Learning to Teach Mathematics in the Secondary School does what it says on the cover. This series of essays by a formidable range of maths educators, takes the student teacher from subject knowledge to classroom practice. As the book says, “I teachers require practical teaching skills as well as good subject knowledge.” The 300 pages of the book are packed with practical ideas that will be of enormous assistance to the novice maths teacher.

It is divided into 12 chapters ranging from how to teach special needs pupils in mainstream maths to the post-16s and the use of ICT. Although written by different hands, the editors have gone to great trouble to ensure that there is a consistency of style and content in the book. There is a refreshing directness about the tone (such as: “You are about to begin learning how to teach mathematics”) and each chapter is well peppered with practical examples, illustrative exercises and learning tasks. The layout of the pages won’t excite you - it is a dense read - but there is a mass of knowledge and expertise to get through. The book comes into its own in the more practical classroom management chapters, such as “Communicating Mathematically”, which provides an excellent overview on the nature of mathematical language.

The Really Useful Maths Book - A Guide to Interactive Teaching is the latest in the Learning to Teach series aimed at student teachers on different types of initial teacher education courses. It is a companion book to the generic volume Learning to Teach in the Secondary School. This revised second edition successfully incorporates the revised national curriculum for maths and takes into account the findings of the 2004 inquiry into the education of 14-19s.

The book’s authors express a wish that it will be of use to tutors and mentors. Given the thorough research and “hands-on” approach to the material, it looks likely that this wish will be granted.

The Really Useful Maths Book - A Guide to Interactive Teaching is jam-packed with exciting and varied ideas that will help bring the subject alive to primary school children. Its 200 or so A4-sized pages are crammed with suggestions that will ensure your lessons go with a mathematical swing. There is little room for white space or cool contemporary design: the book teems with practical lesson ideas that have been gleaned over the years by its authors. The book is divided into two - the practical side of the subject, where you will find lots of good ideas, and the second part, which is more about the theory and practice of teaching maths (how children make sense of it, how to develop personal qualities). The book’s lively style and appropriate tone makes it easy to see how the many classroom ideas can be put into practice.

Children’s Errors in Mathematics is a very neat idea. It deals with the most common misconceptions in primary-age children and shows how they can be dealt with. The authors have hit on a refreshing idea: not how children learn, but how they learn the wrong things. The book starts with a fascinating overview of the literature on how children learn maths - and conversely, how easily they often construct their own misplaced knowledge and understanding. As the book so helpfully reminds us, “we should not see mathematics as something taught, but rather something that is learnt”.

The book ranges through common false constructs. There are scores of examples, such as why some children may think that one object out of four makes up a third of the total. The authors talk about why common errors are made and what can be done to pre-empt them in one’s lesson planning. This is a highly readable and useful book that could be of equal interest to teachers and parents. In working out why things aren’t, we often make clear the reasons why things are.

Learning to Teach Mathematics in the Secondary School Edited by Sue Johnston-Wilder, Peter Johnston-Wilder, David Pimm, John Westwell Routledge, pound;19.99 The Really Useful Maths Book - A Guide to Interactive Teaching Tony Brown and Henry Liebling Routledge, pound;17.99 www.routledge.com

Children’s Errors in Mathematics By Doreen Drews, Alice Hansen, Liz Surtees, John Dudgeon, Fiona Lawton Learning Matters, pound;15 www.learningmatters.co.uk