Two decades ago, in an award-winning paper, Dan Kennedy (1995) likened learning mathematics to climbing a tree, for which there was only one way to climb: up a large and solid trunk. In the limited time that is available, many students give up the climb, impede others, fall off the trunk, or fail to climb the tree sufficiently well. In the case of…

Logarithms continue to play an important role in mathematics (most significantly in calculus), science, and engineering. It is therefore important for students to understand logarithms as real numbers as well as the characteristics of logarithmic functions. Exploration of challenges in understanding logarithms as real numbers and logarithmic…

Since the 1990s, computer algebra systems (CAS) have been available in Australia as hand-held devices designed for students with the expectation that they will be used in the mathematics classroom. The data discussed in this paper was collected as part of a pilot study that investigated first year university mathematics and statistics students'…

The senior school Mathematics syllabus is often restricted to the study of single variable differential equations of the first order. Unfortunately most real life examples do not follow such types of relations. In addition, very few differential equations in real life have exact solutions that can be expressed in finite terms. Even if the solution…

In 2009, four mathematics subjects were offered at the year 12 level in the Victorian Certificate of Education (VCE). The two subjects at the intermediate level--Mathematical Methods and Mathematical Methods CAS--run in parallel, that is, a student can be enrolled in only one or the other, the choice being made at the school level. The curricular…

Graphing utilities, such as the ubiquitous graphing calculator, are often used in finding the approximate real roots of polynomial equations. In this paper the author offers a simple graphing technique that allows one to find all solutions of a polynomial equation (1) of arbitrary degree; (2) with real or complex coefficients; and (3) possessing…

Calculus at the secondary school level has traditionally represented the peak of school mathematics in Australia, and has been available only to the most capable students. Until recently, many calculus curricula have focused on developing standard techniques, such as those concerned with differentiation and integration, with an emphasis on…

Argues that the calculator is fallible as a repository of mathematical knowledge. Suggests that the calculator should be considered not only a labor-saving device but a learning device. Provides examples of the use of calculators as a learning device. Contains 16 references. (ASK)

Introduces the Sharp EL-9600 graphing calculator and its capabilities, and discusses its possible uses in mathematics classrooms. (ASK)

Demonstrates the capabilities of graphics calculators in assisting with a simple mathematical investigation. Subjects covered include Direct Calculation, Tables, Graphing Particular Cases, Logarithms, Parametric Solutions, and Three-Dimensional Plots and Contours. The question posed for investigation with the calculator is, for what pairs of…

Explores and illustrates the range of ways in which the design of mathematics examination tasks can be influenced by graphics calculators from the perspective of the people designing the exams. Also discusses principles for awarding partial credit to student responses. (Author/PVD)

One way to assist students in developing correct intuitive ideas about the effect of sample size is to allow students to simulate similar problems. Describes experiences with classes performing simulation using graphing calculators. (ASK)

Describes students' written answers that seemed technology-assisted in the 1999 Calculus Tertiary Entrance Examination (TEE). Illustrates how in the 1999 Calculus TEE some students used their calculators in flexible ways. (ASK)

Describes the implementation of graphing calculators as teaching and learning aids in an intermediate linear algebra unit at the undergraduate level. Outlines the approach taken and discusses the problems that arose in relation to calculator use. (ASK)

Focuses on three activities using the TI-92 graphing calculator that examine the relationship between the intensity of a light source and its distance from a measurement point, properties of a sound wave, and the relationship between the time elapsed and the temperature of a cooling substance. (ASK)