\input zb-basic
\input zb-matheduc
\iteman{ZMATH 2013a.00657}
\itemau{Colloff, Kate; Tennant, Geoff}
\itemti{The `algebra as object' analogy: a view from school.}
\itemso{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).}
\itemab
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.
\itemrv{~}
\itemcc{H23 C33}
\itemut{elementary algebra; simplification; teaching methods; symbols}
\itemli{}
\end