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How to review a mathematics textbook

John Gough
John Gough has been a teacher–educator for many years, specialising in mathematics education. He is a Senior Lecturer at the School of Scientific and Developmental Studies in Education, Deakin University. Email: jugh@deakin.edu.au

Suppose we want to review a Grade 6 (or a lower Grade, such as Grade 4, or lower still) mathematics textbook, or curriculum system. What do we look for?

Obviously we start by assembling an overview of our own curriculum. We can use this as a topic-coverage checklist when we examine the textbook to see if it will do the things we want it to do.

Consider the following curriculum features:

  • how to develop counting skills, number sense and place-value
  • establishing calculation skills and number facts, as well as mental computation and estimation, and pencil-and-paper algorithms
  • the use, where appropriate, of concrete manipulative materials
  • introduction to and development of measurement facts and skills including the possible use of informal units, the definition and use of conversion between formal units
  • chance (probability)
  • data and graphs and simple statistical analysis and interpretation
  • spatial thinking, location and orientation in space and geometric terms, facts, concepts and skills
  • problem solving, modelling, and logical (deductive, and inferential) reasoning as ways of thinking mathematically
  • problem posing and open-ended investigative approaches based on self-generated curiosity – what is it? how does it work? why does it work? what else can it do?
  • the use of limited closed-ended practice drills and richer open-ended projects and investigations
  • use of ICT (information and communication technologies), including calculators, computers, educational software and CD-ROMs, Logo programming software, dynamic geometry software (such as Geometer’s Sketch Pad or Cabri Geometry), and the Internet.

Of course, as an alternative, we can use other official and unofficial curriculum documents. Consider also the way assessment books provide alternative ways of structuring the large body of knowledge that we know as 'school mathematics'.

Also, don't overlook issues that arise, or should arise, in the unit you are studying that are more broadly classroom-related rather than specific-subject or curriculum-related. They include:

  • gender issues, and the balance of male and female in teaching materials, and the avoidance of unconsidered gender stereotypes
  • sociocultural inclusivity including multiculturalism, the avoidance of racial and cultural stereotypes and the balance of social settings, urban, suburban, rural
  • classroom organisation, including the possibility of whole-class instruction, smaller group cooperative learning, individualised learning, homework, out-of-school experiences (excursions, camps and everyday activities)
  • assessment matters, including topic-entry assessment, topic-exit assessment, cumulative revision assessment, project assessment.

Be guided by commonsense.

Around middle and upper levels of primary school, where students have sufficient reading skills to be able to use a good textbook, there are probably no published criteria that could advise teachers how to judge a textbook. But consider the following further aspects to watch for, apart from the issues that have been touched on already when commenting on topics in the mathematics and broader classroom aspects that apply to all school subjects and to schooling as a large life process.

What is the textbook aiming to do? It may:

  • provide basic teaching, possibly backing up the classroom teacher's instruction (through definitions, illustrations, diagrams, worked examples)
  • give enrichment, especially for more advanced students, or for others needing challenges outside the mainstream curriculum
  • allow for extension beyond the mainstream focus, not just including 'harder' examples to stretch children’s ability to apply focal topics to challenging situations but indicating where the focal ideas lead to next (anticipating higher levels in a possible textbook series)
  • provide repetitive, consolidating, skill-strengthening, skill-maintaining practice
  • offer remedial practice for slower students
  • present self-contained practice activities that students can work on at home without a teacher being available to help
  • individualise student learning.

What special features does the textbook have that can make it more effective as a teaching resource? It may include:

  • an index
  • a glossary and/or dictionary of definitions, preferably illustrated
  • clear and self-explanatory Contents-page listings
  • boxes or panels that highlight important information, and worked examples
  • answers to all questions at the back of the book, preferably with occasional explanations and working
  • self-administered diagnostic topic-entry and topic-progress tests
  • cumulative revision and practice activities, worksheets and tests
  • a diagnostic flow chart suggesting how to work through the textbook, topic by topic
  • tips for overcoming common mistakes and misconceptions
  • discussion of children's own alternative, informal, invented methods of calculation and problem solving
  • suggestions for regular homework
  • ideas for self help and handling occasions when a student is 'stuck' or getting wrong answers but the teacher is not available to help.

What particularly attractive features does the textbook include? There may be:

  • a CD-ROM with individualised interactive diagnostic practice
  • colour illustrations
  • links with everyday materials, concrete manipulatives and common toy equipment such as Lego, Meccano, C’nex and Tinkertoys, matchsticks, blocks, beads, toy cars, toy planes, toy boats
  • real-life photos with real people, with equal numbers of males and females
  • stories of real-life use of mathematics
  • stories about the history of mathematics, mathematicians and uses of mathematics
  • cartoon-style illustrations with speech bubbles
  • book characters who 'speak' to the reader, motivating and explaining
  • websites and tips for Internet browsing
  • suggestions for enrichment using computer software or Logo programming
  • jokes
  • enrichment challenges (mindbenders, puzzles, paradoxes)
  • extension suggestions and challenges (advanced concepts and ideas that will be explored later in mainstream instruction)
  • mathematics games that children can make and play (eg Battleships, rummy-type card games for practising number facts, simple dice games, simple board games, classic games)
  • open-ended problems
  • links with children's books, films, TV and popular culture
  • links with children's hobbies, interests and sport
  • outdoor activities for the school playgrounds, neighbouring communities and beyond
  • ideas for the school’s Mathematics Club
  • links with families and suggested activities for Family Mathematics Nights.

The next step is to look for the implicit audience for this book. What assumptions are made about the children, and the teachers who might use this book? The audience may be:

  • mainstream Australian (or other mainstream)
  • ethnic and cultural minorities
  • urban–central versus rural–regional versus rural–remote
  • native English speakers versus non-English-speaking background
  • mainstream learners versus slower students versus faster students.

I'm sure you'll think of more features that matter to you while you are looking at one grade or year-level:

  • wondering if this textbook is part of a series and how well it links with lower or higher level books in the series
  • whether there is a teachers’ guide
  • whether there are black line masters (BLMs), overhead projection slides (OHPs) or electronic files, practice software, slideshow presentations, video clips on a CD-ROM?

How do your current textbooks or instructional system and materials measure up?

Finally, is this as good as, better or not as good as one of the great classics of the past such as the old Victorian Arithmetic series? Is it as good as a competent teacher in the classroom or would it be useless without the presence of a good teacher?

 

This article originally appeared as 'How to review a textbook' in Prime Number, Volume 19, Number 1, 2004. Republished with permission.

 

References and Further Reading

Board of Studies (1998). CSF: Sample Programs: Mathematics Years 5-6, Board of Studies, Carlton.

Board of Studies (2000). Curriculum & Standards Framework II: Mathematics. Melbourne: Board of Studies, Carlton.

Guidelines in Number. A Framework for a Primary Maths Program, Levels 1–8. Curriculum Branch, Education Department of Victoria, Carlton, 1985 (Levels 1–5 first printed 1983).

Mathematics Curriculum Guide –Measurement. Ministry of Education, Melbourne 1981.

Mathematics Framework P–10. Ministry of Education, Victoria, Melbourne, 1988.

Gough, J (1999). Diagnostic Mathematics Profiles, Deakin University Press, Geelong.

Schleiger, HE, Gough, J (1993). Diagnostic Mathematical Tasks, Deakin University Press, Geelong (revised edition: first edition 1980). 

Key Learning Areas

Mathematics

Subject Headings

Educational evaluation
Primary education
Mathematics teaching