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Teaching Secondary School Mathematics: Research and Practice for the 21st Century.

Teaching Secondary School Mathematics: Research and Practice for the 21st Century

Authors: Merrilyn Goos, Gloria Stillman & Colleen Vale

Published: Allen & Unwin, Crows Nest, 2007

ISBN 978-1-74114-651-6

xiv + 482 pp., soft cover

Available from AAMT:


Overall, the discussion, read sequentially, from first page to last, covers what would be expected in such a textbook. But the discussion is often brief, and sometimes (unintentionally, perhaps) misleading. Problem solving, as a central process in mathematical thinking, is touched on (pp 36-39). But it has no reference to Polya, and is omitted in the Index as a topic on its own. The relationship between a task being a problem, now, for a student, and later being an exercise, is not explored: exploration, assistance, and practice, results in learning--"Oh! That's how I can handle this sort of task!" In short, the experience of problem solving IS "learning". Problem posing seems to be omitted.

Similarly, the listed relationships between beliefs about the nature of mathematics (utilitarian toolkit, platonic j discovery, or human creation?) psychological theories of learning mathematics (varieties of constructivism, behaviourist skill practice) and pedagogical approaches (teacher-centred delivery, student-centred exploration, different emphases on process performance versus conceptual understanding) as tabulated on page 7, suggest that IF you think mathematics is A, then you must teach using method H, and students will learn according to theory Q. Arguably things are not so simple. Student-centred teaching approaches can be combined with the view that the curriculum to be taught is Instrumental, or with any other view. It is extremely difficult, in practice, to make any water-tight distinction between "content" and "process". Any kind of instruction is able to result in students learning by constructing their own sense of what they experience.

There is an Index, for Subjects, but, regrettably, no Author Index. Inspecting the Index suggests that some key topics receive scant treatment, unfortunately. Trigonometry, for example, surely needs more than a few pages (197-8, 201, 223) and a suggestion for further reading. There IS brief mention of the research by Kendall and Stacey into whether trigonometry is learned, initially, more effectively, by traditional ratios, or by the unit-circle approach. But a student-teacher who knows only one of these methods will be unfamiliar with the other, or their uses. Related concepts such as scale, and similarity, are not in the Index, and presumably are not emphasised as part of the Trigonometry curriculum.

In my opinion the Index needs serious development so it can function as an entry-point when seeking information. For example, page 201 refers to dynamic geometry software (which is well indexed) and programming environments such as MicroWorlds: but the latter term is not indexed, nor is there any mention in the Index of Logo (which is the programming language of MicroWorlds, although this is not explained, later, on p 218) or programming software, generally, or programming in Excel.

Throughout the book "Review and Reflect" boxed-sections challenge the (student-teacher) reader to consider what he or she knows, believes, feels, has experienced as a school-student, and to connect this with the ideas, examples, questions and activities presented in the book. As such, reading the book should be conversation between the authors and the reader, leading to professional understanding of the challenges of teaching Secondary mathematics.

Another recurring feature is the use of shaded sections that provide classroom scenarios, introductory questions and suggested activities, conversations between teacher and students, and so on.

I am not sure that a student-teacher whose school and/or undergraduate mathematical experience may have had gaps, or may have been heavily reliant on memorised formulas, will be helped by this book to fill their gaps in curriculum or understanding.

Overall the book covers most essential topics very well: for example, curriculum models, using Information Communication Technologies and computer-based learning tools, assessing learning, curriculum topics (number, measurement, geometry, algebra, data, calculus), gender issues, equity and diversity, learning difficulties and giftedness, and engaging with the community and the profession.

[Although Chapter 11 is about learning to teach Chance and Data, only Data seems to be considered!]

There is a great deal I like about this book, and I congratulate the authors on their excellent work for a task that I know is extremely difficult.

I look forward to a revised Second edition!
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Article Details
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Author:Gough, John
Publication:Australian Mathematics Teacher
Article Type:Book review
Date:Jun 22, 2010
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