
Dr Colin Foster MA(Cantab), PhD, PGCE, CMathTeach, SFHEA
I am an Assistant Professor at the Centre for Research in Mathematics Education in the School of Education at the University of Nottingham. I am interested in the design of rich mathematical tasks and ways in which teachers can use and adapt them in the classroom to support conceptual understanding of mathematics. 
Contact details Centre for Research in Mathematics Education School of Education University of Nottingham Jubilee Campus Wollaton Road Nottingham NG8 1BB UK
Email c@foster77.co.uk Twitter: @colinfoster77 LinkedIn Academia Loop ResearchGate Mendeley Google Scholar ORCID ID: orcid.org/0000000316487485 Scopus Author ID: 16636056500 ResearcherID: F99572016
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 mathematical problem solving and the design of rich tasks and their use in the mathematics classroom. I am particularly interested in the development of mathematical fluency.
I am currently collaborating with Jeremy Hodgen, Margaret Brown, Robert Coe and Steve Higgins on the Investigating Mathematical Attainment and Progress project, funded by the Nuffield Foundation. This aims to provide evidence to inform policy and practice directed at narrowing the achievement gap in mathematics. I am also working with Jeremy Hodgen and Rachel Marks on a review of mathematics teaching for the Education Endowment Foundation. I am studying the development of mathematical fluency in secondary mathematics students in the Mathematical Etudes Project, collaborating with Matthew Inglis on several corpus linguistic studies and with Ian Jones on a comparative judgment study of Alevel mathematics examination papers.
I teach preservice teachers on the University of Nottingham PGCE course and supervise masters and PhD students in mathematics education. 
Selected publications (more)
Foster, C. (in press). Developing mathematical fluency: Comparing exercises and rich tasks. Educational Studies in Mathematics.
Inglis, M., & Foster, C. (in press). Five decades of mathematics education research. Journal for Research in Mathematics Education.
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.
Conference presentations
15 April 2019 
Association of Teachers of Mathematics Conference. Opening plenary. 
24 October 2017 
Graduate School of Education, University of Exeter. Developing mathematical fluency: exercises or rich tasks? 
20 October 2017 
Yorkshire Maths Hubs Conference, National STEM Centre, York. Opening keynote: What makes good mathematics teaching? 
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.
Current research students
Barichello, Leo (PhD): Use of mathematical tasks to enhance the visual ability of low achieving students.
Calleja, James (PhD): Supporting teachers in learning to teach mathematics through inquiry: A case study of CPD in Malta.
Guimarães, Rita Santos (PhD): A teacher learning initiative to engage disadvantaged students.
Saralar, Ipek (PhD): Teachers’ beliefs and goals regarding Geogebra.
Former research students
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.
Website 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. 

© Colin Foster 2017