Abstracts of Research Papers:

Monitoring Progress in Algebra in a CAS Active Context: Symbol Sense, Algebraic Insight and Algebraic Expectation
Robyn Pierce* and Kaye Stacey +
* University of Ballarat, Victoria, 3353, Australia; rpierce@ballarat.edu.au
+ The University of Melbourne, Victoria, 3052, Australia; k.stacey@unimelb.edu.au

The purpose of this paper is to provide researchers with a shared framework, terminology and tool to improve the coherence of research into learning mathematics with CAS and to assist its findings to accumulate into a significant body of knowledge. Experience with calculators in arithmetic led to a framework for number sense. There is an obvious parallel for algebra, where the development of algebraic insight to monitor symbolic work will assume high importance. We present a framework for algebraic insight then explore one aspect, algebraic expectation, in detail. Just as estimation is a valued skill for monitoring arithmetic calculations, we suggest that expectation should be a focus in teaching algebra, especially when symbolic technology is available. Through typical examples, we demonstrate the value of the algebraic insight framework for monitoring students’ work with CAS.

Efficient Use of Graphics Calculators in High School Calculus
Patricia A. Forster
Institute of Service Professions, Edith Cowan University, Western Australia
p.forster@ecu.edu.au

This paper provides a pragmatic view of efficient use of graphics calculators. Efficiency is described in terms of quick and easy calculation, as debated and evidenced in a Year 12 calculus class. Students’ methods of calculation are analysed in terms of the algebraic understanding and technical skills that underpinned them. Patterns in students’ selection of methods from the available possibilities and the social promotion of methods are described. I argue that students showed critical attitudes towards quickness in calculation, that some were innovative and performed advanced algebra in their pursuit of quickness, and I identify implications of the students’ actions for teaching and learning.

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Computer Algebra versus Manipulation
Hossein Zand and David Crowe
The Open University, Milton Keynes, UK
h.zand@open.ac.uk , w.d.crowe@open.ac.uk

In the UK there is increasing concern about the lack of skill in algebraic manipulation that is evident in students entering mathematics courses at university level. In this note we discuss how the computer can be used to ameliorate some of the problems. We take as an example the calculations needed in three dimensional vector analysis in polar coordinate systems, and argue that these form a deterrent to many students. We illustrate how a computer algebra package may be used to shorten the length and complexity of these calculations with only modest effort from the teacher.

Playing with Powers
Bharath Sriraman¹ and Pawel Strzelecki ^2
1Dept. of Mathematical Sciences, The University of Montana, USA,
sriramanb@mso.umt.edu
² Institute of Mathematics, Warsaw University, Poland.
pawelst@mimuw.edu.pl

This paper explores the wide range of pure mathematics that becomes accessible through the use of problems involving powers. In particular we stress the need to balance an applied and context based pedagogical and curricular approach to mathematics with the powerful pure mathematics beneath the simplicity of easily stated and understandable questions in pure mathematics. In doing so pupils realise the limitations of computational tools as well as gain an appreciation of the aesthetic beauty and power of mathematics in addition to its far-reaching applicability in the real world.

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