Two important pedagogical techniques for developing deeper mathematical understanding are to prove a given theorem in different ways and to unify the proofs of different theorems. Trigonometric angle sum and difference identities are introduced in Unit 2 of Specialist Mathematics in the Australian Curriculum (Australian Curriculum, Assessment and…

Transitional engineering students are those who are academically ineligible to enter a bachelor's engineering program but are enrolled in an associate engineering program with a university. Successful completion of such an associate engineering program allows the higher achievers to transfer to a full bachelor's engineering program. The associate…

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…

This paper being an extension of Bhattacharjee (2012) is very much relevant to Year 9 to Year 10A in the "Australian Curriculum: Mathematics". It also falls within the purview of class IX to class XII curriculum of Mathematics in India (Revised NCERT curriculum) for students aged 14-17 years. In Bhattacharjee (2012), the discovery of…

Trigonometry is an integral part of the draft for the Senior Secondary Australian National Curriculum for Mathematics, as it is a topic in Unit 2 of both Specialist Mathematics and Mathematics Methods, and a reviewing topic in Unit 1, Topic 3: Measurement and Geometry of General Mathematics. However, learning trigonometric ideas is difficult for…

There is an old saying that "there is more than one way to skin a cat." Such is the case with finding the height of tall objects, a task that people have been approximating for centuries. Following an article in the "Australian Primary Mathematics Classroom" (APMC) with methods appropriate for primary students (Brown, Watson,…

In this article, the authors present a lesson whose goal is to utilise a scientific environment to immerse a trigonometry student in the process of mathematical modelling. The scientific environment utilised during this activity is a physics simulation called "Wave on a String" created by the PhET Interactive Simulations Project at…

The authors hypothesize that a means-end strategy places a load on cognitive processing capacity which retards knowledge acquisition. Three experiments using trigonometry problems with high school students were conducted in which the problem goal was modified to disrupt strategy used by novices. Results supported the authors' hypothesis.…

Describes a kangaroo simulation which can be adapted for use with radio tracking activities for other animals. Outlines procedures and information to help implement the activity. Provides a map of Australia, calculations, and sample kangaroo movement data. (RT)