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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 interests in mathematics education focus on the design of rich mathematical tasks and ways in which teachers can use and adapt them in the classroom to support students' conceptual understanding of mathematics. I have particular interests in problem solving and in the development of mathematical fluency.

The four areas highlighted below may be of interest to teachers and researchers.

 

 

Mathematical Etudes are creative, imaginative and thought-provoking 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
MA(Cantab), PhD, PGCE, CMathTeach, SFHEA

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 2005-2008 I co-edited the journal Mathematics Teaching, published by the Association of Teachers of Mathematics.

 

Alongside my research, I teach pre-service 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.

 

My Erdős number is 4.

 

Memberships

British Society for Research into Learning Mathematics (BSRLM)

International Group for the Psychology of Mathematics Education (IGPME)

Association of Teachers of Mathematics (ATM)

Mathematical Association (MA)

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 and in the use of confidence assessment in school mathematics.

 

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 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 A-level mathematics examination papers.

 

I recently collaborated with Jeremy Hodgen and Rachel Marks on a review of mathematics teaching, Improving Mathematics in Key Stages Two and Three, for the Education Endowment Foundation.

 

I teach pre-service teachers on the University of Leicester PGCE course and supervise PhD students in mathematics education.

 

I recently appeared as a guest on the Mr Barton Maths Podcast: click here to listen.

Current research students

Alzahrani, Mohammed (PhD): English language teachers’ perceptions of integration of ICT within teaching the modular curriculum in Saudi Arabian secondary schools.

Barichello, Leo (PhD): Use of mathematical tasks to enhance the visual ability of low achieving students.

Bustang (PhD): Design-Based Research on Probability: Finding the convergence of proportional and probabilistic reasoning.

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.

Former research students

McCance, Lorna (2014). How do students’ solutions to a problem-solving task change after attempting to understand an algebra-focused 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 problem-solving lessons do pupils value and why? Unpublished MA dissertation. Nottingham: University of Nottingham.

 

Selected publications (more)

Foster, C. (2018). Developing mathematical fluency: Comparing exercises and rich tasks. Educational Studies in Mathematics, 97(2), 121–141. https://doi.org/10.1007/s10649-017-9788-x

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/s10649-017-9750-y

Foster, C. (2016). Confidence and competence with mathematical procedures. Educational Studies in Mathematics, 91(2), 271–288. https://doi.org/10.1007/s10649-015-9660-9

Wake, G., Swan, M., & Foster, C. (2016). Professional learning through the collaborative design of problem-solving lessons. Journal of Mathematics Teacher Education, 19(2), 243–260. https://doi.org/10.1007/s10857-015-9332-9

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), 10651088. https://doi.org/10.1007/s10763-014-9515-3

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), 2334. 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). Student-generated 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 Sixth-Form Mathematics: Further pure mathematics & mechanics. Derby: Association of Teachers of Mathematics.

Foster, C. (2012). Ideas for Sixth-Form 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

15 April 2019

Association of Teachers of Mathematics / Mathematical Association Joint Conference, Warwick. Opening plenary.

6 October 2018

ATM/MA meeting, UCL Institute of Education, London. Mathematical etudes as alternatives to exercises.

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: BCME-9, University of Warwick. Investigating Mathematical Attainment and Progress. With Jeremy Hodgen.

5 April 2018

British Congress of Mathematics Education: BCME-9, University of Warwick. Mathematical etudes: procedural fluency through rich tasks.

4 April 2018

British Congress of Mathematics Education: BCME-9, University of Warwick. What does research say about teaching mathematics at Key Stage 2 and 3? A review of reviews and meta-analyses. 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 hands-on introduction to Bayesian statistics. With Matthew Inglis and Ian Jones.

20-21 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, Stratford-upon-Avon. Mathematical fluency without exercises.

10 April 2017

Association of Teachers of Mathematics Conference, Crowne Plaza, Stratford-upon-Avon. 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 meta-analysis. 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. Re-conceptualising 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 (PME-NA 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.

2122 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, Mid-Levels, 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

E-ACT Academies: Heartlands Academy, Nechells, Birmingham. Responding to the new mathematics national curriculum.

16 April 2014

British Congress of Mathematics Education: BCME-8, University of Nottingham. Connected Expressions.

15 April 2014

British Congress of Mathematics Education: BCME-8, 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 problem-solving 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. Joined-up dots: Isometric graphs.

1 February 2008

Becta Hard-to-Teach 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

School of Education

University of Leicester

21 University Road

Leicester LE1 7RF

UK

 

Email  c@foster77.co.uk             

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ORCID ID: orcid.org/0000-0003-1648-7485

Scopus Author ID: 16636056500

ResearcherID: F-9957-2016

 

© Colin Foster 2018