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Ferguson, Robert – Australian Senior Mathematics Journal, 2018

The radius of curvature formula is usually introduced in a university calculus course. Its proof is not included in most high school calculus courses and even some first-year university calculus courses because many students find the calculus used difficult (see Larson, Hostetler and Edwards, 2007, pp. 870- 872). Fortunately, there is an easier…

Descriptors: Mathematics Education, Algebra, Geometry, Mathematical Logic

Ollerton, Richard L. – Australian Senior Mathematics Journal, 2018

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…

Descriptors: Mathematics Instruction, Geometry, Geometric Concepts, Trigonometry

Roepke, Tena L. – Australian Senior Mathematics Journal, 2018

Discovery learning has long been a part of mathematics teaching in the elementary and middle grades. Since the 1960s and 1970s, based on the work of Jean Piaget, Jerome Bruner, and others, helping students 'discover' or 'construct' their own understandings of mathematical concepts through well-designed activities facilitated by a competent teacher…

Descriptors: Mathematics Instruction, Mathematical Concepts, Calculus, Concept Formation

Taylor, Janet A.; Brickhill, Michael J. – Australian Senior Mathematics Journal, 2018

Enabling education has existed in Australia for over 40 years. It is a significant entry pathway for students who have not been able to access university education through the traditional school pathways. Such programs routinely include mathematics subjects as part of the core curriculum. To prepare students for the rigours of university study…

Descriptors: Curriculum Design, Remedial Programs, Remedial Mathematics, Mathematics Curriculum

Hooper, Malcolm; Bang, Samuel; Dharmasena, Vihanga; Cui, Mingqian – Australian Senior Mathematics Journal, 2018

In this age of easy access to the internet and to spreadsheets, easy-to-apply numerical methods exist that are vastly superior to Simpson's rule and the (corrected) trapezoidal rule. Gaussian quadrature (GQ) is such a method. What follows tells how enthusiastic Year 9 students with a physics problem provoked a science teacher into re-discovering a…

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

Stupel, Moshe; Oxman, Victor – Australian Senior Mathematics Journal, 2018

The solution of problems and the provision of proofs have always played a crucial part in mathematics. In fact, they are the heart and soul of this discipline. Moreover, the use of different techniques and methods of proof in the same mathematical field, or by combining fields, for the same specific problem, can show the interrelations between the…

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

Ahmad, Shair – Australian Senior Mathematics Journal, 2018

We have observed that over 90% of our students, both undergraduate and graduate, know little about the existence and multiplicity of real roots of real numbers; for example the fifth root of -2. Most of those who may know the answers are unable to give a logical explanation of the validity of their answers.

Descriptors: College Students, College Mathematics, Number Concepts, Mathematical Logic

Teia, Luis – Australian Senior Mathematics Journal, 2018

In mathematics, three integer numbers or triples have been shown to govern a specific geometrical balance between triangles and squares. The first to study triples were probably the Babylonians, followed by Pythagoras some 1500 years later (Friberg, 1981). This geometrical balance relates parent triples to child triples via the central square…

Descriptors: Number Concepts, Geometric Concepts, Geometry, Equations (Mathematics)

Farmer, Jim – Australian Senior Mathematics Journal, 2018

In issue 31(2) of the "Australian Senior Mathematics Journal", Kok (2017) describes a useful four-step process for investigating number patterns and identifying the underlying function. The process is demonstrated for both linear and quadratic functions. With respect to the quadratic example, I provide an additional idea relevant to step…

Descriptors: Mathematical Formulas, Mathematical Concepts, Problem Solving, Algebra

Teixeira, Ricardo – Australian Senior Mathematics Journal, 2018

This article summarises activities that happened during the first three weeks of a fictitious high-school-level linear algebra section that used magic squares as a teaching tool to inspire students to further investigate the topics. The author has been working with students from high school and college levels for years, and although this situation…

Descriptors: Algebra, Secondary School Mathematics, Mathematics Instruction, Foreign Countries

Teia, Luis – Australian Senior Mathematics Journal, 2018

The purpose of this paper is to explore new geometrical relations in the Pythagorean theorem, and open doors for new interpretations of the physical world. Pythagoras is included in secondary education around the world including in Australian Curriculum (ACARA, n.d.), and hence this paper will be of interest to all.

Descriptors: Geometry, Secondary School Mathematics, Mathematical Logic, Equations (Mathematics)

Mills, Terrence – Australian Senior Mathematics Journal, 2018

The sudden perception of a connection between ideas is exhilarating. We might call these moments 'Aha!' moments. The purpose of this paper is to demonstrate how several different ideas can come together in Year 12 mathematics. The subject Further Mathematics in the Victorian Certificate of Education (VCE) is the Victorian adaptation of General…

Descriptors: Grade 12, Secondary School Mathematics, Mathematics Instruction, Foreign Countries

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