2nd Edition

Supporting Early Mathematical Development Practical Approaches to Play-Based Learning

By Caroline McGrath Copyright 2022
    516 Pages 354 B/W Illustrations
    by Routledge

    516 Pages 354 B/W Illustrations
    by Routledge

    Supporting Early Mathematical Development is an essential text, combining theory and practice to enable successful mathematical education for children from birth to 12 years. This text considers how students, academics, parents and professionals can develop their mathematical thinking practice whilst acknowledging there will always be a road yet to travel; we will always be practising the craft of teaching mathematics. Charting the delivery of mathematical development in playgroups, children’s centres, nurseries and primary schools, the book promotes an effective pedagogy for mathematics.

    This new edition provides a conceptualisation of mathematics and places a fresh emphasis on mathematical literacy to empower children. New chapters include the following:

    ■ Mediators of Mathematical Thinking

    ■ Understanding Pattern, Pre-Algebraic and Algebraic Thinking

    ■ Naming, Renaming and Processing Numbers

    ■ Statistics, Statistical Diagrams and Probability

    ■ Measure

    ■ Geometry

    Throughout the book, Caroline McGrath navigates the complexity of teaching and learning mathematics, through careful thought and consideration of mediators of mathematical thinking. This supportive book is designed for educators who want to know how to reconstruct mathematical ideas with children and respond in the moment. Returning to the root of understanding, using the adaptive pedagogical style recommended in this text, you can create satisfying mathematical experiences for children.


    Anne D. Cockburn


    1. Mediators of Mathematical thinking: Models and Minds

    2. Mathematical Thinking and Problem Solving

    3. Fear, anxiety and other emotions

    4. General Principles and Practical Implications for Early Years Mathematics

    5. Specific Principles and Practical Implications for Early Years Mathematics

    6. Early Years Mathematics

    7. Understanding Pattern, Pre-algebraic and Algebraic thinking

    8. Naming, Renaming and Processing Numbers

    9. Understanding Addition and Subtraction: Mental Strategies

    10. Understanding Addition and Subtraction: Formal Algorithms

    11. Multiplication and Division: Mental Strategies

    12. Understanding Multiplication and Division: Formal Algorithms

    13. Statistics, Statistical diagrams and Probability

    14. Measure

    15. Geometry



    Caroline McGrath began her studies in Dublin on an analytical science degree. After qualifying with a Post Graduate Certificate in Education she worked as an early years teacher and lectured in early childhood studies. She achieved the Postgraduate Diploma in Professional Studies in Education (Specific Learning Difficulties/Dyslexia) and was awarded the Hornsby Certificate of Professional Practice. She completed a master’s and a doctorate and writes from first-hand experience teaching.

    "This is a detailed, thorough and comprehensive guide to teaching mathematics to young children. It is reflective and philosophical, yet also full of practical advice and examples from someone who works with young children.

    McGrath sees teaching as a professional thinking craft, backed by pertinent theories and principles, which are freely quoted throughout this book.

    She encourages teachers to use thoughtful, and thought-provoking questioning in their classes. That implies using the important, if not crucial, skill of listening to your pupils.

    There are some delightful nuggets in this book. I particularly liked the comparison of emotions to a spectrum of colours from sage green satisfaction to mid-red fear to dark black dread.

    McGrath advocates teaching a range of methods and perceptions to her learners, encouraging metacognition and reflection. Reading about this makes us, the readers also reflect on our own practices. She also emphasises the developmental nature of mathematics and illustrates this with a comprehensive explanation of all the components of a typical maths curriculum as used by children up to the age of around 12 years."

    Steve Chinn, Visiting Professor, University of Derby, UK, Author of The Trouble with Maths and More Trouble with Maths