Network of ideas
In these days of league tables, performance management for teachers and target-setting for pupils, there is a danger that successful teaching becomes equated with short-term gains. Faced with an important exam, teachers are tempted to rely on instrumental "this is what you do" approaches. When this is "teaching to the test", we can end up with pupils who can "achieve" a national curriculum level without a secure understanding of the maths involved.
However, the most effective teachers think longer term: they aim to build understanding and to portray maths as a network of interconnected ideas. They continually reflect on their teaching and seek to extend their knowledge of the maths they are teaching and its associated pedagogy. The big question is, how to ensure that new teachers become successful (in the sense of targets) and effective (in the sense of developing understanding).
In Becoming a Successful Teacher of Mathematics, Howard Tanner and Sonia Jones nail their colours firmly to the mast: they think that "teaching for understanding" beats "instrumental" teaching on both counts. Because they quote research evidence to support their opinions, their book transcends its primary market of those in initial teacher training. There are references to educational theory (for example, Piaget, Skemp and Vygotsky), classroom observation (including Effective teachers of Numeracy by Askewet al, Hart's work on misconceptions, and the authors' own work), and comparative research (TIMSS, but surprisingly not Liping Ma's Knowing and Teaching Elementary Mathematics). There are chapters on what makes a good maths lesson, classroom management, planning and evaluation, effective teaching approaches, the role of pupil misconceptions in learning, thinking mathematically, calculators and ICT, assessment and learning, and continuing professional development.
The book is aimed at all key stages, not just at secondary. Even the two chapters that focus separately on primary and secondary maths are linked by extensive references to the Raising Standards in Numeracy project, in which the authors were involved. There are frequent references to the national curriculum and the National Numeracy Strategy. The positive influence of the latter is recognised, but readers are cautioned: "It is important, however, that the superficial, structural aspects do not overshadow the more important issues of the quality of the teaching and classroom interactions." In other words, the numeracy framework does not obviate the need for teachers to know their subject thoroughly.
This well-constructed book has much to commend it to experienced teachers, yet remains a highly effective study guide for trainee teachers. It also merits a wide readership among training providers, advisers and numeracy consultants.
Steve Abbott is a deputy head on secondment as Suffolk's key stage 3 numeracy manager.