Extending mathematical understanding and pedagogy Semester 1 and 2 a lecturer

Developing primary mathematics teaching: reflecting on practice with the Knowledge Quartet  2009 (electronic resource)
Book Recommended This is a key text for this module. Rowland et al provide a framework to help student teachers and NQTs reflect on, evaluate and improve their mathematics teaching. We use ideas from this text extensively in the module sessions that lead up to your assignment.

Developing primary mathematics teaching: reflecting on practice with the Knowledge Quartet  2009
Book Recommended This is a key text for this module. Rowland et al provide a framework to help student teachers and NQTs reflect on, evaluate and improve their mathematics teaching. We use ideas from this text extensively in the module sessions that lead up to your assignment.

Developing primary mathematics teaching: reflecting on practice with the Knowledge Quartet  20091412948487,9781412948487
Book Recommended This is a key text for this module. Rowland et al provide a framework to help student teachers and NQTs reflect on, evaluate and improve their mathematics teaching. We use ideas from this text extensively in the module sessions that lead up to your assignment.

General Texts 66 itemsHere are a selection of texts that you may find useful in this year's module.

Teaching number sense  2006082648686X,0826486878
Book This book takes as its central theme the need for children to understand the relationships between numbers, as opposed to just knowing isolated number facts. Julie Anghileri argues that ‘number sense’ can be taught, and the book includes chapters on counting, each of the number operations, fractions and written methods. In each case there are teaching ideas designed to encourage this deep learning.

Transforming primary mathematics: understanding classroom tasks, tools and talk  20169781138953604
Book Written by a leading expert in mathematics education, this book contains chapters that may be useful when analysing teaching and learning of mathematics including: Chapter 5  Mathematical activity: mindful or fluent?; Chapter 6 Variation theory (which links to 'Intelligent Practice'); Chapters 9, 10 and 1 on Tasks, Tools and Talk.

Transforming primary mathematics: understanding classroom tasks, tools, and talk  2016 (electronic resource)
Book Written by a leading expert in mathematics education, this book contains chapters that may be useful when analysing teaching and learning of mathematics including: Chapter 5  Mathematical activity: mindful or fluent?; Chapter 6 Variation theory (which links to 'Intelligent Practice'); Chapters 9, 10 and 1 on Tasks, Tools and Talk.

A practical guide to transforming primary mathematics: activities and tasks that really work  20169780415738446,9780415738453
Book

Primary mathematics: teaching for understanding  20090335229255,0335229263,9780335229253,9780335229260
Book This very practical book explores each of the key mathematical topics in depth focusing on how to develop understanding through using representations, promoting reasoning, considering potential misconceptions and communicating mathematical ideas.

Primary mathematics: teaching for understanding  2009 (electronic resource)
Book This very practical book explores each of the key mathematical topics in depth focusing on how to develop understanding through using representations, promoting reasoning, considering potential misconceptions and communicating mathematical ideas.

Understanding and enriching problem solving in primary mathematics  , , 20149781909330696
Book This easy to read book explores all the key aspects of problem solving that should be included in the primary curriculum for mathematics. It includes lots of examples of problem solving in the classroom. The chapter on representing problems is particularly relevant for this module.

Understanding and enriching problem solving in primary mathematics  , , 2014 (electronic resource)
Book This easy to read book explores all the key aspects of problem solving that should be included in the primary curriculum for mathematics. It includes lots of examples of problem solving in the classroom. The chapter on representing problems is particularly relevant for this module.

Multilingualism in mathematics classrooms: global perspectives  20091847692044,1847692052,9781847692047,9781847692054
Book

The dyscalculia toolkit: supporting learning difficulties in maths  2007 (multimedia)9781412947640,9781412947657
Book This book contains a collection of teaching activities and game that teachers can use to provide structured mathematical learning activities for learners who are struggling to understand key number concepts.

The elephant in the classroom: helping children learn and love maths  20090285638475,9780285638471,9780285638754
Book Jo Boaler has carried out extensive research into mathematics education, both in England and the US. In this book, she draws on her findings to outline what sometimes goes wrong for children in the mathematics classroom today and to offer concrete solutions for teachers. She is a strong advocate of mixedability grouping in mathematics lessons and offering learners opportunities to work collaboratively on engaging problems as a powerful means of developing mathematical understanding. The chapter on 'Making Low Ability Children' is particularly relevant for this module.

Primary curriculum: teaching the core subjects  , 20080826488390,9780826488398
Book This book focuses on how to teach the core curriculum subjects effectively to the 511 age group. It covers a range of areas including: planning, assessment and evaluation along with crosscurricular links and guidance on teaching beyond the classroom.

Creative teaching: mathematics in the primary classroom  , 20159780415713863
Book This text encourages the teacher to consider their position in relation to creativity and mathematics. It offers teachers a stimulus to develop their practice and includes a focus on different starting points for mathematical learning, different ways of working and making effective use of opportunities for exploiting crosscurricular links.

Creative teaching: mathematics in the primary classroom  , 2015
Book This text encourages the teacher to consider their position in relation to creativity and mathematics. It offers teachers a stimulus to develop their practice and includes a focus on different starting points for mathematical learning, different ways of working and making effective use of opportunities for exploiting crosscurricular links.

The trouble with maths: a practical guide to helping learners with numeracy difficulties  20179781138187467
Book In this book Steve Chinn explores some of the potential reasons that children may experience difficulties in learning maths and suggests some practical ways to help such children to be successful.

The trouble with maths: a practical guide to helping learners with numeracy difficulties  2017
Book In this book Steve Chinn explores some of the potential reasons that children may experience difficulties in learning maths and suggests some practical ways to help such children to be successful.

Mathematical misconceptions: a guide for primary teachers  , 20081847874401,184787441X,9781847874405,9781847874412
Book With contributors comprised of teachers, teacher educators, mathematicians and psychologists, Mathematical Misconceptions brings together information about pupils' work from four different countries, and looks at how primary children think about numbers and use them. It explores the reasons for their successes, misunderstandings and misconceptions and aims to broaden the reader's own mathematical knowledge.

Mathematical misconceptions: a guide for primary teachers  , 2008 (electronic resource)
Book With contributors comprised of teachers, teacher educators, mathematicians and psychologists, Mathematical Misconceptions brings together information about pupils' work from four different countries, and looks at how primary children think about numbers and use them. It explores the reasons for their successes, misunderstandings and misconceptions and aims to broaden the reader's own mathematical knowledge

Understanding and teaching primary mathematics  2016
Book This very practical book is aimed at early career teachers who wish to develop their mathematical and pedagogic knowledge. It explores each mathematical topic in depth and also considers key aspects of the mathematics curriculum, including problem solving and issues around inclusion. There are many practical and reflective tasks to help the reader engage with the material.

Understanding and teaching primary mathematics  20169781138906402
Book This very practical book is aimed at early career teachers who wish to develop their mathematical and pedagogic knowledge. It explores each mathematical topic in depth and also considers key aspects of the mathematics curriculum, including problem solving and issues around inclusion. There are many practical and reflective tasks to help the reader engage with the material

Connecting primary maths & science: a practical approach  , 20169780335261888
Book This is an excellent new book looking at crosscurricular links between maths and science. This fits excellently with our sessions after Christmas!

Using resources to support mathematical thinking: primary and early years  , 20071844450570,9781844450572
Book This book offers ideas on how children learn, why use resources in teaching mathematics, mathematical models and images, how to adapt resources for children with SEN, cross curricular resources for mathematics and the environment and outdoor classroom as a mathematics resource.

Using resources to support mathematical thinking: primary and early years  , 2007 (electronic resource)
Book This book offers ideas on how children learn, why use resources in teaching mathematics, mathematical models and images, how to adapt resources for children with SEN, cross curricular resources for mathematics and the environment and outdoor classroom as a mathematics resource.

Mathematical difficulties: psychology and intervention  20080123736293,9780123736291
Book This detailed book explores research around children's difficulties in learning mathematics. It considers how to use assessment tools to identify particular difficulties and also looks at research around specific intervention programmes.

Mathematical difficulties: psychology and intervention  2008 (electronic resource)
Book This detailed book explores research around children's difficulties in learning mathematics. It considers how to use assessment tools to identify particular difficulties and also looks at research around specific intervention programmes.

Maths and ICT in the primary school: a creative approach  20061843123770
Book English offers a balanced approach to the use of ICT when teaching mathematics. He describes the benefits gained from the use of interactive whiteboards, calculators and computers, but also wisely warns that substance should never be sacrificed for ‘awe and wonder’.

Maths and ICT in the primary school: a creative approach  2006 (electronic resource)
Book English offers a balanced approach to the use of ICT when teaching mathematics. He describes the benefits gained from the use of interactive whiteboards, calculators and computers, but also wisely warns that substance should never be sacrificed for ‘awe and wonder’

Curriculum provision for the gifted and talented in the primary school: English, maths, science and ICT  , 2001 (electronic resource)
Book This book contains an interesting chapter on curriculum provision for high attaining pupils in mathematics.

Curriculum provision for the gifted and talented in the primary school: English, maths, science and ICT  , 20011853467715
Book This book contains an interesting chapter on curriculum provision for high attaining pupils in mathematics.

Children's errors in mathematics 20149781446274439,9781446274422
Book A useful series of articles discussing common misconceptions and errors found in the primary school including a range of teaching responses and strategies. Chapter 2 discusses the teacher's role in dealing with errors in the mathematics classroom.

Primary mathematics across the curriculum  , 20120857259679,9780857259677
Book This book is designed to help teachers consider how mathematics can support learning across the curriculum. It includes examples of rich contexts for mathematics drawn from across the curriculum and beyond.

Understanding mathematics for young children: a guide for teachers of children 38  , c20139781446248652,9781446248669
Book This text looks in depth and key concepts involved in early stages of learning for each of the key mathematics topics. The opening chapter considers some big issues including understanding as making connections and developing understanding of mathematical symbols. Each chapter includes reflection tasks and references to related research.

Low attainers in primary mathematics: the whisperers and the maths fairy  20040415315549,0415315530
Book Houssart draws on close observations with children in lower mathematics sets in primary schools to investigate why some children opt out of mathematics at an early age. After introducing us to the children, she addresses a particular type of mathematical task in each chapter, including: using number equipment; mental, practical and written work and mathematical tasks.

Reflective primary mathematics: a guide for student teachers  20159781446295106
Book The aim of this text is to support trainee teachers in considering the kind of mathematics teacher they wish to become and support them in developing their philosophy and practice. It contains interesting chapters on attitudes to maths, mathematical engagement and subject knowledge.

Teaching mathematics to able children  20011853466875
Book The accessible and practical book will help to give you the confidence and knowledge to effectively challenge and develop the skills of able children in mathematics. The book demonstrates how to identify high mathematical ability in a pupil, how to plan suitably challenging activities and how to implement strategies for differentiation.

Teaching mathematics to able children  2001 (electronic resource)
Book The accessible and practical book will help to give you the confidence and knowledge to effectively challenge and develop the skills of able children in mathematics. The book demonstrates how to identify high mathematical ability in a pupil, how to plan suitably challenging activities and how to implement strategies for differentiation.

Thinking mathematically  , , 20100273728911,9780273728917
Book This book explores the development of problem solving skills in a broad sense. It also includes many examples of rich starting points for problem solving. The last chapter on 'Powers, Themes, Worlds and Attention' is particularly relevant to this module as it considers some generic problem solving approaches we can use to provide rich learning opportunities in the classroom.

Thinking mathematically  , , 2010 (electronic resource)
Book This book explores the development of problem solving skills in a broad sense. It also includes many examples of rich starting points for problem solving. The last chapter on 'Powers, Themes, Worlds and Attention' is particularly relevant to this module as it considers some generic problem solving approaches we can use to provide rich learning opportunities in the classroom.

Designing and using mathematical tasks  , , 20061899618651,9781899618651
Book Mason and JohnstonWilder are experts in analysis and design of mathematical learning tasks. This indepth texts contains useful chapters on mathematical tasks, mathematical activity, interactions and progression in mathematics.

Improving primary mathematics teaching and learning  20129780335246762,9780335246779
Book This text contains chapters by different authors on aspects of mathematics pedagogy that are highly relevant to this module. The book includes chapters exploring: using children's mathematical misconceptions; mathematical learning beyond the classroom; learning difficulties in mathematics; challenging able children; mathematical talk; evidencebased mathematics teaching; selfknowledge, pupil knowledge and subject knowledge

Improving primary mathematics teaching and learning  2012 (electronic resource)
Book This text contains chapters by different authors on aspects of mathematics pedagogy that are highly relevant to this module. The book includes chapters exploring: using children's mathematical misconceptions; mathematical learning beyond the classroom; learning difficulties in mathematics; challenging able children; mathematical talk; evidencebased mathematics teaching; selfknowledge, pupil knowledge and subject knowledge

Supporting early mathematical development: practical approaches to playbased learning  20100415491622,0415491614,9780415491624,9780415491617
Book In this text McGrath combines theory and practice. She considers key principles that underpin teaching and learning of mathematics in the early years as well as considering how to develop understanding of number and number operations and how to solve mathematical problems. There is an interesting chapter on 'connecting across the curricula'.

Supporting early mathematical development: practical approaches to playbased learning 
Book In this text McGrath combines theory and practice. She considers key principles that underpin teaching and learning of mathematics in the early years as well as considering how to develop understanding of number and number operations and how to solve mathematical problems. There is an interesting chapter on 'connecting across the curricula'.

Mathematics in early years education  , , , 20189781138731127
Book 4th ed. This book explores how to integrate learning of all of the key mathematical topics into planning and learning in an early years setting.

Mathematics in early years education  , , 2012 (electronic resource)
Book 3rd ed. This book explores how to integrate learning of all of the key mathematical topics into planning and learning in an early years setting.

Primary mathematics: teaching theory and practice  , , , 20149781446295595
Book This text is designed to support early career teachers in developing their practice. It includes a chapter on teaching strategies and chapter on key mathematics topics including algebra. Each chapter includes reflective tasks and suggestions for further reading which includes relevant research

Big ideas in primary mathematics  20179781473913172
Book This new book from Robert Newell is a highlyengaging text that covers a number of key topics in mathematics. The chapter on algebra is particularly useful.

Pattern in the teaching and learning of mathematics  20050826477704
Book Like the Anghileri book, this book of readings takes as its central theme the ability of children to think mathematically, and to see the patterns and interconnectedness of number. As an example, the excellent chapter by John Threlfall and Len Frobisher considers the relatively limited range of relationships between numbers that children need to know in order to move from known number facts to unknown ones.

Pattern in the teaching and learning of mathematics  2005 (electronic resource)
Book Like the Anghileri book, this book of readings takes as its central theme the ability of children to think mathematically, and to see the patterns and interconnectedness of number. As an example, the excellent chapter by John Threlfall and Len Frobisher considers the relatively limited range of relationships between numbers that children need to know in order to move from known number facts to unknown ones.

Primary mathematics  20051844450368
Book This reader contains many thoughtprovoking chapters that are highly relevant for this module. Topics include teaching children to think mathematically, using contexts for children’s mathematical thinking, problemsolving and catering for a range of abilities in mathematics. Chapter 2 on Teaching Children to Think Mathematically provides an interesting starting point for think about algebra in primary schools.

Teaching mathematics creatively  , 20159781138800557
Book This book develops some of the key themes from this module including motivating children through problemsolving, the use of creative contexts for developing mathematical thinking and exploiting opportunities to use mathematics across the curriculum. Chapter 2 I hate maths! Positive feelings, creative dispositions and mathematics explores the way in which children's emotions affect their learning in maths and how the mathematical learning environment we create as teachers influences children's feelings about their learning.

Teaching mathematics creatively  , 2015
Book This book develops some of the key themes from this module including motivating children through problemsolving, the use of creative contexts for developing mathematical thinking and exploiting opportunities to use mathematics across the curriculum. Chapter 2 I hate maths! Positive feelings, creative dispositions and mathematics explores the way in which children's emotions affect their learning in maths and how the mathematical learning environment we create as teachers influences children's feelings about their learning.

Essential primary mathematics  20139780335247028
Book This text is aimed at early career teachers and explores each key mathematics topic in detail. Chapter 6 on Algebra is particularly relevant for this module.

Essential primary mathematics  2013 (electronic resource)
Book This text is aimed at early career teachers and explores each key mathematics topic in detail. Chapter 6 on Algebra is particularly relevant for this module.

Mathematics in the primary school  19890415025192
Book Although old, this text is included on your reading list as it was highly influential. In it Skemp looks in depth at how children construct mathematical knowledge. Skemp promoted a theory about learning that identifies two contrasting modes of understanding: relational understanding (based on connecting new concepts to previous learning) and instrumental understanding (based on the learning of set procedures).

Mathematics in the primary school  1989 (electronic resource)
Book Although old, this text is included on your reading list as it was highly influential. In it Skemp looks in depth at how children construct mathematical knowledge. Skemp promoted a theory about learning that identifies two contrasting modes of understanding: relational understanding (based on connecting new concepts to previous learning) and instrumental understanding (based on the learning of set procedures).

Navigating numeracies: home/school numeracy practices  , , , c20081402057067,9781402057069
Book The aim of the book, and the associated research, is to explore the wide range of factors that might contribute to low attainment in numeracy. The authors look beyond the school to consider influences in the home and wider society.

Navigating numeracies: home/school numeracy practices  , , c2005 (electronic resource)
Book The aim of the book, and the associated research, is to explore the wide range of factors that might contribute to low attainment in numeracy. The authors look beyond the school to consider influences in the home and wider society.

How the brain learns mathematics  20159781483368467
Book This text explores uses research on the way the brain works to consider issues around the learning of mathematics. It includes an interesting chapter on recognising and addressing mathematical difficulties.

Issues in teaching numeracy in primary schools  20100335241530,9780335241538
Book Some useful background reading from a range of contributors. It explores some of the debates about numeracy. Chapters cover a variety of topics including: effective teaching of numeracy; talk and groupwork in mathematics; making connections using resources; teaching for understanding; learning from errors and misconceptions.

Issues in teaching numeracy in primary schools  2010 (electronic resource)
Book Some useful background reading from a range of contributors. It explores some of the debates about numeracy. Chapters cover a variety of topics including: effective teaching of numeracy; talk and groupwork in mathematics; making connections using resources; teaching for understanding; learning from errors and misconceptions.

Teaching primary mathematics  20130857028790,0857028804,9780857028792,9780857028808
Book An uptodate and accessible textbook combining practical guidance for the classroom with key theoretical coverage. It covers many of the themes we look at in this module including: teacher subject knowledge and beliefs; teaching approaches; use of representations in mathematics; what we can learn from other countries. Each chapter offers a suggestions for further reading.

Making connections in primary mathematics: a practical guide  , 20041843120887
Book This book has interesting chapters on crosscurricular application of mathematics and the outdoor learning of mathematics.

Numeracy and learning difficulties: approaches to teaching and assessment  20041843121948
Book This book contains practical advice about how to tackle common learning difficulties and how to identify and bridge gaps in students' knowledge. It contains useful sections on learning theories in mathematics including constructivism; approaches and strategies to improve attainment including the role of questioning and use of resources; assessment.

Numeracy and learning difficulties: approaches to teaching and assessment  2004 (electronic resource)
Book This book contains practical advice about how to tackle common learning difficulties and how to identify and bridge gaps in students' knowledge. It contains useful sections on learning theories in mathematics including constructivism; approaches and strategies to improve attainment including the role of questioning and use of resources; assessment.


Academic Journals and Reports 16 items

Developing the use of visual representations in the primary classroom  , , , 2013
Document This report summarises the findings of a research project carried out for the Nuffield Foundation by Patrick Barmby, David Bolden, Stephanie Raine & Lynn Thompson in 2011 about the impact for pupils and teachers of developing wider use of representations in mathematics classrooms.

Learning outside the classroom: how far should you go?  2008
Document

Educational studies in mathematics (electronic resource)
Journal

Journal

Journal for research in mathematics education (electronic resource)
Journal

The journal of mathematical behavior (electronic resource)
Journal

Journal of mathematical behavior
Journal

Journal

Journal

Mathematics teaching (electronic resource)
Journal

Journal

Micromath (electronic resource)
Journal


Mathematics Websites 9 items

National Centre for Excellence in the Teaching of Mathematics  NCETM
Website National Centre for the Excellence in Teaching of Mathematics

Webpage NRICH – fantastic site for problemsolving activities, investigation, articles...

BBC  Schools Ages 411  Numeracy Sites
Webpage BBC Mathematics

Webpage Ask Dr Math (maths search)

Website Mathematics Association

Mathematics Teaching and Learning Support • ATM
Website Association of Teachers of Mathematics

A Maths Dictionary for Kids by Jenny Eather
Website Mathematics dictionary

Website BEAM (BE A Mathematician)

Webpage TES (Times Educational Supplement) resources includes Teachers TV clips


Other resources 8 itemsThere are a number of resources in the school experience section that I would suggest you investigate prior to SBT3. The library has recently invested in a range of new textbooks which give you an indication of the kind of materials recently adopted by some of our local schools. Below are copies of the Maths No Problem (the only government approved Mastery textbook) for Years 2 and 6. We looked at these in our session on adapting and enhancing schemes of work.

Maths  no problem!: Singapore Maths English National Curriculum 2014, Textbook 2A  , , , 20161910504025,9781910504024
Book

Maths  no problem!: Singapore Maths English National Curriculum 2014, Workbook 2A  , , 20179781910504031
Book

Maths  no problem!: Singapore Maths English National Curriculum 2014, Textbook 2B  , , , 20159781910504086
Book

Maths  no problem!: Singapore Maths English National Curriculum 2014, Workbook 2B  , , 20159781910504093
Book

Maths  no problem!: Singapore Maths English National Curriculum 2014, Textbook 6A  , 20159781910504161
Book

Maths  no problem!: Singapore Maths English National Curriculum 2014, Workbook 6A  20159781910504178
Book

Maths  no problem!: Singapore Maths English National Curriculum 2014, 6B: Workbook  , , 20169781910504239
Book
