Teaching Problems and the Problems of Teaching

There have been many excellent books published about teaching but this book has something very special about it. I am currently in my thirty seventh year of teaching and I must say that I have never read anything quite like it.

The author is a professor of education but she has kept in touch with the teaching chalk-face by continuing to teach mathematics to a Grade Five (U.K. Year Six) class. As is perhaps clear from the title, the book has two interlinked themes. The first is that mathematics is best taught through problem solving. The second is that teaching is an enormous skill but it is a skill that can be learned.

That mathematics is best learned through problem solving is not news to many but in several parts of the world teachers are still to be found who teach the subject merely by rote learning of data and dry as dust repetition of barren exercises. The author's contention is that her job as a teacher is to help her students understand mathematics and by that she means enabling the students to see, for example, the links between addition and multiplication through the setting of problems which lend themselves to the exploration of such links. Part of the book is dedicated to approaching mathematics through various problems arising from a cross-curricular video story of a group of enthusiasts traveling by boat to see some whales. Whereas other subject teachers presumably used the story to elicit creative writing or to deal with biological and ecological themes, the author uses it to help the students come to terms with some quite difficult mathematical problems arising from the navigation – speed, distance, position, etc. The author leads us into the complexity of these problems as faced by the children. Teachers who teach as part of a team using a cross-curricular theme, such as teachers of the International Baccalaureate Primary Years and Middle Years Program, would find this section particularly rewarding.

However, it is the second strand, the problems of teaching, which makes this book different. The author videoed her lessons, had observers carefully record what took place and herself made copious notes after each lesson. She used all this evidence to explain exactly what was going through her mind every minute of the lesson. Although the author was teaching a whole Grade Five class, she was acutely aware of the needs, concerns, worries, blind spots and skills of every single student in the group. Every good teacher is constantly thinking "How do I get Jemima to contribute to the lesson?", "How do I manage to get Loretta to give other students a chance without offending her or putting her off?", "How do I explain this so that Gene really understands it?", "How do I use Paul's wrong answer to advance his and every other student's understanding of the problem without putting him down?". However, I had never come across a book that makes all these thoughts of a teacher explicit until I read this one.

The uniqueness of the book lies in the weaving together of the two strands. The various chapters of the book deal with a number of mathematical problems. The author skillfully explains how she approached each problem and how she encouraged the students to use their already existing mathematical skills to travel down fresh avenues, study more complex problems, acquire new skills and see the links between what they had already known and what they now knew. All the time the author is relating these developments, she is also telling us of her concerns about every child in the class and informing us of how she is trying to support her/him and why she is doing it.

This book is a great deal more than just another book about teaching. The psychology of teaching mathematics through problems, when allied to a detailed analysis of the psychology involved as the teacher reflects on the needs of every individual child in the class and the way her own responses are going to best support them, is such a fruitful combination that many people and not just teachers of mathematics would find this book extremely illuminating. I think that all teachers would find a great deal to help them. In particular, trainee and inexperienced teachers would find it a tremendous help. One problem that trainee and new teachers find particularly intractable is how they should teach a whole class while at the same time teaching every individual in it when those individuals bring such a diversity of skills, knowledge, aptitudes, interests and problems into the classroom. This book shows how one very experienced teacher went about squaring this perennial circle.

© 2004 Kevin Purday

Kevin M. Purday is Head of the Cambridge International High School in Jordan and is currently a distance-learning student on the Philosophy & Ethics of Mental Health course in the Philosophy Dept. at the University of Warwick.