Pedagogy References

Our new course is built around a pedagogy based on leading mathematics educational research and best practice from teachers in the UK. A selection of this research is listed below:


Watson, A., Jones, K. and Pratt, D. (2013) Key Ideas in Teaching Mathematics. Oxford: Oxford University Press.


Concrete – pictorial - abstract

Hoven, J. and Garelick, B. (2007) ‘Singapore Math: Using the bar model approach, Singapore textbooks enable students to solve difficult math problems – and learn how to think symbolically’. In Singapore Math: Simple or Complex? Education Leadership 65, 3, pp.28-31.

Jackson, B. (2012) Singapore Math Bar Model Strategy. US: Scarsdale Public Schools. [Online] Available at: [Accessed July 2012]

Sowell, E. J. (1989) ‘Effects of manipulative materials in mathematics instruction’. Journal for Research in Mathematics Education, 3, pp. 498–505.



Ashcroft, M. H. (2002) ‘Math Anxiety: Personal, Educational and Cognitive Consequences’,Current Directions in Psychological Science, 11 (5), pp.181–185.

Nunes, T., Bryant, P., Sylva, K. and Barros, R. (2009) Research brief DCSF-RB118: Development of Maths Capabilities and Confidence in Primary School, London: DCSF



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), pp. 765-774.  

Pegg, J., & Graham, L. (2007) ‘Addressing the Needs of low-achieving mathematics students: Helping students ‘trust their heads’. Invited Key Note Address to the 21st Biennial Conference of the Australian Association of Mathematics Teachers, In K. Milton, H. Reeves, & T. Spencer (Eds.), Mathematics: Essential for learning, essential for life. Hobart: AAMT, pp. 33-46.



Frykholm, J., & Glasson, G. (2005) ‘Connecting science and mathematics instruction: Pedagogical context knowledge for teachers’, School Science and Mathematics, 105 (3), pp.127-141.

House, P. & Coxford, A. F. (Eds) (1995) ‘Connecting mathematics across the curriculum’,Reston, VA: National Council of Teachers of Mathematics.

Stinson, K., Sheats Harkness, S., Meyer, H., and Stallworth, J. (2009) ‘Mathematics and Science Integration: Models and characteristics’. School Science and Mathematics, 109(3),pp.153-161.


Mathematical reasoning

Raimi, R. (2002) ‘On Mathematical Reasoning in School Mathematics: Part 2 of A Mathematical Manifesto’ Unpublished: University of Rochester, NY, US.

Steen, L. A. (1999) ‘Twenty Questions about Mathematical Reasoning’ In Stiff, L. (Ed) NCTM's 1999 Yearbook. Reston, VA: National Council of Teachers of Mathematics, 1999, pp. 270-285., pp. 270-285.



Greer, B. (1997) ‘Modelling reality in mathematics classrooms: The case of word problems. Learning and Instruction, 7, (4), pp.293-307.

Verschaffel, L., Van Dooren, W., Greer, B. and Mukhopadhyay, S. (2010) ‘Reconceptualising word problems as exercises in mathematical modelling’, Journal Math Didaktik, no. 31 pp. 9-29.

Watson, A. (2009) Paper 7: ‘Modelling, problem-solving and integrating concepts’, in Key understandings in mathematics learning. London: Nuffield Foundation.


Multiplicative reasoning

Brown, M., Küchemann, D., and Hodgen, J. 2010 ‘The struggle to achieve multiplicative reasoning 11-14’, in M.Joubert & P. Andrews (Eds.), Proceedings of the Seventh British Congress of Mathematics Education (BCME7) (Vol. 30, pp. 49-56). University of Manchester: BSRLM.

Küchemann, D., Hodgen, J. And Brown, B. 2011, ‘Models and representations for the learning of multiplicative reasoning: Making sense using the Double Number Line’, in C. Smith (Ed.), Proceedings of the British Society for Research into Learning Mathematics 31(1). [Online] Available at:


Problem solving

Fan, L. and Zhu, Y. (2007) ‘From convergence to divergence: the development of mathematical problem solving in research, curriculum, and classroom practice in Singapore’, ZDM Mathematics Education (2007) 39, pp. 491–501

Polya G. (1990) ‘How to solve it: a new aspect of mathematical method’, London: Penguin.

Schoenfeld, A. H. (1992) ‘Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics’,  In D. Grouws (Ed.), Handbook for research on mathematics teaching and learning (pp. 334-370). New York: Macmillan.

Vilenius-Tuohima, P.M, Aunola, K. and Nurmi, J. (2008) ‘The association between mathematical word problems and reading comprehension’ Educational Psychology, Vol. 28, No. 4, July 2008, pp. 409–426.



Barnosky, B. R. (2012) ‘The Spiral vs Mastery Debate: A Discussion of High School (Homeschool) Mathematics.’, Peterborough NH, USA: CandleStar Educational Services. 

Kaur, B. (2008) ‘Teaching and Learning of mathematics: what really matters to teachers and students?’ Mathematics Education, 40, pp. 951 – 962.

Ministry of Education Singapore (2013), Primary and Secondary Mathematics Syllabus [online]. Both available at:


Lee, N. H., Chang, A. and Lee, P. Y. (2001) ‘The Role of Metacognition in the Learning of Mathematics among Low Achieving Students’, Source Teaching and Learning, 22(2), pp.18–30.

Yoong, W. K. (2001) ‘Helping Your Students to Become Metacognitive in Mathematics: A Decade Later’, Singapore: National Institute of Education, Nanyang Technological University.



Boaler, J. (1993) ‘The Role of Contexts in the Mathematics Classroom: Do they make Mathematics More “Real”?’ For the learning of mathematics 13 (2), pp.12-17.

Brown, S. (2001) ‘Reconstructing School Mathematics: Problems with Problems and the

Real World’, New York: Peter Lang Publishing.

Meyer, D. (2010) ‘Math Class needs a Makeover’,[Online]]. Available at: [Accessed March 2012


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