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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, open mathematical tasks and how teachers and learners use, adapt and own them in the classroom.

Read more…

 

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     ResearchGate     Mendeley     Google Scholar     ORCID ID: orcid.org/0000-0003-1648-7485     Scopus Author ID: 16636056500     ResearcherID: F-9957-2016

 

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.

 

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 studying the development of mathematical fluency in secondary mathematics students in the Mathematical Etudes Project and working with Matthew Inglis on several corpus linguistic studies.

 

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

Selected publications (more)

Foster, C. (2016). Confidence and competence with mathematical procedures. Educational Studies in Mathematics, 91(2), 271–288.

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.

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.

Foster, C. (2015). Closed but provocative questions: Curves enclosing unit area. International Journal of Mathematical Education in Science and Technology, 46(5), 776–783.

Foster, C. (2015). Exploiting unexpected situations in the mathematics classroom. International Journal of Science and Mathematics Education, 13(5), 10651088.

Foster, C. (2015). Expression polygons. Mathematics Teacher, 109(1), 62–65. (Resource sheet doc)

Foster, C. (2015). The convergent–divergent model: An opportunity for teacher–learner development through principled task design. Educational Designer, 2(8).

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, 4(1), 2334.

Foster, C. (2013). Resisting reductionism in mathematics pedagogy. Curriculum Journal, 24(4), 563–585.

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.

Foster, C. (2011). Peripheral mathematical knowledge. For the Learning of Mathematics, 31(3), 24–26.

Foster, C. (2011). Student–generated questions in mathematics teaching. Mathematics Teacher, 105(1), 26–31.

Foster, C. (2011). Productive ambiguity in the learning of mathematics. For the Learning of Mathematics, 31(2), 3–7.

 

For my other papers, click here.

Selected books (more)

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.

Conference presentations

24-31 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.

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, 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.

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.

Loveridge, Nerys (PhD): Investigating socio-cultural factors influencing children’s primary school mathematics performance.

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.

 

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 2016