# 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:

## General

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: http://www.thedailyriff.com/WordProblems.pdf [Accessed July 2012]

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

## Confidence

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

## Fluency

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.

## Linking

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.

## Modelling

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: http://www.bsrlm.org.uk/wp-content/uploads/2016/02/BSRLM-IP-31-1-15.pdf

## 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.

## Progression

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: https://www.moe.gov.sg/

## Reflection

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.

## Relevance

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:http://www.youtube.com/watch?v=NWUFjb8w9Ps [Accessed March 2012

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