Young pupils’ generalisation strategies for the ‘handshakes’ problem. (English)

Ubuz, Behiye (ed.) et al., CERME 8. Proceedings of the eigth congress of the European Society of Research in Mathematics Education, Antalya, Turkey, February 6‒10, 2013. Ankara: Middle East Technical University (ISBN 978-975-429-315-9). 420-429 (2013).

Summary: In describing the strategies that young pupils employ for algebraic generalisation, most research focuses on linear rather than quadratic problem situations. The strategies identified by {\it J. Lannin} et al. [Math. Educ. Res. J. 18, No. 3, 3‒28 (2006; ME 2007e.00236)] for the cube sticker (linear) problem include counting, recursion, chunking and development of an explicit formula. However, erroneous solutions are often given for ‘high’ numbers because of the tendency by students to use inappropriate proportional reasoning in such instances. In this paper I describe the strategies that pupils aged 9‒10 years used in whole-class conversation to solve the ‘handshakes’ problem, an example of a quadratic generalising situation. They used many (but not all) of the strategies that apply to linear problems and were able to verify the explicit formula that they developed with reference to the structural elements of the problem.