Discovering Mathematics with Four to Seven-year-olds is the third and most recent title in a promising new series, Managing Primary Mathematics. The mathematical education of young children offers the prospect of the greatest excitement and reward to teachers. At key stage 1, most children are eager and receptive; while they certainly do not come to school tabula rasa, their progress is rapid and observable. At the same time, these young minds are not dulled, socialised and compliant. They need and demand something qualitatively different from a diet of “sums”.

In her book, Anna Lewis declares that learning must be engaging, interesting, self-driven, challenging, active and intelligent. She begins from the belief that Using and Applying represents the basis of mathematical thinking and is the cornerstone of the key stage 1 mathematics curriculum. She has produced a book that will support teachers who share such ideals.

In primary circles, it is often claimed that “mathematics is all around us”. Anna Lewis reminds us of Richard Skemp’s caveat that “This is not accurate: mathematics is in people’s minds . . . to understand and organise what is around us”. The first of two major sections of this book considers where this “hidden” mathematics curriculum may be found Q in class projects, in everyday activities and in other curriculum areas. The following section tackles an approach to overtly mathematical activities (“no pages of sums”) for the early years.

The book has been carefully researched, and draws on a wide range of literature to support the author’s experience as a former infant teacher and advisory teacher for mathematics. This is not really a book to dip into; ideally, you need to read the entire vision and its practical realisation, through to the final recognition that every reader must make the author’s ideas their own, personal and relevant to their circumstances. Anna Lewis can write: she knows how to arrest and hold the reader. If you teach young children, you will enjoy and be inspired by this book.

Using and Applying Mathematics for 5 to 7-year-olds is less likely to kindle such emotions, but may provide a more instant solution for mathematics activity in key stage 1. The format is loose-leaf, in a robust ring binder. Each double spread is an activity, with some teacher guidance opposite a photocopiable worksheet. There are about 35 such activities for Number (each with a suggested age-range from Reception to Year 2) and about 20 for Shape, Space and Measures. The good reputation of the authors assures the value of these activities, but I retain my unease about the recent proliferation of expensive publications which are just a little too helpful to professional teachers, who badly need ownership of what goes on in their classrooms. But sometimes, perhaps, almost any help is gratefully accepted.

Tim Rowland is Lecturer in Mathematics, Homerton College, Cambridge