id: 06451918
dt: a
an: 2015d.00692
au: Dooley, Thérèse
ti: Young pupils’ generalisation strategies for the ‘handshakes’ problem.
so: 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).
py: 2013
pu: Ankara: Middle East Technical University
la: EN
cc: H22 K22
ut: problem solving; algebraic generalisation; whole-class conversation;
handshakes problem
ci: ME 2007e.00236
li:
ab: 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.
rv: