
Dr Colin Foster
I am an Associate Professor of Education and Director of Research in the School of Education at the University of Leicester, England. My research interests in mathematics education focus on the learning and teaching of mathematics in ways that support students’ conceptual understanding. I am particularly interested in the design and use of rich tasks in the mathematics classroom, and in finding ways to enable students to develop the necessary fluency in mathematical processes to support them in solving mathematical problems. I am also exploring the use of confidence assessment as a tool for formative assessment. For more details, please click on 'Research interests' above. The four aspects of my work highlighted below may be of interest to teachers and researchers. 
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Mathematical Etudes are creative, imaginative and thoughtprovoking ways to help learners of mathematics develop their fluency in important mathematical procedures. They are an alternative to traditional, tedious exercises. Click here to take a look. 
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.

This popular series of three books of lesson ideas, published by Nelson Thornes, is now available free. The three volumes address Number and Algebra, Shape and Space, and Data Handling and ICT. Click here to take a look.

I have written nearly 200 articles, both academic papers and articles for teacher professional journals, as well as 13 books. Many of these contain lesson plans and teaching resources. Click here and here to take a look.

Dr
Colin Foster I am an Associate Professor in the School of Education at the University of Leicester. Previously, I was at the University of Nottingham, and before that I taught mathematics in secondary schools for 12 years. My first degree and PhD are from Magdalene College, Cambridge, and I obtained my PGCE from the University of Cambridge Faculty of Education.
I have been designing mathematical tasks and writing books and articles for mathematics teachers for over 15 years. During 20052008 I coedited the journal Mathematics Teaching, published by the Association of Teachers of Mathematics.
Alongside my research, I teach preservice teachers on the PGCE secondary mathematics course at the University of Leicester, supervise masters and PhD students and lead professional development for mathematics teachers. I write regularly for the magazine Teach Secondary and for mathematics teacher professional journals. I was a member of the Department for Education Expert Group for the mathematics national curriculum and I devise questions for University of Cambridge International Examinations.
I am a Chartered Mathematics Teacher, a Fellow of the International Society for Design and Development in Education, a Senior Fellow of the Higher Education Academy and a member of the International Group for the Psychology of Mathematics Education, the National Council of Teachers of Mathematics and the Association of Mathematics Education Teachers.
Before mathematics education, I worked in chemistry. Click here for my thesis and a related paper.
If you are interested in studying for a PhD in an area that matches my research interests, then please email me with your ideas.

Memberships British Society for Research into Learning Mathematics (BSRLM) International Group for the Psychology of Mathematics Education (IGPME) Association of Teachers of Mathematics (ATM) Association of Mathematics Education Teachers (AMET) National Council of Teachers of Mathematics (NCTM)
Fellowships Fellow of the International Society for Design and Development in Education (ISDDE) Fellow of the Cambridge Philosophical Society Senior Fellow of the Higher Education Academy

Research
My research interests in mathematics education focus on the learning and teaching of mathematics in ways that support students’ conceptual understanding. I am particularly interested in the design and use of rich tasks in the mathematics classroom, and in finding ways to enable students to develop the necessary fluency in mathematical processes to support them in solving mathematical problems. I am also exploring the use of confidence assessment as a tool for formative assessment.
I am currently working on four major projects.
The first is the Investigating Mathematical Attainment and Progress project, funded by the Nuffield Foundation, in which I am collaborating with Jeremy Hodgen, Margaret Brown, Robert Coe and Steve Higgins. This project aims to provide evidence to inform policy and practice directed at narrowing the achievement gap in mathematics.
The second project, with Jeremy Hodgen and Rachel Marks, is a metaanalysis of interventions involving number lines, which follows our recent review of mathematics teaching, Improving Mathematics in Key Stages Two and Three, funded by the Education Endowment Foundation.
The third project is the Mathematical Etudes Project, which is a study into the development of mathematical fluency in secondary mathematics students.
The fourth project is the Confidence Assessment Project, which is looking at how asking students to indicate how sure they are about the answers they give in lowstakes mathematics tests can contribute to formative assessment.
In addition, I am also involved in two smaller projects, one with Matthew Inglis, employing techniques from corpus linguistics, and one with Ian Jones, using comparative judgment to examine standards in Alevel mathematics examination papers.
I recently appeared as a guest on the Mr Barton Maths Podcast: click here to listen.
I supervise PhD students across a variety of topics within mathematics education.
Current research students
Alzahrani, Mohammed (PhD): English language teachers’ perceptions of integration of ICT within teaching the modular curriculum in Saudi Arabian secondary schools.
Bustang (PhD): DesignBased research on probability: Finding the convergence of proportional and probabilistic reasoning.
Calleja, James (PhD): Learning to Teach Mathematics through Inquiry: A case study of continuing professional development in Malta.
Guimarães, Rita Santos (PhD): A teacher learning initiative to engage disadvantaged students.
Completed research students
Barichello, Leo (2018). An investigation into how lowachieving secondary students learn fractions through visual representations. Unpublished PhD dissertation (CAPESNottingham). Nottingham: University of Nottingham.
McCance, Lorna (2014). How do students’ solutions to a problemsolving task change after attempting to understand an algebrafocused sample solution? Unpublished MA dissertation. Nottingham: University of Nottingham.
Peake, Eleanor (2014). When and how do Year 2 pupils use the Bar Model to solve mathematical word problems? Unpublished MA dissertation. Nottingham: University of Nottingham.
Roberts, Katherine (2013). Which aspects of mathematical problemsolving lessons do pupils value and why? Unpublished MA dissertation. Nottingham: University of Nottingham.
Selected publications (more)
Inglis, M., & Foster, C. (2018). Five decades of mathematics education research. Journal for Research in Mathematics Education, 49(4), 462–500. https://doi.org/10.5951/jresematheduc.49.4.0462
Foster, C. (2018). Developing mathematical fluency: Comparing exercises and rich tasks. Educational Studies in Mathematics, 97(2), 121–141. https://doi.org/10.1007/s106490179788x
Foster, C., & Inglis, M. (2017). Teachers’ appraisals of adjectives relating to mathematics tasks. Educational Studies in Mathematics, 95(3), 283–301. https://doi.org/10.1007/s106490179750y
Foster, C. (2016). Confidence and competence with mathematical procedures. Educational Studies in Mathematics, 91(2), 271–288. https://doi.org/10.1007/s1064901596609
Wake, G., Swan, M., & Foster, C. (2016). Professional learning through the collaborative design of problemsolving lessons. Journal of Mathematics Teacher Education, 19(2), 243–260. https://doi.org/10.1007/s1085701593329
Foster, C., & De Villiers, M. (2016). The definition of the scalar product: An analysis and critique of a classroom episode. International Journal of Mathematical Education in Science and Technology, 47(5), 750–761. https://doi.org/10.1080/0020739X.2015.1117148
Foster, C. (2015). Closed but provocative questions: Curves enclosing unit area. International Journal of Mathematical Education in Science and Technology, 46(5), 776–783. https://doi.org/10.1080/0020739X.2014.992989
Foster, C. (2015). Exploiting unexpected situations in the mathematics classroom. International Journal of Science and Mathematics Education, 13(5), 1065–1088. https://doi.org/10.1007/s1076301495153
Foster, C. (2015). The convergent–divergent model: An opportunity for teacher–learner development through principled task design. Educational Designer, 2(8).
Foster, C. (2015). Expression polygons. Mathematics Teacher, 109(1), 62–65.
Foster, C. (2014). Minimal interventions in the teaching of mathematics. European Journal of Science and Mathematics Education, 2(3), 147–154.
Foster, C. (2014). Confidence trick: The interpretation of confidence intervals. Canadian Journal of Science, Mathematics, and Technology Education, 14(1), 23–34. https://doi.org/10.1080/14926156.2014.874615
Foster, C. (2013). Resisting reductionism in mathematics pedagogy. Curriculum Journal, 24(4), 563–585. https://doi.org/10.1080/09585176.2013.828630
Foster, C. (2013). Mathematical études: Embedding opportunities for developing procedural fluency within rich mathematical contexts. International Journal of Mathematical Education in Science and Technology, 44(5), 765–774. https://doi.org/10.1080/0020739X.2013.770089
Foster, C. (2011). Peripheral mathematical knowledge. For the Learning of Mathematics, 31(3), 24–26.
Foster, C. (2011). Productive ambiguity in the learning of mathematics. For the Learning of Mathematics, 31(2), 3–7.
Foster, C. (2011). Studentgenerated questions in mathematics teaching. Mathematics Teacher, 105(1), 26–31.
For my other papers, click here.
Selected books (more)
Foster, C. (2017). Questions Pupils Ask. Leicester: Mathematical Association.
Foster, C. (2013). The Essential Guide to Secondary Mathematics: Successful and enjoyable teaching and learning. London: Routledge.
Foster, C. (2012). Ideas for SixthForm Mathematics: Further pure mathematics & mechanics. Derby: Association of Teachers of Mathematics.
Foster, C. (2012). Ideas for SixthForm Mathematics: Pure mathematics & statistics. Derby: Association of Teachers of Mathematics.
Foster, C. (2012). Flowchart Investigations: Explorations in mathematics. Leicester: Mathematical Association.
Foster, C. (2011). Resources for Teaching Mathematics 11–14. London: Continuum.
Foster, C. (2010). Resources for Teaching Mathematics 14–16. London: Continuum.
Foster, C. (2009). Mathematics for Every Occasion. Derby: Association of Teachers of Mathematics.
Foster, C. (2008). Variety in Mathematics Lessons. Derby: Association of Teachers of Mathematics.
Foster, C. (2008). 50 Mathematics Lessons: Rich and engaging ideas for secondary mathematics. London: Continuum.
For my other books, and further details, click here.
Conferences and seminars
17 April 2019 
Association of Teachers of Mathematics / Mathematical Association Joint Conference, Warwick. Pushing calculus to its limits. With Bob Burn. 
15 April 2019 
Association of Teachers of Mathematics / Mathematical Association Joint Conference, Warwick. Opening plenary. 
23 March 2019 
ResearchED, Blackpool. Using confidence assessment to improve attainment. 
12 March 2019 
Mathematics and Statistics Department, Open University, Milton Keynes. Alternatives to exercises for developing procedural fluency. 
12 December 2018 
Mathematics Education Centre, Loughborough University. Confidence assessment in secondary mathematics. 
9 November 2018 
School of Education, University of Leicester. Confidence assessment in mathematics. 
6 October 2018 
ATM/MA meeting, UCL Institute of Education, London. Mathematical etudes as alternatives to exercises. 
12 September 2018 
British Education Research Association Annual Conference, Northumbria University, Newcastle. The effectiveness of strategies aimed at addressing low attainment in secondary mathematics: Findings from a systematic review. 
14 June 2018 
UCL Institute of Education, London. How teachers describe mathematics tasks. 
2 May 2018 
School of Mathematics, University of Edinburgh. Alternatives to exercises for developing mathematical fluency. 
6 April 2018 
British Congress of Mathematics Education: BCME9, University of Warwick. Investigating Mathematical Attainment and Progress. With Jeremy Hodgen. 
5 April 2018 
British Congress of Mathematics Education: BCME9, University of Warwick. Mathematical etudes: procedural fluency through rich tasks. 
4 April 2018 
British Congress of Mathematics Education: BCME9, University of Warwick. What does research say about teaching mathematics at Key Stage 2 and 3? A review of reviews and metaanalyses. With Jeremy Hodgen and Rachel Marks. 
28 March 2018 
Centre for Studies in Science and Mathematics Education, School of Education, University of Leeds. Developing mathematical fluency using rich tasks. 
19 March 2018 
The Prince’s Teaching Institute, Pimlico, London. Lecture: Rich mathematics tasks for deep understanding. 
3 March 2018 
British Society for Research into Learning Mathematics, Mathematics Education Centre, University of Nottingham. Statistics Working Group: A handson introduction to Bayesian statistics. With Matthew Inglis and Ian Jones. 
2021 February 2018 
Tikka Matematika Conference, Department for Curriculum, Research, Innovation and Lifelong Learning, Floriana, University of Malta. Questions for rich mathematical activity. 
20 February 2018 
Tikka Matematika Conference, Department for Curriculum, Research, Innovation and Lifelong Learning, Floriana, University of Malta. Keynote lecture: Using rich tasks to develop mathematical fluency. 
30 November 2017 
UCL Institute of Education, London. Addressing low attainment in mathematics in lower secondary: What do teachers believe and how do they teach? With Jeremy Hodgen. 
24 October 2017 
Graduate School of Education, University of Exeter. Developing mathematical fluency: exercises or rich tasks? 
29 September 2017 
ESRC Conference: Bayesian Data Analysis in the Social Sciences Curriculum, Nottingham Trent University. Bayes factors show equivalence between two contrasting approaches to developing school pupils’ mathematical fluency. 
11 April 2017 
Association of Teachers of Mathematics Conference, Crowne Plaza, StratforduponAvon. Mathematical fluency without exercises. 
10 April 2017 
Association of Teachers of Mathematics Conference, Crowne Plaza, StratforduponAvon. Investigating Mathematical Attainment and Progress. With Jeremy Hodgen. 
8 April 2017 
Mathematical Association Conference, Royal Holloway, University of London. Mathematical fluency without exercises. 
8 April 2017 
Mathematical Association Conference, Royal Holloway, University of London. Investigating Mathematical Attainment and Progress. With Jeremy Hodgen. 
9 March 2017 
UCL Institute of Education, London. Interventions for low attainment in mathematics: a metaanalysis. With Jeremy Hodgen. 
26 July 2016 
13th International Congress on Mathematical Education, University of Hamburg, Germany. Formative Assessment Lessons for Concept Development and Problem Solving. With Malcolm Swan. 
11 June 2016 
British Society for Research into Learning Mathematics, Mathematics Education Centre, Loughborough University. Developing procedural fluency: exercises or rich tasks? 
3 March 2016 
National Association of Mathematics Advisers Annual Conference, National STEM Centre, York. Opening keynote: Confidence and learning mathematics. 
27 February 2016 
British Society for Research into Learning Mathematics, Faculty of Education, Manchester Metropolitan University. Five decades of mathematics education research. With Matthew Inglis. 
19 November 2015 
University of Oxford, Department of Education. Teachers’ descriptions of mathematical tasks. 
21 July 2015 
International Community of Teachers of Mathematical Modelling and Applications 17, University of Nottingham. Developing boundary objects to support teachers’ teaching and learning of modelling. With Geoff Wake and Malcolm Swan. 
10 June 2015 
University of Cambridge, PGCE workshop. Mathematics task design. 
6 June 2015 
British Society for Research into Learning Mathematics, Durham University. Distinguishing conceptual and procedural understanding in mathematics. With Geoff Kent. 
9 May 2015 
ATM/MA meeting, University of Leicester. Rich mathematics from closed questions. Click here for a blog about this session. 
31 March 2015 
Mengo Senior School, Lubaga, Kampala, Uganda. Solving mathematical problems. 
5 February 2015 
Ninth Congress of European Research in Mathematics Education. Faculty of Education, Charles University, Prague. Reconceptualising conceptual understanding in mathematics. With Geoff Kent. 
1 September 2014 
Association of Mathematics Education Teachers Conference, Birmingham. Opening plenary: Practice and fluency. 
16 July 2014 
Joint Meeting of the International Group for the Psychology of Mathematics Education (PME 38) and the North American Chapter of the Psychology of Mathematics Education (PMENA 36), University of British Columbia, Vancouver, Canada. Mathematical knowledge for teaching problem solving: Lessons from lesson study. 
11 June 2014 
University of Cambridge, PGCE workshop. Mathematics task design. 
23 May 2014 
English Schools Foundation, South Island School, Aberdeen, Hong Kong. Mathematical études: Developing mathematical fluency without exercises. 
21–22 May 2014 
English Schools Foundation, South Island School, Aberdeen, Hong Kong. Rich, open tasks for learning mathematics. 
20 May 2014 
Hong Kong ATM meeting, Island School, MidLevels, Hong Kong. Mathematical tasks for the classroom. 
17 May 2014 
La Salle College, Kowloon, Hong Kong. Rich mathematical problems for deep understanding. 
14 May 2014 
La Salle College, Kowloon, Hong Kong. Teaching mathematical problem solving. 
13 May 2014 
Visiting Scholar, University of Hong Kong. Mathematical problem solving and task design. 
6 May 2014 
EACT Academies: Heartlands Academy, Nechells, Birmingham. Responding to the new mathematics national curriculum. 
16 April 2014 
British Congress of Mathematics Education: BCME8, University of Nottingham. Connected Expressions. 
15 April 2014 
British Congress of Mathematics Education: BCME8, University of Nottingham. “Can’t you just tell us the rule?”: Teaching procedures relationally. 
11 March 2014 
Centre for Research in Mathematics Education, University of Nottingham. Analysing teachers’ descriptions of mathematical tasks. 
1 March 2014 
British Society for Research into Learning Mathematics, King’s College, London. Analysing teachers’ descriptions of mathematical tasks. 
15 February 2014 
Birmingham joint ATM/MA meeting, University of Birmingham. Mathematical études: Developing mathematical fluency without exercises. 
9 October 2013 
International Society for Design and Development in Education Conference, Lawrence Hall of Science, University of California, Berkeley. Designing lessons for problemsolving processes: Experiences from Japanese lesson studies in England. With Malcolm Swan and Geoff Wake. 
2 April 2013 
Association of Teachers of Mathematics Conference, Sheffield. When real life appears in the mathematics classroom: Responding mathematically to unexpected events. 
20 June 2012 
London Borough of Croydon Local Authority ‘Exploring Excellence’ conference. Keynote presentation: Putting problem solving and investigation at the heart of mathematics teaching. 
24 March 2012 
The Marches joint ATM/MA meeting, Tenbury High School, Tenbury Wells. Variety in the learning of mathematics. 
21 April 2011 
Association of Teachers of Mathematics Conference, University of Wolverhampton. Possibility tables. 
3 April 2008 
Association of Teachers of Mathematics Conference, Keele University. Joinedup dots: Isometric graphs. 
1 February 2008 
Becta HardtoTeach Mathematics Conference, London. Functions and graphs. 
4 April 2007 
Association of Teachers of Mathematics Conference, Loughborough University. Writing to publish in Mathematics Teaching. With Helen Williams. 
11 April 2006 
Association of Teachers of Mathematics Conference, Edgehill College of Further Education, Ormskirk. Still reading Mathematics Teaching without having written for it yet? With Helen Williams. 
I also regularly participate in the Institute of Mathematics Pedagogy.
Dr Colin Foster Associate Professor University of Leicester 21 University Road Leicester LE1 7RF UK
Email c@foster77.co.uk Twitter Follow @colinfoster77 
© Colin Foster 2018