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MathsWorks for Teachers series

ACER review

MathsWorks for Teachers series. Leigh-Lancaster, D 2005, Functional Equations, MathsWorks for Teachers series, ACER Press, Melbourne, Australia. RRP $36.95. Tout, D & Motteram, G 2006, Foundation Numeracy in Context, MathsWorks for Teachers series, ACER Press, Melbourne, Australia. RRP $36.95. Evans, L 2006, Complex Numbers and Vectors, MathsWorks for Teachers series, ACER Press, Melbourne, Australia. RRP $36.95


According to a study conducted over the last ten years by the International Centre for Education in Mathematics, senior secondary school students in Australia are shirking higher-level studies of maths. Participation in Year 12 Mathematics across Australia 1995-2004 by Dr Frank Barrington was published in June 2006 (see media release). It shows that while the proportion of the school population choosing to enrol in one or more mathematics subjects at Year 12 has remained static at approximately 80 per cent, more and more of these students are choosing elementary maths over intermediate or advanced studies.

Nationally, the percentage of Year 12 students taking higher level (intermediate or advanced) mathematics subjects dropped from 41 per cent in 1995 to 34 per cent in 2003, while the percentage of students choosing elementary mathematics rose from 37 per cent to 46 per cent over the same timeframe.

Professor Garth Gaudry, Director of the International Centre for Education in Mathematics has blamed the trend on declining standards in secondary school assessment systems and university entry requirements, along with a shortage of qualified and effective maths teachers.

Gaudry claims that anti-intellectual pressure in education bureaucracies results in ‘soft’ subjects being rewarded equally with more difficult subjects such as advanced mathematics. This encourages students to opt for easier subjects in which they can perform better and thus score higher on exams and other assessments which will count towards their tertiary entrance scores. Universities, in turn, attempt to lure students into courses by lowering entrance standards and dropping prerequisite subjects. The problem arises when students who have not studied higher-level maths gain entry to challenging tertiary courses in science and business areas. These courses may not state advanced secondary-school-level mathematics as an entry requirement, or base their curriculums on advanced secondary-school-level mathematics as assumed knowledge. Nevertheless, they require a strong grasp of maths and students who take them may need remedial maths classes to get up to speed and avoid growing frustrated and dropping out.

The research findings have raised qualms about our nation’s ability to compete on an international stage in fields such as the sciences, engineering and technology, where a shortage of skilled Australian professionals seems imminent.

Gaudry believes the key is to encourage and reward students for choosing harder subjects. This is where education professionals come into the equation – but what can school administrators and senior-level secondary teachers do to lure students back into the study of hard maths?

According to Les Evans, the author of Complex Numbers and Vectors in the MathsWorks for Teachers series published by ACER Press, teachers and students need ‘to have the courage to think outside the square, we need to be intrigued by a problem.'

The MathsWorks for Teachers series aims to provide teachers and curriculum coordinators with a range of ideas to engage and inspire students so that they enjoy mathematics and see the worth in studying the subject. The six texts in the series have been developed to provide a coherent and contemporary framework for conceptualising and implementing aspects of middle and senior mathematics curriculums. The series has been specifically designed to assist teachers to illustrate mathematical concepts using real-world examples.

Its informal style makes the MathsWorks for Teachers series accessible, practical and stimulating. Each text includes examples of daily applications of maths, such as GPS, business or finance, as well as comprehensive illustrative examples with related tables, graphs and diagrams throughout. Indepth discussion of key concepts, skills and processes keep up a commentary on approaches to teaching and learning. Student activities, sample solution notes and references are provided for each chapter.

The ‘Curriculum Connections' chapter in each title links the content of the book with specific State, national and international mathematics curriculums, while the references and further reading section is a comprehensive guide to self-motivated extended learning.

The first text in the series is Functional Equations by series editor David Leigh-Lancaster. Functional Equations provides an introduction to elementary aspects of functional equations. These equations are linked to function in various topics of the senior secondary mathematics curriculum including transformations, identities, difference equations and mathematical modelling. A computer algebra system has been used to generate tables and graphs, as well as carrying out symbolic computation for the illustrative examples.

Leigh-Lancaster makes a convincing argument about the importance and relevance of the contemporary study of functional equations to modelling a range of practical and theoretical situations such as characterising the algebraic properties of functions and the use of mathematical software for computation.

The second text in the MathsWorks series, Les Evans’s Complex Numbers and Vectors draws on the power of intrigue and uses appealing applications from navigation, global positioning systems, earthquakes, circus acts and stories from mathematical history to explain the mathematics of vectors and the discoveries in complex numbers.

The first part of Complex Numbers and Vectors provides teachers with background material, ideas and teaching approaches to complex numbers; models for complex numbers and their geometric and algebraic properties; their role in providing completeness with respect to the solution of polynomial equations of a single complex variable (the fundamental theorem of algebra); the specification of curves and regions in the complex plane; and simple transformations of the complex plane.

The second part of this resource provides an introduction to vectors and vector spaces, including matrix representation. It covers vectors in two- and three-dimensions, their application to specification of curves, vector calculus and their elementary application to geometric proof. Technology has been used throughout the text to construct images of curves, graphs and two- and three-dimensional shapes.

Foundation Numeracy in Context by David Tout and Gary Motteram is the third text in the MathsWorks series. Foundation Numeracy in Context describes an approach to teaching mathematics based on applied and contextual learning principles. This means that the teaching and learning of mathematics proceeds from a contextual, task-based and investigative point of view where the mathematics involved is developed from a modelled situation or practical task. Practical investigations and projects are principal vehicles for student learning in such an approach.

This text is written for teachers working with students who have become disengaged from learning mathematics during the middle to senior years of secondary schooling, and who are likely to have had limited success with mathematics. The approach used will be helpful for teachers of students who need a practical rather than a formal mathematical background for their everyday life skills and further education, training or career aspirations. Foundation Numeracy in Context illustrates how this approach works in contexts such as cars and driving, sport, cooking and catering, and draws together mathematics from the areas of number, measurement, space, data and statistics, and algebra.

Other titles in the series, to be released throughout 2006 and 2007, are Contemporary Calculus by Michael Evans, Data Analysis Applications by Kay Lipson, and Matrices by Pam Norton.

This article was provided by the Australian Council for Educational Research (ACER).

Key Learning Areas

Mathematics

Subject Headings

Mathematics teaching
Mathematics