Recently added articles from Australian Senior Mathematics Journal:
Editorial.(Editorial)
Jul 01, 2008; ... We are excited to present the second edition of the Australian Senior Mathematics Journal for 2008 and hope that you enjoy this special Calculus Focus Issue. Amongst the articles submitted, a key theme that emerged was the value of reflecting on the history of calculus in order to inform ...
A historical perspective on teaching and learning calculus.(Report)
Jul 01, 2008; ... Introduction Calculus is one of those topics in mathematics where the algorithmic manipulation of symbols is easier than understanding the underlying concepts. Around 1680 Leibniz invented a symbol system for calculus that codifies and simplifies the essential elements of ...
Some calculus affordances of a graphics calculator.(Report)
Jul 01, 2008; ... Introduction 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 ...
Where is the rate in the rule?(Report)
Jul 01, 2008; ... Introduction A well-developed understanding of rate is foundational to conceptual understanding of introductory calculus. Many students achieve procedural competence with the application of rules for differentiation without developing an awareness of the connection between ...
Integration: reversing traditional pedagogy.(Report)
Jul 01, 2008; ... Introduction The Ancient Greeks knew something about integration. They did not have our modern concept of function, were uneasy with limits, and they certainly did not know about antiderivatives or fundamental theorems. Nevertheless, Antiphon and Bryson calculated the area of a ...
Differentiation from first principles using spreadsheets.(Report)
Jul 01, 2008; ... INTRODUCTION Students, when they are introduced to differential calculus in Year 11, often have a number of difficulties. There is the difficulty of understanding what a limit is (Juter, 2006; Tall, 1993). Many students have difficulty seeing a tangent as the limiting case of a ...
Problem solving in calculus with symbolic geometry and CAS.(computer algebra systems)(Report)
Jul 01, 2008; ... Computer algebra systems (CAS) have been around for a number of years, as has dynamic geometry. Symbolic geometry software is new (Todd, 2007). It bears a superficial similarity to dynamic geometry software, but differs in that problems may be set up involving symbolic variables and ...
A literature review of pedagogical research on mathematical induction.(Report)
Jul 01, 2008; ... Introduction Many students experience considerable difficulties when they learn and then attempt to construct and communicate proofs of conjectures using the principle of mathematical induction (e.g., Avital & Libeskind, 1978; Blumfiel, 1974; Dubinsky, 1986, 1989; Dubinsky & ...
Ponder this.
Jul 01, 2008; ... As the focus of this issue of ASMJ is the teaching of calculus in the senior secondary and upper tertiary level, so is the focus of this problems section. The purpose of the section is to provide teachers and students with a selection of calculus problems. In the time since the ...
Editorial.(Editorial)
Jan 01, 2008; ... We are pleased to present this first edition of ASMJ for 2008, which contains very interesting reading for mathematical educators at many levels and in varied spheres of interest. In 2007, we reviewed several aspects of ASMJ, and as a result of discussions that were held in Hobart at the ...
Using pedagogical maps to show the opportunities afforded by CAS for improving the teaching of mathematics.(Computer Algebra Systems )(Report)
Jan 01, 2008; ... Experience and research in teaching secondary school mathematics with Computer Algebra Systems (CAS) has been building over the past two decades. For Australian experience see for example Ball & Stacey (2005), Flynn (2003), Garner (2004), Geiger (2003), Goos et al. (2003), Kendal & Stacey ...
The mathematics of sundials.
Jan 01, 2008; ... As early as 3500 years ago, shadows of sticks were used as a primitive instrument for indicating the passage of time through the day. The stick came to be called a "gnomon" or "one who knows." Early Babylonian obelisks were designed to determine noon. The development of trigonometry by ...
A lesson in number pattern.
Jan 01, 2008; ... Following is a guided investigation into the spatial relationships between the centres of the squares in a Fibonacci tiling. It is essentially a lesson in number pattern but includes work with surds, coordinate geometry and some elementary use of complex numbers. The student worksheet is ...
An application of elementary functions to a resource allocation problem *.(Report)
Jan 01, 2008; ... In 1998, the West Report on tertiary education considered proposals for changing the proportion of funds given to universities on the basis of two criteria: research and teaching. An article by David Phillips, a former Head of the Higher Education Division of the Department of Employment, ...
The Lutterloh dress patterns: an unexpected application of polar co-ordinates.
Jan 01, 2008; ... The Lutterloh method of making dress patterns was developed in Germany in the 1930s, and even back then there were classes held in Australia in its use. However, the time was hardly propitious for such cultural dissemination, and it is only in recent years that it is making a reappearance ...
Reflections on symmetry and proof.
Jan 01, 2008; ... This article uses notions of symmetry to approach the solutions to a broad range of mathematical problems. It responds to Krutetskii's criteria for mathematical ability as well as the outcomes which guide the Extension 1 & 2 Mathematics courses of the Board of Studies NSW. The ...
Towards a constructivist pedagogy for Year 12 mathematics.(Report)
Jan 01, 2008; ... Introduction Constructivist pedagogies are generally not considered to support the teaching of mathematics for externally assessed examination-based courses. In large part, we (teachers) have believed that such approaches are inefficient in covering a set syllabus. This paper ...
Understanding statistical variation: a response to Sharma.
Jan 01, 2008; ... Issue 21(2) of the Australian Senior Mathematics Journal contains the paper "Exploring pre-service teachers' understanding of statistical variation: Implications for teaching and research" by Sashi Sharma. Sharma describes a study "designed to investigate pre-service teachers' ...
Ponder this.
Jan 01, 2008; ... This edition marks the start of a regular problems section in the ASMJ. I would like to express my sincere gratitude to the editors of the journal, Robyn Pierce and Sue Garner, without whose energetic work and inspiration, this section would not have come to be. This section ...
Editorial.
Jul 01, 2007; ... This edition of ASMJ has a different flavour to it. 2007 has been a year that, as editors, we have reviewed several aspects of the content, spacing and nature of articles that are sent to us. To maintain ASMJ as a peer-reviewed journal it has been decided that we will send all papers that ...