Introduction
SECTION A: MATHEMATICAL UNDERSTANDING
Primary Teachers′ Insecurity about Mathematics
Mathematics in the Primary Curriculum
Learning How to Learn Mathematics
SECTION B: MATHEMATICAL REASONING AND PROBLEM-SOLVING
Key Processes in Mathematical Reasoning
Modelling and Problem Solving
SECTION C: WHOLE NUMBERS AND CALCULATIONS
Number and Place Value
Addition and Subtraction Structures
Mental Strategies for Addition and Subtraction
Written Methods for Addition and Subtraction
Multiplication and Division Structures
Mental Strategies for Multiplication and Division
Written Methods for Multiplication and Division
SECTION D: FURTHER NUMBER CONCEPTS AND SKILLS
Multiples, Factors and Primes
Integers: Positive and Negative
Fractions and Ratios
Decimal Numbers and Rounding
Calculations with Decimals
Proportionality and Percentages
Squares, Cubes and Number Shapes
SECTION E: ALGEBRA
Algebraic Reasoning
Coordinates and Linear Relationships
SECTION F: MEASUREMENT
Concepts and Principles of Measurement
Perimeter, Area and Volume
SECTION G: GEOMETRY
Angle
Transformations and Symmetry
Classifying Shapes
SECTION H: STATISTICS AND PROBABILITY
Handling Data
Comparing Sets of Data
Probability
Answers to Self-Assessment Questions
References
Index
Derek Haylock is an education writer, with an extensive list of
publications in the field of mathematics education. He worked for
over 30 years in teacher education, both initial and in-service,
and was Co-Director of Primary Initial Teacher Training and
responsible for the mathematics components of the primary
programmes at the University of East Anglia (UEA) in Norwich. He
has considerable practical experience of teaching and researching
in primary classrooms. His work in mathematics education has taken
him to Germany, Belgium, Lesotho, Kenya, Brunei, India and Sweden.
As well as his publications in the field of education, he has
written seven books of Christian drama for young people and a
Christmas musical (published by Church House/National Society). For
15 years after his time at UEA, he was in great demand as a
consultant and professional speaker. His work as a writer
continues.
Ralph Manning is an independent consultant in primary education. He
has worked as a primary teacher and as a lecturer in primary
teacher education for 18 years, following an earlier career in the
IT industry. Ralph led the mathematics and physical education
programmes for the Primary PGCE at the University of East Anglia
until 2013. His other specific interests are in developing
children’s higher thinking skills, assessment for learning and
planning for teaching effectively. He was a former founding member
of the General Teaching Council for England and is engaged in
supporting developing education projects in India.
′Some students refer to the book as their "maths bible" and I
have spoken to and have had e-mails from former students who
continue to refer to it (we recommend that they buy it from Day
One), saying "Thank goodness for Haylock!"′
*Debra Crouch*
′Now in its 5th edition, Mathematics Explained for Primary
Teachers is available for the first time as an interactive
eBook. The book is written in the accessible and engaging style we
have come to expect from Derek Haylock, and is informed by his
wealth of experience. With access to a range of new interactive
features (such as step by step screencasts, access to selected SAGE
journal articles and the companion website) and the flexibility of
an accompanying student workbook, Mathematics Explained for
Primary Teachers represents a complete solution for primary
mathematics educators.′
*Dr John West*
′Throughout this book, there is a clear sense of the importance of
preserving children’s understanding of mathematics rather than
resorting to ‘tricks and recipes’. This is done while still
ensuring that children are able to meet the demands of the new
National Curriculum. The explanation of key terms will enable
primary mathematics teachers to navigate their way through the new
curriculum document. Clear, worked examples of calculation methods
are combined with useful insights into the prior knowledge and
understanding that children need. The self-assessment tasks and
suggestions for further reading should ensure that teachers feel
well prepared to teach the mathematics contained in the book. This
book will be an invaluable source of practical help to all teachers
of primary mathematics.′
*Dr Marcus Witt*
′The physical structure of chapters are well presented, and there
is a good balance of colour, text, symbols, and pictorial
representations. Access to the content is well supported
through the chapter overview that provides a ready reference point
for locating the content. Within the chapters, each element
is easily located through the use of clear headings. Explicit
examples are used to clarify the meaning of the mathematical
terminology and the structure of the Learning and Teaching Point
provides a clear summary of the elements in the corresponding text.
Good visual supports, such as number lines, base 10 blocks and
arrow cards, supplement the written text and consolidate
understanding. Throughout the text, common misconceptions are
identified and comprehensively explained. The glossary of
terminology at the end of each chapter is a useful and well used
resource.′
*Theresa Shellshear*
′The book combines clear guidance about meeting the expectations of
the new curriculum, with a strong call to preserve children’s
mathematical understanding. The explanation of key terms will
enable primary mathematics teachers to navigate their way through
the new curriculum document. Worked examples of calculation methods
are combined with useful insights into essential prior knowledge
and understanding. The book will be invaluable source of practical
help to all teachers of primary mathematics.′
*Dr Marcus Witt*
′This book can rightly be considered the ultimate reference for
securing appropriate mathematics subject knowledge for primary
teaching. In the chapter ‘Written methods for Multiplication
and Division’ the concepts behind the methods are explained clearly
and thoroughly. Of particular use are the ‘teaching points’
sections and links to video explanations and further practice. It
is clear that this book is written by a teacher for teachers and
its main objective is to ensure teachers understand the concepts
behind what that they teach so that children will not just learn
mathematics but understand mathematics. This book will be a key
text for primary BA Ed and PGCE students.′
*Rachel Wallis*
‘This edition presents the clarity and detail I have come to expect
from Haylock and it continues to be our first choice in mathematics
subject knowledge support for students and teachers.’
*Nancy Barclay*
‘This edition tackles written calculation algorithms with clarity
and detail; the emphasis on children understanding these processes
and how to support this is maintained throughout.’
*Nancy Barclay*
′The new edition provides up to date information related to both
current research and practice. I particularly found the chapter on
mental strategies useful for explaining how the laws of
multiplication and division work and for encouraging ad hoc
approaches to multiplication. The teaching points throughout help
to draw relevant links between theory and practice and the
self-assessment questions focus on developing teachers’ own content
and pedagogical content knowledge.′
*Dr Tracey Muir*
′As always this book will prove to be an invaluable asset to not
only trainee teachers, but as many have agreed also after school
experience placements. There is a growing awareness in primary
schools of this book being an asset for all members of staff no
matter whether they have two or twenty-two years of classroom
experience.′
*Andrew Gallacher*
′Here is another accessible text from Derek Haylock that supports
the development of subject knowledge for student teachers and
experienced teachers alike. Haylock emphasises the importance of
teaching written methods with understanding and one key strategy he
exemplifies to achieve this is the use of representation.
There are good illustrations on the use of physical representations
to support addition and subtraction with very clear guidance on how
to use base ten materials and coins. The inclusion of a section on
using addition to check subtraction is well explained - this
is a useful addition to the fifth edition.′
*Alison Barnes*
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