Questions Pupils Ask
Colin Foster, Mathematical Association, 2017, ISBN 978-0-906588-91-8

If two minuses make a plus, why don't two pluses make a minus? Is there a formula for factorial? And why isn't pi a whole number? In this collection of over 40 articles from the journals Mathematics in School and Symmetry Plus, Colin Foster takes Questions Pupils Ask about mathematics as his starting point for a series of reflections on learning and teaching secondary mathematics.

Also included are articles addressing a diverse array of mathematical topics, spanning number, algebra, geometry and statistics, and involving puzzles, applications of mathematics to daily life and tasks to take into the classroom.

For details, click here.

"Covering a diverse range of topics including number, algebra, geometry and statistics, each essay is thought-provoking, engagingly written, and accessible for KS3 and 4 students, as well as teachers".
Review in (2017) Teach Secondary, 6(5), 52 - click here to read the entire review.

"Throughout this short book he gives us example after example of the dialogue between teacher and learner which is essential to the development of mathematical ability, and he makes it clear that even the most banal question can lead to an interesting exchange of ideas and a growth in confidence and enjoyment - for both pupil and teacher."
Gerry Leversha (2018) The Mathematical Gazette, 102(555), 555-557. https://doi.org/10.1017/mag.2018.144 - click here to read the entire review.

"Very relevant to today's teachers and students ... an excellent addition to a mathematics department's bookshelf".
Darren Brumby (2019) Mathematics in School, 48(2), 34 - click here to read the entire review.

The Essential Guide to Secondary Mathematics: Successful and Enjoyable Teaching and Learning
Colin Foster, Routledge, 2013, ISBN 978-0-415-52770-5 (hbk), ISBN 978-0-415-52771-2 (pbk), ISBN 978-0-203-11883-2 (ebk)

Combining research-based theory with fresh, practical guidance for the classroom, this book is a stimulating new resource for all student and practising teachers looking for new ideas and inspiration. With an emphasis on exciting your mathematical and pedagogical passions, it focuses on the dynamics of the classroom and the process of designing and using rich mathematical tasks. The text is punctuated throughout by frequent tasks, some mathematical and others more reflective, which are designed to encourage independent thinking.

Key topics covered include:

·         Preparing yourself: thinking about mathematics and pedagogy, taking care of your health and dealing with stress

·         Different styles of learning and teaching mathematics

·         Ideas for lessons: what does it take to turn an idea into a lesson?

·         Tasks, timings and resources

·         Equality and dealing positively with difference

·         Mathematical starters, fillers and finishers: achieving variety

·         The mathematical classroom community: seating layouts, displays and practical considerations

·         Assessment: effective strategies for responding to learners‘ mathematics and writing reports.

The Essential Guide to Secondary Mathematics is a valuable resource both for beginning teachers interested in developing their understanding, and for experienced teachers looking to re-evaluate their practice. Aiming to develop all aspects of your mathematics teaching, this book will help you to devise, adapt and implement ideas for successful and enjoyable teaching and learning.

For more details, click here. Click here for sample pages.

"Worthy of further study even for the experienced teacher ... There will be very few teachers who will not glean some useful information or at least prompt memories from past experiences. An essential book for every department."
Grant MacLeod (2013) Review in Mathematics in School, 42(2), 38-39 - click here to read the entire review.

"This is a book for all teachers of mathematics, whether you are new to the profession or well established. Colin Foster's book is a distillation of his experience as a mathematics teacher, learner and researcher in mathematics education. It provides a well-judged mixture of practical advice, informed by his extensive reading in research and theory. ... There is much here which could be immediately applied in all mathematics classrooms to benefit your teaching and your learners. ... It deserves to be widely read."
David Wright (2013) Review in Learning & Teaching Update, 64, 4 - click here to read the entire review.

Ideas for Sixth-Form Mathematics: Pure Mathematics & Statistics
Colin Foster, Association of Teachers of Mathematics, 2012, ISBN 978-1-898611-74-5

This book offers a wealth of innovative lesson ideas for important areas of post-16 mathematics teaching, bringing variety to the Pure Mathematics and Statistics curriculum areas within AS/A2 mathematics and IB. The material is arranged by topic and enables teachers to move away from an over-emphasis on routine textbook-based work. Hints and suggestions are included to make it clear where the ideas may lead as well as additional material for extension.

Click on the image to buy from www.atm.org.uk. Click here for sample pages.

"Another excellent book ... superbly illustrated with clear graphs and diagrams ... a very useful resource."
Grant MacLeod (2012) Review in Mathematics in School, 41(4), 43

"Many tempting and curious takes on curriculum topics that are central to higher school mathematics curricula."
Melissa Rodd, Institute of Education, London, UK; Association of Teachers of Mathematics - click here to read the entire review.

"This book offers a range of problems at many different levels of difficulty so there is something to suit every mathematical palate! ... this book has a place on the bookshelf of every A level Maths teacher, however experienced, as there are so many ideas that can easily form part of their repertoire of activities. I only wish I had it sooner in my career!"
Heather Davis, Lead Consultant for Mathematics, Cornwall Learning; Association of Teachers of Mathematics - click here to read the entire review.

Ideas for Sixth-Form Mathematics: Further Pure Mathematics & Mechanics
Colin Foster, Association of Teachers of Mathematics, 2012, ISBN 978-1-898611-75-2

This book complements the first volume, offering a wealth of innovative lesson ideas for important areas of post-16 mathematics teaching, bringing variety to the Further Pure Mathematics and Mechanics curriculum areas within AS/A2 mathematics and IB. As in the previous volume, the material is arranged by topic and enables teachers to move away from an over-emphasis on routine textbook-based work. Hints and suggestions are included to make it clear where the ideas may lead as well as additional material for extension.

"Another excellent book ... All the main topics are covered."
Grant MacLeod (2013) Review in Mathematics in School, 42(2), 39 - click here to read the entire review.

"As a marker for Mechanics 1 I would highly recommend using these activities with each topic ... The section on Further Pure topics had me reaching for my pen and paper to try out some of the activities!"
Heather Davis, Lead Consultant for Mathematics, Cornwall Learning; Association of Teachers of Mathematics- click here to read the entire review.

Flowchart Investigations: Explorations in Mathematics
Colin Foster, Mathematical Association, 2012, ISBN 978-0-906588-76-5

Flowcharts are a visually engaging way of describing mathematical processes and can offer a starting point for rich mathematical activity. The 20 flowcharts in this book (also available on an enclosed CDROM) provoke purposeful mathematics and are accompanied by questions and prompts inviting learners to experiment, form conjectures, test their ideas and work on justification and proof. There is ample opportunity for learners to approach the tasks in different ways, to modify the flowcharts and to pose their own questions. Teacher pages for each task give details of the relevant mathematics and some suggestions of how the tasks might be used. This book is aimed at all teachers of mathematics at Key Stages 3 & 4, though it will also find some use at Key Stage 2.

"A collection of 20 intriguing mathematical adventures. Instantly inviting engagement, and naturally allowing students to extend themselves without undue pressure, the charts are presented with questions and prompts that encourage independent investigation, whilst teacher pages for each task draw attention to relevant mathematical concepts, and suggest ways in which learners might be gently guided towards exciting discoveries."
Review in (2012) Teach Secondary, 2, 82 – click here to read the entire review.

"Challenging and thought provoking ... An excellent resource."
Kevin Higham, Association of Teachers of Mathematics - click here to read the entire review.

"There is something in Flowchart Investigations for everybody and I would suggest every mathematics department should have a copy of it and use it!"
John Sykes (2012) Review in Mathematics in School, 41(5), 47 - click here to read the entire review.

Resources for Teaching Mathematics 11-14
Colin Foster, Continuum, 2011, ISBN 978-1-441142-27-6

This resource contains 50 ready-to-use mathematics lesson plans suitable for the whole department to use with learners aged 11-14. Each plan consists of a teacher's sheet which breaks down the lesson into time-allocated sections from starter through to homework, together with a photocopiable (or downloadable) student task sheet to give out. There is also a companion website with extra material to support the lesson plans in the book, giving teachers the time and confidence to try new activities in the classroom with minimal preparation.

The lesson tasks are open-ended and encourage deep mathematical thinking, allowing learners to explore different topics creatively through solving problems in their own way. This is an essential resource for any busy teacher of mathematics.

To preview the book, click here; for the online resources, click here.

"The problems in this book would enrich the mathematical learning of any class; they are clear and challenging whilst being easily differentiable. Colin Foster has produced a resource that will extend the mathematical learning of any student, helping them to engage with mathematics, instead of just doing mathematics."
James Robinson, Teacher of Mathematics, Ripley St Thomas School, Lancaster, UK

"Colin Foster has once again provided a rich treasure-trove of lesson ideas that will undoubtedly serve to excite the imagination of all learners. Each lesson holds the potential to be explored for a week (if not more!). An exciting resource that I look forward to continuing to use with all of my classes."
Christopher Martin, Teacher of Mathematics, Haverstock School, London, UK

"Resources For Teaching Mathematics 11-14 is by far and away the most comprehensive collection of high quality mathematical activities that I have ever seen. The tasks cover such a wide range of different activities which are both accessible and interesting to reluctant mathematicians and will challenge and fascinate the most able. There are so many different ways of exploring each idea, which are clearly explained in the very detailed plans, that it makes it easy for every mathematics teacher to give their students a positive experience of exploring mathematics. Colin has written the book that every maths teacher should have."
Catherine Scarlett, Teacher of Mathematics, Driffield School, East Yorkshire, UK

"Each lesson is designed to make pupils think about mathematics in a stimulating and at times, unusual way ... The lessons vary quite considerably to include all kinds of activities."
Grant MacLeod (2012) Review in Mathematics in School, 41(2), 38-39

Resources for Teaching Mathematics 14-16
Colin Foster, Continuum, 2010, ISBN 978-0-826436-03-0

This book contains 70 ready-to-use mathematics lessons suitable for students aged 14-16. Some lessons offer alternative routes through the curriculum, such as practising indices by solving radical equations, while others concentrate on difficult ideas, like appreciating that not all mathematical relationships are linear. The lessons focus on problem solving and putting mathematics into context, and are suitable for a variety of qualifications, including GCSE and IGCSE. This is an essential resource for any busy teacher of mathematics.

For the online resources, click here.

"This is an essential resource book for all secondary mathematics teachers ... so many lovely ideas to introduce students to concepts through investigative approaches to learning. Colin offers an approach which teachers can adopt and adapt to existing schemes of work and which takes on board key issues of differentiated learning and teaching without a textbook. I shall definitely recommend this book to friends and acquaintances who teach mathematics ... in fact I already have done."
Mike Ollerton, experienced Teacher, Teacher Trainer and Consultant, UK

"The title of this book understates what it provides. This is far more than a book of resources ... this is a book of gems. These are lessons that will engage the students (and the teachers) in some quality mathematical thinking."
Karen Hancock, Advanced Skills Teacher, Oriel High School, Crawley, UK

"I refuse to believe a teacher could not find something useful ... the ideas are well presented ... I would recommend every department having a copy on their shelves ... the ideas presented make for strong foundations."
Grant MacLeod (2011) Review in Mathematics in School, 40(2), 35

"Each lesson has a very rich feel to it, giving lots of opportunity for class discussion ... The notes provide a clear sense of direction, and many many questions and prompts to ensure the lesson has many possible outcomes - all of which represent a significant learning experience for the students ... This is just the right book at the right time - as we're looking to new GCSE courses and would like more rich tasks to help our students think, and think more widely, about each topic - this is ideal."
Peter Hall, Advanced Skills Teacher of Mathematics, Imberhorne School, East Grinstead; Association of Teachers of Mathematics - click here to read the entire review.

"Accessible to groups of learners with a wide range of attainment ... All of the activities have well designed resources, allowing a busy teacher to adopt them with very little extra preparation ... While the main use of this resource will be for working with students studying for their GCSE or similar qualifications, many of the activities could be profitably adapted to be used with either younger or more advanced learners, particularly where a teacher might want to introduce a more enquiry based approach to a group of learners unused to it. Highly recommended!"

David Wright (2011) Review in Learning & Teaching Update, 48, 11

Mathematics for Every Occasion
Colin Foster, Association of Teachers of Mathematics, 2009, ISBN 978-1-898611-60-8

This book offers suggestions for rich mathematical tasks inspired by topical themes occurring throughout the school year. It includes twenty-one different occasions with several suggestions for each. All the activities lead to interesting mathematical possibilities that capitalise on the moment in question.

Click on the image to buy from www.atm.org.uk.

"This book has some lovely ideas ... a fantastic inspiration for rich ideas and drawing a little colour and interest into mathematics lessons."
Emma Folman, Association of Teachers of Mathematics - click here to read the entire review.

"For the sake of a tenner, every department should have a copy."
Grant MacLeod (2010) Review in Mathematics in School, 39(3), 42

Variety in Mathematics Lessons
Colin Foster, Association of Teachers of Mathematics, 2008, ISBN 978-1-898611-54-7

This book is a guide for teachers who wish to offer a greater diversity of experiences in their school mathematics lessons. It offers twelve different models or styles of lesson, with examples of how each one might be realised in practice. A 'must' for any maths teacher who feels that lessons are too "samey" and wants to inject more variety and enthusiasm into their teaching.

Click on the image to buy from www.atm.org.uk. Click here for sample pages.

For the online resources, click here.

"I absolutely love this book."
Mike Ollerton, freelance consultant; Association of Teachers of Mathematics - click here to read the entire review.

"All teachers, from trainees to those with years of experience, will find ideas here that will add variety and interest for them and for their pupils. Every maths department should own a copy and every maths teacher should use it."
Mark Dawes, Advanced Skills Teacher of Mathematics, Comberton Village College, Cambridge; Association of Teachers of Mathematics - click here to read the entire review.

"A fascinating and challenging set of ideas ... it would be impossible to read the book and not find something new on every page ... this book is a real gem and cannot fail to help develop our teaching."
Peter Hall, Advanced Skills Teacher of Mathematics, Imberhorne School, East Grinstead; Association of Teachers of Mathematics - click here to read the entire review.

"A valuable resource for all teachers."
Grant MacLeod (2008) Review in Mathematics in School, 37(5), 35

50 Mathematics Lessons: Rich and Engaging Ideas for Secondary Mathematics
Colin Foster, Continuum, 2008, ISBN 978-1-847061-02-7

This book contains details for 50 varied and interesting mathematics lessons, covering core topics from the 11-16 curriculum. Minimal preparation time is required, and the lessons seek to bring the ideas to life in unusual or memorable ways.

For the online resources, click here.

"This collection is a 'must have' for every teacher who wants to inspire students to be excited by mathematics, yet not stray too far from core topics. Every lesson contains key insights into mathematics, using ideas, links and contexts which are mysterious, fun, silly, bizarre, practical and historical."

Anne Watson, Professor of Mathematics Education, Oxford University

"This is an excellent book, which no mathematics department should be without. Its 50 self-contained lessons offer amusing, fascinating and mathematically worthwhile tasks which are supported by excellent teacher notes. Most books are not worth recommending, but this is different."
Paul Andrews, Senior Lecturer in Mathematics Education, Cambridge University

"A set of very good tasks indeed ... This is a great resource."
Peter Hall, Advanced Skills Teacher of Mathematics, Imberhorne School, East Grinstead; Association of Teachers of Mathematics - click here to read the entire review.

"The activities are very varied and very accessible to busy teachers without being patronising in terms of their mathematical content ... The book would make a very useful resource for teachers in a secondary school or possibly even the top end of Key Stage 2."
Martin Marsh (2009) Review in Equals, 15(1), 24 - click here to read the entire review.

"...the author has succeeded in creating a nice collection of problems that teachers can easily incorporate into their lessons."
Michael Davis (2009), Sebastian River High School, Sebastian, Florida. Review in Mathematics Teacher, 103(2), 106 - click here to read the entire review.

Instant Maths Ideas for Key Stage 3 Teachers: Number and Algebra
Colin Foster, Nelson Thornes, 2003, ISBN 0748786686
NOW AVAILABLE FREE ONLINE: click here

"Colin Foster has probably done what many teachers or Maths departments wish had been done a long while ago."
Karen Hancock, Association of Teachers of Mathematics - click here to read the entire review.

"I was pleasantly surprised at the number of ideas (old and new)."
Peter Ransom (2005) Times Educational Supplement: Teacher, 7 January

Instant Maths Ideas for Key Stage 3 Teachers: Shape and Space,
Colin Foster, Nelson Thornes, 2003, ISBN 0748786694
NOW AVAILABLE FREE ONLINE: click here

"These books are just what their titles suggest they should be. They are packed with ideas for starters, investigations, extension work, plenaries and for generally enhancing the routine work done in the classroom ... simply a collection of excellent ideas ... an inspiring source of ideas ... I thoroughly recommend these books."
Cordelia Myers (2006) Review in Mathematics in School, 35(1), 31-32

Instant Maths Ideas for Key Stage 3 Teachers: Data Handling, Numeracy and ICT,
Colin Foster, Nelson Thornes, 2003, ISBN 0748786708
NOW AVAILABLE FREE ONLINE: click here

"With only a little preparation these ideas can be incorporated or attached to a scheme of work to reinforce and vary the approach ... It is a useful addition to your bookshelf."
Jane Foxon, Association of Teachers of Mathematics - click here to read the entire review.

"No time to plan? Too busy to be creative? These books fulfil the dreams of busy teachers who need to teach core curriculum topics in ways which stimulate, excite and challenge all their students. Every idea in these books encourages mathematical thinking, deep understanding, and learning key mathematical ideas. Colin Foster has collected a wide range of tried-and-tested tasks and contexts to teach core curriculum topics and organised them to be accessible for quick planning. Indispensable!"

Anne Watson, Professor of Mathematics Education, Oxford University