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Kenan, Kok Xiao-Feng – Australian Senior Mathematics Journal, 2017

This paper outlines an approach to definitively find the general term in a number pattern, of either a linear or quadratic form, by using the general equation of a linear or quadratic function. This approach is governed by four principles: (1) identifying the position of the term (input) and the term itself (output); (2) recognising that each…

Descriptors: Foreign Countries, Secondary School Mathematics, Mathematics Instruction, Number Concepts

Mahmood, Munir; Al-Mirbati, Rudaina – Australian Senior Mathematics Journal, 2017

In recent years most text books utilise either the sign chart or graphing functions in order to solve a quadratic inequality of the form ax[superscript 2] + bx + c < 0 This article demonstrates an algebraic approach to solve the above inequality. To solve a quadratic inequality in the form of ax[superscript 2] + bx + c < 0 or in the…

Descriptors: Problem Solving, Mathematics Instruction, Mathematical Logic, College Mathematics

Keane, Therese; Loch, Birgit – Australian Senior Mathematics Journal, 2017

While the flipped classroom has found much discussion recently, peer tutoring using screencast resources produced by students has not yet. In this paper, we describe student responses to the approach taken at a secondary Catholic school in Melbourne, Australia, where the mathematics teachers used the roll out of tablet PCs to all teachers and…

Descriptors: Peer Teaching, Tutoring, Student Developed Materials, Mathematical Concepts

Vozzo, Enzo – Australian Senior Mathematics Journal, 2017

Ever since their serendipitous discovery by Italian mathematicians trying to solve cubic equations in the 16th century, imaginary and complex numbers have been difficult topics to understand. Here the word complex is used to describe something consisting of a number of interconnecting parts. The different parts of a complex number are the…

Descriptors: Mathematics Instruction, Mathematics, Professional Personnel, Numbers

Haggar, Fred; Kricic, Senida – Australian Senior Mathematics Journal, 2017

Subdividing an equilateral triangle into four congruent triangles, then doing likewise to each of the three non-central triangles, and then again and again, leads to the Sierpinski gasket, from which the chaos game originated. An analogous procedure is hereforth applied to a circle, where a subdivision consists of two pairs of inscribed circles,…

Descriptors: Geometric Concepts, Mathematics Instruction, Equations (Mathematics), Mathematical Concepts

Nillsen, Rodney – Australian Senior Mathematics Journal, 2017

In this paper, an investment problem is investigated in terms of elementary algebra, recurrence relations, functions, and calculus at high school level. The problem comes down to understanding the behaviour of a function associated with the problem and, in particular, to finding the zero of the function. A wider purpose is not only to formulate…

Descriptors: Comparative Analysis, Foreign Countries, Mathematics Instruction, Algebra

Thompson, Ian – Australian Senior Mathematics Journal, 2017

In this paper, an example is offered of a problem-solving task for senior secondary school students which was given in the context of a story. As the story unfolds, the task requires progressively more complex forms of linear programming to be applied. Coding in MATLAB is used throughout the task in such a way that it supports the increasing…

Descriptors: Foreign Countries, Programming, High School Seniors, Mathematics Education

Vincent, Jill; Pierce, Robyn; Bardini, Caroline – Australian Senior Mathematics Journal, 2017

In this article the authors analyze the written solutions of some first year undergraduate mathematics students from Victorian universities as they answered tutorial exercise questions relating to complex numbers and differentiation. These students had studied at least Mathematics Methods or its equivalent at secondary school. Complex numbers was…

Descriptors: Mathematics Instruction, College Mathematics, Undergraduate Study, Foreign Countries

Fitzherbert, John – Australian Senior Mathematics Journal, 2017

Jagadguru Shankaracharya Swami Bharati Krishna Tirtha (commonly abbreviated to Bharati Krishna) was a scholar who studied ancient Indian Veda texts and between 1911 and 1918 (vedicmaths.org, n.d.) and wrote a collection of 16 major rules and a number of minor rules which have collectively become known as the "sutras of Vedic…

Descriptors: Mathematics, Professional Personnel, Mathematics Instruction, Equations (Mathematics)

Turner, Paul; Thornton, Steve – Australian Senior Mathematics Journal, 2017

This article draws on some ideas explored during and after a writing workshop to develop classroom resources for the reSolve: Mathematics by Inquiry (www.resolve.edu.au) project. The project develops classroom and professional learning resources that will promote a spirit of inquiry in school mathematics from Foundation to year ten. The…

Descriptors: Mathematics Instruction, Inquiry, Teaching Methods, Elementary Secondary Education

Ferguson, Robert – Australian Senior Mathematics Journal, 2017

Students are often asked to plot a generalised parent function from their knowledge of a parent function. One approach is to sketch the parent function, choose a few points on the parent function curve, transform and plot these points, and use the transformed points as a guide to sketching the generalised parent function. Another approach is to…

Descriptors: Mathematics, Mathematics Instruction, Equations (Mathematics), Secondary School Mathematics

Kissane, Barry – Australian Senior Mathematics Journal, 2016

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…

Descriptors: Technology Integration, Mathematics, Mathematics Education, Comparative Analysis

Jourdan, Nicolas; Yevdokimov, Oleksiy – Australian Senior Mathematics Journal, 2016

The paper explores and clarifies the similarities and differences that exist between proof by contradiction and proof by contraposition. The paper also focuses on the concept of contradiction, and a general model for this method of proof is offered. The introduction of mathematical proof in the classroom remains a formidable challenge to students…

Descriptors: Validity, Mathematical Logic, Mathematics Instruction, Mathematical Concepts

Stupel, Moshe; Segal, Ruti; Oxman, Victor – Australian Senior Mathematics Journal, 2016

In this article, we present investigative tasks that concern loci, which integrate the use of dynamic geometry software (DGS) with mathematics for proving the obtained figures. Additional conditions were added to the loci: ellipse, parabola and circle, which result in the emergence of new loci, similar in form to the original loci. The…

Descriptors: Geometric Concepts, Courseware, Mathematics Instruction, Task Analysis

Hassani, Mehdi; Kippen, Rebecca; Mills, Terence – Australian Senior Mathematics Journal, 2016

Life tables are mathematical tables that document probabilities of dying and life expectancies at different ages in a society. Thus, the life table contains some essential features of the health of a population. Probability is often regarded as a difficult branch of mathematics. Life tables provide an interesting approach to introducing concepts…

Descriptors: Probability, Mathematical Concepts, Death, Mortality Rate