequently in our classrooms, concluding that although both games may prepare the student for success in school only one of the games prepares the student for success in life.

Computers were invented to help mathematicians perform long and complicated calculations more efficiently. By the time that a computing area became a familiar space in primary and secondary schools, the initial motivation for computer use had been submerged in the many other functions that modern computers now accomplish. Not only the mathematics…

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.

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…

Before primitive man had grasped the concept of number, the written word or even speech, he was able to count. This was important for keeping track of food supplies, sending messages, trading between villages and even keeping track of how many animals were in their herd. Counting was done in various ways, but in all cases, the underlying principle…

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…

This paper describes a "hands-on task" called Number Tiles, which is Task 43 in the collection constructed for the Mathematics Task Centre Project, and available at www.blackdouglas.com.au or www.curriculum.edu.au. This task is rich in possibilities and directions. It should be used as a planned curriculum experience at several year levels to…

Bases such as 5 and 12 provide the same structural place value benefits as base 10. However, when numbers less than one are concerned, base 10 provides friendly decimals for the most common fractions of half, quarter, three-quarters. Base 5 is not user friendly at all in this regard. Base 12 would provide nice dozenimals(?) for the same…

Investigating the relationship between fractions and their equivalent decimal representations helps clarify to students that both representations stand for a single (rational) number on the number line. Since students are taught to perform computations with fractions and also to compute with decimals, performing these computations side-by-side…