Worthington, Maulfry and Carruthers, Elizabeth. (2003) Children’s Mathematics: Making Marks, Making Meaning. Paul Chapman Publishing, London, 2003.

      "This publication will stimulate the thinking of early years practitioners with an enthusiasm for mathematics and will strike a chord with those whose particular interest lies in literacy and mark-making. Notions of good practice long accepted in literacy are developed in the context of mathematics in this thought-provoking book. The text begins with a clearly stated intention to help adults understand children’s mathematical development. Carefully recorded observations and examples of children’s work are important features of the book, helping to bring to life some of the complex theories that are examined. The reader is successfully drawn in by the evident enthusiasm of the authors and this helps to make accessible the extensive references to theory and research.

      The authors bring together their many years of observation and research, set in context with current thinking on early childhood education, in a though literature reviews. Four major learning theories are critically examined in terms of how each influences teachers’ beliefs about children’s representations in mathematics. In a brief table the view of the child embedded in each theory is set out alongside the pedagogy it supports. Useful links are made between how children learn and practical strategies to support their mathematical learning specifically.

      It is widely accepted that mark making is encouraged and valued in early years settings and the authors contrast this with responses to children’s informal mathematical recording. They suggest that children are ‘bi-numerate’, using their won recording alongside the formal mathematical symbols they are learning. In this model practitioners are encouraged to engage with what children individually and independently record and describe. Observations of children’s work are used to help the reader understand what being ‘bi- numerate’ might look like and to provide suggestions for extending learning. The comparison with strategies to understand, respect and support early literacy development is useful. It is widely accepted that early years practitioners have moved towards valuing mark making as children develop literacy skills. Mathematical literacy can be equally effectively supported and environments which do this are described. A social context for mathematics is emphasised, with practical suggestions for increasing the mathematical experiences a setting can offer.

      The authors use and extend work by Athey (19990) on schemas (patterns of repeated behaviour into which new learning is assimilated) in early learning. They describe some frequently observed schemas and draw out the mathematical nature of much of this learning. How mark making is used by children to express schema and the importance of self-initiated activities to pursue particular schema is made clear. Observations in a reception classroom illustrate this effectively in the text and engage the reader with the concepts that children are working on. The example of a schema on spirals is comprehensive and clearly shows the practical pedagogical skill of the authors. Children working on this schema engage in a wide range of child- initiated activities, scaffolded by reflective practitioners. To interpret children’s mathematical marks might prove more difficult for less confident or less knowledgeable readers but this book goes some way to addressing this difficulty with the examples previously mentioned. For those less confident or knowledgeable about mathematics and additional text could usefully be used alongside this book, focusing on the content of an early years’ curriculum for mathematics. Montague-Smith’s (2002) Mathematics in Nursery Education would provide such supplementary information in a clear and structured way.

      Working with parents and families is the focus of one of the later chapters in the text. The mathematical activities that children experience in the home environment are valued by the authors, who describe oral and written mathematical experiences that children bring to early years settings. They go on to show how parents can be included in the approach to mathematics that teachers use in reception classes. This enabling model of working with parents and carers is illustrated in the section of ‘frequently asked questions’ which could be a real confidence booster for practitioners addressing the concerns of the children’s families.

      Inclusion of children with additional needs is briefly addressed in the final chapter, from the standpoint of working from where the child is. Specific examples of inclusive practice are not provided here though many earlier examples illustrate the approach to inclusive practice that is advocated. Most of this chapter focuses on practicalities – both children’s and teachers’ questions are used to illustrate the argument for an approach to early mathematics that values the child’s recording methods. These will communicate powerfully to more sceptical readers. The book concludes with a reflection on the importance of valuing mathematics as a medium for communication and the importance of valuing what children bring to the subject as well as what it offers them.

      This is a book rich with detail yet easy to read. A short review cannot do justice to the range of insights it offers to a wide audience. Practitioners wishing to extend their work in mathematics would enjoy and benefit from delving into this book, students and researchers with mathematical concerns will find useful summaries of previous work linked to established theory, and teachers of children over five will find useful insights into working with parents to help children become effective mathematicians. This book is likely to appeal to a wide readership. It is well constructed and provides a range of interesting examples of effective pedagogy in early mathematics. Is successfully meets its aim of helping adults to understand children’s mathematical mark making and shows how the pedagogy that is needed to support this can be achieved. It is an excellent stimulus for those who want to develop their practice as well as their knowledge." Anna Cox, Early Years Coordinator, Derbyshire LEA.