Further Reading

Data sets for investigation can be found on the Office for National Statistics website: www.ons.gov.uk/

The article ‘Enriching Data Handling, which includes some practical ideas for the classroom, can be found here: https://nrich.maths.org/5449

Battista, M.T. (2006) ‘Understanding the development of students’ thinking about length’, Teaching Children Mathematics, vol. 13, no. 3, pp. 140–7.

Swift, J. (1726) Gulliver’s Travels [Online]. Available at /www.planetebook.com/free-ebooks/gullivers-travels.pdf (Accessed 1 February 2019)..

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

Arcavi, Abraham, Drijvers, Paul and Stacey, Kaye (2017) The learning and teaching of algebra: ideas, insights. and activities, Abingdon, Oxon; New York, NY, Routledge/Taylor & Francis Group.

Kieran, Carolyn, Pang, JeongSuk, Schifter, Deborah and Ng, Swee Fong (2016) Early Algebra, ICME-13 Topical Surveys, Cham, Springer International Publishing, [online] Available from: http://link.springer.com/10.1007/978-3-319-32258-2 (Accessed 30 March 2018).

Data sets for investigation can be found on the Office for National Statistics website: www.ons.gov.uk/

The article ‘Enriching Data Handling, which includes some practical ideas for the classroom, can be found here: https://nrich.maths.org/5449

This article on Manipulatives in the Primary Classroom by Jenni Back can be found on the NRich website here: https://nrich.maths.org/10461

This research support provides further in-depth reading on how children learn number: http://www.nuffieldfoundation.org/sites/default/files/P2.pdf

This is the reference for the article by Richard Skemp:

Skemp, R. (1973). ‘Relational versus instrumental understanding. Mathematics Teaching’, vol. 77, pp.20–26.

This link takes you to an nrich web page with different methods of multiplication demonstrated: https://nrich.maths.org/5612

This is the link to an nrich article on developing the conceptual understanding of division: https://nrich.maths.org/5450

The nrich.maths.org website has lots of articles and activities about place value:

A story about absolutely nothing: https://nrich.maths.org/5598

Arrange the digits: https://nrich.maths.org/1976

Digit sum: https://nrich.maths.org/534

Orange drink problem and solution: https://nrich.maths.org/2420/note

Golden ratio activities: https://nrich.maths.org/7668

The online Cuisenaire ‘environment’ can be found here: https://nrich.maths.org/4348

There are a range of mathematical problems relating ratio and proportion to STEM applications here: https://nrich.maths.org/9003

Bruner, J. (1966) Toward a Theory of Instruction, Harvard University Press, Cambridge.

Peet, M. (2012) Tamar, London, Walker Books.

Radford, L. (2014) ‘The Progressive Development of Early Embodied Algebraic Thinking’, Mathematics Education Research Journal, 26(2), pp. 257–277.