
06643704
a
2016f.01085
K\"uchemann, Dietmar
Hodgen, Jeremy
A look at two algebra tasks involving sequential data, that seem to prompt a scalar rather than function approach to the underlying linear relation.
Adams, G. (ed.), Proceedings of the British Society for Research into Learning Mathematics (BSRLM). Vol. 35, No. 3. Proceedings of the day conference, University of Reading, UK, November 7, 2015. London: British Society for Research into Learning Mathematics (BSRLM). 7277 (2016).
2016
London: British Society for Research into Learning Mathematics (BSRLM)
EN
H23
I23
D53
educational research
interviews
finding rules
generalisation
number pattern tasks
generic patterns
figurative patterns
sequences
elementary algebra
linear relationships
coordinates
function relations
recursive relations
scalar view
function view
http://www.bsrlm.org.uk/IPs/ip353/BSRLMIP35313.pdf
Summary: In this paper we discuss an interview undertaken by the first author with a group of three Year 8 students and their teacher as part of the design research work of the ICCAMS project. The interview involved two tasks in which pairs of values connected by a linear relationship were presented sequentially, either in a table or as coordinate points on a Cartesian grid. The students were asked to make near and far generalisations, which they tended to do by adopting a scalar (or recursive) approach, either in a stepbystep manner or by chunking. From the interviewer's point of view, the scalar and function perspectives are intimately linked, and on occasions during the interview it was easy to believe that this was true for the students too. However, a closer examination suggests that for these students at least, the connection is still tenuous.