Ideas to support the development of mathematical communication in A-Level Mathematics (dissertation)
In Mathematics, especially at the advanced level, use of specific language and notation is important in developing both basic and deeper understanding of concepts. This dissertation outlines the details of a small-scale project which offers some suggestions about how we might be able to support the mathematical communication of learners studying A-Level Mathematics. Work samples were analysed using a semiotic framework which I developed for the purpose of analysing mathematical texts from the ideas of Chandler (1996; 2017) and Vile (1999). As a result of the analysis, ideas for ways in which we might be able to develop or improve the mathematical communication of A-Level Mathematics students are suggested. These ideas were not empirically tested as part of the project, and should therefore be only considered as suggestions at this stage.
How can ‘effective learning of mathematics’ be achieved?
What do students do in the mathematics classroom? Or more importantly, what do teachers ask or expect students to do in the mathematics classroom? Is mathematics learning a social activity? How do we define ‘effective learning of mathematics’, and how does classroom culture effect this? These questions are the source of inspiration for this assignment which discusses the perspective held by Swan (2007), considering his four key aspects for the ‘effective learning of mathematics’.
What are the understandings, knowledge, skills, attitudes, dispositions and capacities which, to different degrees, an educated 19-year-old should have developed through their mathematics education?
A number of key questions can be asked about the meaning of education and it is important to consider what we aim to achieve through schooling (Fielding and Moss 2011). The title question for this assignment has been adapted from the central question posed by Pring, Hogson and Spours (2009, p.12) to a mathematics education perspective. I consider Michael Young’s idea of ‘powerful knowledge’ (Young 2014) and proceed to discuss how this might be defined in a mathematical context.
Issues with Language and Learning: Mathematics as a Language
In this assignment I considered research by Halliday (1978) and Pimm (1987) into the ideas surrounding the use of a mathematical register, and how this can impact the learning of pupils in school. I also consider ideas from Vygotsky (1962) and Skemp (1987), and in particular the social constructivist approach to learning.
The ‘Lack of Closure’ Dilemma
In this assignment, using the Watson, Jones and Pratt (2013) Key ideas in teaching mathematics as the source text, I try to review the difficulties pupils have with the lack of closure in algebraic expressions. This includes the development of activities implemented with a year 7 class in my first school placement.
Chandler, D. (1996). Semiotics for beginners. Retrieved 23 July 2018 from: http://s3.amazonaws.com/szmanuals/bb72b1382e20b6b75c87d297342dabd7.
Chandler, D. (2017). Semiotics: the basics. New York, NY: Routledge.
Fielding, M. and Moss, P. (2011). ‘The state we’re in’ in Radical education and the common school: a democratic alternative, (Ch. 1, pp. 1-38), London: Routledge.
Halliday, M. A. K. (1978). Language as social semiotic. London: Edward Arnold.
Pring, R., Hogson, A. and Spours, K. (2009). ‘Aims and values’ in Education for all: The future of Education and Training for 14-19 year olds, pp. 12-25, London: Routledge.
Pimm, D. (1987). Speaking mathematically. London: Routledge & Kegan Paul.
Skemp, R. (1987). The Psychology of Learning Mathematics. L. Erlbaum Associates.
Swan, M. (2007). What constitutes the effective learning of mathematics? In NCETM, Mathematics Matters: Deriving practices from what constitutes effective learning of mathematics (Appendix iii). Retrieved 7 January 2017 from: https://www.ncetm.org.uk/public/files/30091176/Mathematics+Matters+-+The+Full+Report.pdf.
Vile, A. (1999). What can semiotics offer mathematics education? Proceedings of the British Society for Research into Learning Mathematics 17 (1&2) March/June 1997. Retrieved 16 February 2018 from: http://www.bsrlm.org.uk/wp-content/uploads/2016/02/BSRLM-IP-17-12-16.pdf.
Vygotsky, L. S. (1962). Thought and language. New York: MIT Press/Wiley.
Watson, A., Jones, K. & Pratt, D. (2013). Key Ideas in Teaching Mathematics: Research-based guidance for ages 9-19. Oxford University Press.
Young, M. (2014). Powerful knowledge as a curriculum principle. In M. Young and D. Lambert (Eds), Knowledge and the future school: curriculum and social justice (pp. 65-88), London, Bloomsbury.