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.

Categories: Psychology