Colin Foster
King Henry VIII School
Warwick Road
Coventry
CV3 6AQ
UK
I am second in the mathematics department at King Henry VIII School in Coventry, UK, teaching all ages from 11 to 18. I also write books and articles on mathematics teaching.
In 1995 I obtained my BA in Natural Sciences from Magdalene College, Cambridge, and began postgraduate research at the University Chemical Laboratory, completing a PhD in Organic Synthesis under the supervision of Professor Ian Fleming. I followed this with a year supervising around eighty undergraduate chemistry students (of all years) from seven colleges, alongside doing numerous regular laboratory demonstrations. After taking a Postgraduate Certificate in Education (PGCE) in Secondary Mathematics at the University of Cambridge Faculty of Education, I taught mathematics (and a little science) at Bottisham Village College before taking up my current post.
I am a member of the Association of Teachers of Mathematics, the Mathematical Association and the British Society for Research into Learning Mathematics and I have regularly participated in the Institute of Mathematics Pedagogy. I have co-edited the education journal Mathematics Teaching, published by the Association of Teachers of Mathematics, and I have been a University Subject Tutor for the Warwick University Secondary Mathematics PGCE course. In 2010 I obtained Chartered Mathematics Teacher (CMathTeach) status and in 2012 I was elected a Fellow of the International Society for Design and Development in Education. I am currently a consultant for the Mathematics Assessment Resource Service project at the University of Nottingham and a question writer for the AS/A Level Thinking Skills (9694) examination, administered by University of Cambridge International Examinations.
I have written the free website www.mathematicalbeginnings.com, which contains over 40 starting points (beginnings) for mathematical activity.
Books
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Coming soon... |
The Essential Guide to
Secondary Mathematics: Successful and Enjoyable Teaching and Learning 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. |
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Ideas for Sixth-Form Mathematics: Pure
Mathematics and Statistics Click on the image to buy from www.atm.org.uk. Click here for sample pages. “Many tempting and curious
takes on curriculum topics that are central to higher school mathematics
curricula.” |
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Coming soon...
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Ideas for Sixth-Form
Mathematics: Further Pure Mathematics and Mechanics |
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Flowchart
Investigations: Explorations in Mathematics |
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Resources for Teaching Mathematics 11–14 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.” "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." “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.” “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.” |
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Resources for Teaching Mathematics 14–16 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.” “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.” “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.” “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.”
“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
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Mathematics for Every Occasion 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.”
"For the sake of a tenner, every department should have a
copy."
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Variety in Mathematics Lessons 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.” “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.” “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.” "A valuable resource for all teachers."
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50 Mathematics Lessons: Rich and Engaging Ideas for Secondary
Mathematics 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.” “A set of very good tasks indeed ... This is a great
resource.” “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.”
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Instant
Maths Ideas for Key Stage 3 Teachers: Number and Algebra "Colin Foster has probably done what many teachers or
Maths departments wish had been done a long while ago." "I was pleasantly surprised at the number of ideas (old
and new)." |
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Instant
Maths Ideas for Key Stage 3 Teachers: Shape and Space, "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." |
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Instant Maths Ideas for Key Stage 3 Teachers: Data
Handling, Numeracy and ICT, “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 |
Website
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www.mathematicalbeginnings.com
This website contains a free collection of over 40 starting points (beginnings) for mathematical activity. They could be used with learners aged around 11 upwards as a part of normal mathematics lessons or as something ‘a little different’. Some prompts are provided to help learners find mathematics to work on and some brief teacher’s notes are also offered, indicating possible mathematics that could emerge. Click here to take a look. |
Articles
Foster, C. (2012) HCF
and LCM – Beyond Procedures, Mathematics in School, 41(3), 30–32
Foster, C. (2012) Trigonometry
Without Right Angles, Mathematical Spectrum, 44(3), 98–101
Foster, C. (2012) The
Probability Distribution for a Biased Spinner, Teaching Statistics,
34(1), 41-43, doi:10.1111/j.1467–9639.2011.00481.x
Foster, C. (2012) Odd
and Even Fractions, Mathematical Spectrum, 44(2), 69–72
Foster, C. (2012) Symmetrical
Cubics, Mathematical Gazette, 96(536), 96.07, 109–112
Foster, C. (2012) Orthogonal
Mappings, Mathematical Gazette, 96(536), 96.08, 112–115
Foster, C. (2012) Taking
a Short Cut Through Pascal’s Triangle, Mathematical Gazette,
96(536), 96.19, 142–145
Foster, C. (2012) A Day at
the C-Side: Introducing Pythagoras’ Theorem, Teach Secondary,
1, 30-33
Foster, C. (2012) When
is a Parabola not a Parabola?, Mathematics Teacher, 105(7), March,
486–487
Foster, C. (2012) How
to Manipulate Test Scores, The College Mathematics Journal, 43(2),
121-122
Foster, C. (2012) Plus–Minus
Graphs, Mathematics in School,
41(2), 32–33
Foster, C. (2011) The
Significance of a Square-Root Rule, The American Statistician, 65(4),
222, doi:10.1198/tas.2011.11160
Foster, C. (2011) Rooting
for You, Math Horizons, Playground Problem 266, November, 30
Foster, C. (2011) Peripheral
Mathematical Knowledge, For the Learning of Mathematics, 31(3), 24–26
Foster, C. (2011) A Picture is Worth a Thousand
Exercises, Mathematics Teaching, 224, 10–11 (extra material)
Foster, C. (2011) A
Comment on Schnell and Mendoza, Mathematical Gazette,
95(533), 357
Foster, C. (2011) Twenty–One
Forever!, Journal of Recreational Mathematics, 36(3), 194–195
Foster, C. (2011) Student–Generated
Questions in Mathematics Teaching, Mathematics Teacher, 105(1), 26–31
Foster, C. (2011) A
Slippery Slope: Resolving Cognitive Conflict in Mechanics, Teaching
Mathematics and its Applications, 30(4), 216–221, doi:10.1093/teamat/hrr015
Foster, C. (2011) Productive
Ambiguity in the Learning of Mathematics, For the Learning of
Mathematics, 31(2), 3–7
Foster, C. (2011) Straight
Dice, Symmetry Plus, 45(2), 9–10
Foster, C. (2011) Small Is Beautiful After All,
Mathematics Teaching, 222, 38–39
Foster, C. (2011) Marking Time, Mathematics
Teaching, 222, 3–6
Foster, C. (2011) Clock
Problem: 469, The New York State Mathematics Teachers’ Journal, 61(2),
92
Foster, C. (2011) Table
Settings, Symmetry Plus, 44(1),
6–7
Foster, C. (2011) Odd
Questions Pupils Ask, Mathematics in School, 40(1), 34–35
Foster, C. (2010) A Formula for a Square Root,
Mathematics Teaching, 220, 6
Foster, C. (2010) A
Fortuitous Value, Mathematical Gazette, 94(530), 335
Foster, C. (2009) Isometric
Graphs, Mathematical Gazette, 93(527), 289–292
Foster, C. (2009) Knowing
Your Limitations, Teaching Statistics, 31(2), 59–60,
doi:10.1111/j.1467–9639.2009.00349.x
Foster, C. (2009) Consistency
– it’s a foolish obsession, SecEd, 206, 12 March, 6
Foster, C. (2009) Reflections On Editing MT 2005–2008,
Mathematics Teaching, 212, 3
Foster, C. (2008) String Along, Times
Educational Supplement – Magazine, 28 November, 30
Foster, C. (2008) Dead Good, Times
Educational Supplement – Magazine, 21 November, 30
Foster, C. (2008) Add Some Fun, Times
Educational Supplement – Magazine, 7 November, 31
Foster, C. (2008) How
Many Detentions Will I Get?, Mathematics in School, 37(5), 26–27
Foster, C. (2008) Anyone
For Consistency?, Times Educational Supplement –
Magazine, 31 October, 62
Foster, C. (2008) Who Is
Missing?, Times Educational Supplement – Magazine,
24 October, 36
Foster, C. (2008) Exam
Boards Should Stick To Examining, Times Educational Supplement,
26 September, 45
Foster, C. (2008) Ready
To Shake On It, Times Educational Supplement, 5
September, 34
Foster, C. (2008) Element
of Surprise Keeps Learning Alive, Times Educational Supplement,
8 August, 21
Foster, C. (2008) Touching
Story, Times Educational Supplement – Magazine,
18 July, 30
Foster, C. (2008) Name Your
Price, Times Educational Supplement – Magazine,
6 June, 34
Foster, C. (2008) If The Answer Is Instant, The Question Is Pointless, Times
Educational Supplement, 23 May, 33
Foster, C. (2008) Higher
Priorities, Mathematics in School, 37(3), 17
Foster, C. (2008) Leaping Around, Mathematics
Teaching, 208, 48
Foster, C. (2008) Avoiding
Pythagoras, Mathematical Gazette, 92(523), 110–111
Foster, C. (2008) All My
Own Work?, SecEd, 170, 13 March, 7
Foster, C. (2008) You’re
Having A Graph, Times Educational Supplement – Magazine,
7 March, 58–59
Foster, C. (2008) In The Area,
Times
Educational Supplement – Magazine,
25 January, 52
Foster, C. (2008) Beware
The Rise Of Helicopter Teachers, Times Educational Supplement,
18 January, 29
Foster, C. (2007) Counting
Cubes, Times Educational Supplement – Magazine,
14 December, 45
Foster, C. (2007) Getting
Your Bearings, SecEd, 156, 8 November, 12
Foster, C. (2007) Impossibility,
Mathematics
in School, 36(5), 13
Foster, C. (2007) Solving
The X Factor, Times Educational Supplement – Magazine,
16 November, 48–49
Foster, C. (2007) Stage
Fright Does Not Equal Lack Of Involvement, Times Educational Supplement,
12 October, 29
Foster, C. (2007) Pencils
Make A Point, Times Educational Supplement – Magazine,
28 September, 48–49
Foster, C. (2007) Start
Making Money, Times Educational Supplement –
Magazine, 21 September, 52
Foster, C. (2007) The Warwick Dials,
Symmetry
Plus, 34(3), 4
Foster, C. and Williams, H. (2007) Mathematics
is a Spectator Sport, Mathematics Teaching, 204,
40–41
Foster, C. (2007) Line Multiplication, Mathematics
Teaching, 203, 29
Foster, C. (2007) Make
Maths Sparkle, SecEd,
24 May, 12
Foster, C. (2007) Pushing
the Limits, Times Educational Supplement – Magazine,
18 May, 50
Foster, C. (2007) A Degree of
Confusion, Symmetry Plus, 33(2), 7
Foster, C. (2007) Triangles
and Parabolas – The Hard Part!, Symmetry Plus,
33(2), 3
Foster, C. (2007) Economies
of Scale, Times Educational Supplement – Magazine,
11 May, 54
Foster, C. (2007) There's
a Positive Side to Negative Marking, Times Educational Supplement,
11 May, 27
Foster, C. (2007) Mathematical Behaviour, Mathematics
Teaching, 202, 12–13
Foster, C. (2007) As
Easy As 1, 2, 3, ...?, Mathematics Today, 43(2), 76
Foster, C. (2007) Petrol–Pump
Learning Won't Fuel Thinking Skills, Times Educational Supplement, 2 March, 27
Foster, C. (2007) Right–Angled
Triangles and Parabolas, Symmetry Plus 32(1), 10–11
Foster, C. (2007) Stop
Interrupting!, Equals, 13(1), 10–11
Foster, C. (2007) Introducing
... Maths–man!, Mathematics in School, 36(1), 15
Foster, C. (2007) Model
Lessons Put Spontaneity in a Straitjacket, Times Educational Supplement,
5 January, 27
Foster, C. (2006) To
Infinity and Beyond, Times Educational Supplement – Magazine,
24 November, 54
Foster, C. (2006) A
Different Pictorial Way of Looking at Simultaneous Equations, Mathematics in
School, 35(5), 20–21
Foster, C. (2006) Targets
Miss the Point, Times Educational Supplement, 17 November,
27
Foster, C. (2006) Emily's Discovery, Mathematics
Teaching, 199, 30–31
Foster, C. (2006) Anamorphic Art, Mathematics
Teaching, 199, 24–25
Foster, C. (2006) Asking
Questions, Mathematics in School, 35(4), 24
Foster, C. (2006) Pointless
Compasses?, SecEd, 14 September, 113,
13
Foster, C. (2006) 'Wordsworth' Puzzle, Mathematics
Teaching, 196, 48
Foster, C. (2006) Tessellations in Word, Mathematics
Teaching, 196, 24–25
Foster, C. (2006) '2006' Puzzle, Mathematics
Teaching, 195, 48
Foster, C. (2006) My Accidental Parabola, Mathematics
Teaching, 195, 33
Foster, C. et al. (2006) How Do We Get
Them Going?, Times Educational Supplement: Friday, 20
January
Foster, C. (2006) Preparing
the Lesson or Preparing the Teacher?, Report: Association of Teachers
and Lecturers, January, 11
Foster, C. (2006) Webwatch, Mathematics
Teaching, 194, 47
Foster, C. (2006) Getting Confused, Mathematics
Teaching, 194, 18
Foster, C. (2005) Reflections, Mathematics
Teaching, 192, 2
Foster, C. (2005) What
We Did In Our Easter Holiday!, Mathematics Today, 41(3),
71–72
Foster, C., Galligan, L., Mackrell, K., Mason, J., Melville, A., Piggott, J.
and Watson, A. (2005) Freedom and Constraint,
Mathematics
Teaching, 191, 37–39
Foster, C. (2005) Another Look at
Revision, Mathematics Teaching, 191, 6–7
Foster, C. (2005) Slippery
Slopes, Mathematics in School,
34(3), 33–34
Foster, C. (2005) Golden Opportunities for
Creativity, Mathematics Teaching, 190,
26–27
Foster, C. (2004) Differences
over Differences Methods: Pros and Cons of Different Ways of Finding the Nth
Term of a Sequence of Numbers, Mathematics in School, 33(5), 24–25
Foster, C. (2004) Trapezium
Artist: Some Thoughts on the Formula for the Area of a Trapezium, Mathematics
in School, 33(5), 6–7
Foster, C. (2004) Y8 Area Lesson, Mathematics
Teaching, 188, 31
Foster, C. (2004) The Nth Term, Mathematics
Teaching, 188, 30–31
Foster, C. (2003) Mean
Difference, Times Educational Supplement: Teacher, 14 March, 5
Forthcoming
Foster, C. (2012) Quadratic Doublets, Mathematical Gazette,
97(537), July,
Foster, C. (2012) Squares Within Squares, Mathematical
Gazette, 97(537), July
Foster, C. (2012) Changing the Subject, Teach Secondary,
Foster, C. (2012) Making Twelve, Journal of Recreational Mathematics,
37(1),
Foster, C. (2012) Straight to the Point, Learning and Teaching Mathematics,
13,
Back, J., Foster, C., Tomalin, J., Mason, J., Swan, M. and Watson, A. (2012) Tasks
and their place in mathematics teaching and learning (part 1)
Back, J., Foster, C., Tomalin, J., Mason, J., Swan, M. and Watson, A. (2012) Tasks
and their place in mathematics teaching and learning (part 2)
Foster, C. (2012) Connected Codes, Journal of Recreational Mathematics,
37(2)
Foster, C. (2012) Creationism as a Misconception: Socio-Cognitive Conflict in
the Teaching of Evolution, International Journal of Science Education,
Foster, C. () Triangular Roots, Mathematical Spectrum,
Foster, C. () A Straight Question, Mathematics in School,
Foster, C. () Connected Expressions, Mathematics in School,
Foster, C. () Parking Problem, Mathematics Teaching,
Foster, C. () Unequal Reasoning, Mathematics in School,
Foster, C. () Non-Linear Inequalities, Mathematics in School,
Foster, C. () Problems Teaching Mechanics
Foster, C. () Using Possibility Tables to Stimulate Learner-Generated Examples
and Increase Learner Autonomy
Foster, C. () Proof Without Words
Foster, C. () Working Without A Safety Net
Foster, C. () Confidence Trick: The Interpretation of Confidence Intervals
Foster, C. () Mapping Open-Ended Journeys in Mathematics Through Task Spaces
Foster, C. () Reductionism in the Learning of Mathematics
Foster, C. () Pythagoras in N Dimensions
Foster, C. () Are you sure? Confidence and Competence in the Learning of Mathematics
Foster, C. () Sets of Simultaneous Equations with Integer Solutions
Foster, C. () Minimal Interventions in the Teaching of Mathematics
With thanks to ATM for permission to post the pdf versions of my Mathematics Teaching articles above.
Chemistry
© Colin Foster 2012