id: 06113384
dt: a
an: 2013a.00657
au: Colloff, Kate; Tennant, Geoff
ti: The ‘algebra as object’ analogy: a view from school.
so: Smith, C. (ed.), Proceedings of the British Society for Research into
Learning Mathematics (BSRLM). Vol.31, No. 3. Proceedings of the day
conference, Oxford, UK, November 2011. London: British Society for
Research into Learning Mathematics (BSRLM). 19-22 (2011).
py: 2011
pu: London: British Society for Research into Learning Mathematics (BSRLM)
la: EN
cc: H23 C33
ut: elementary algebra; simplification; teaching methods; symbols
ci:
li:
ab: Summary: Treating algebraic symbols as objects (e.g. ‘$a$’ means
‘apple’) is a means of introducing elementary simplification of
algebra, but causes problems further on. This current school-based
research included an examination of texts still in use in the
mathematics department, and interviews with mathematics teachers, year
7 pupils and then year 10 pupils asking them how they would explain,
“$3a+2a=5a$" to year 7 pupils. Results included the notion that the
‘algebra as object’ analogy can be found in textbooks in current
usage, including those recently published. Teachers knew that they were
not ‘supposed’ to use the analogy but not always clear why,
nevertheless stating methods of teaching consistent with an ‘algebra
as object’ approach. Year 7 pupils did not explicitly refer to
‘algebra as object’, although some of their responses could be so
interpreted. In the main, year 10 pupils used ‘algebra as object’
to explain simplification of algebra, with some complicated attempts to
get round the limitations. Further research would look to establish
whether the appearance of ‘algebra as object’ in pupils’ thinking
between year 7 and 10 is consistent and, if so, where it arises.
Implications also are for on-going teacher training with alternatives
to introducing such simplification.
rv: