Our regular feature highlighting an article or research paper that will, we hope, have a helpful bearing on your teaching of mathematics
In this issue, It Stands to Reason focusses on pupils reasoning in algebra, so our library article this month is The ‘algebra as object’ analogy: a view from school by Kate Colloff and Geoff Tennant. This paper discusses the ‘algebra as object’ analogy (eg "saying that ‘a’ means ‘apple’”) and finds out how pupils would explain a simplification like 3a+2a = 5a.
The authors report that:
"When asked directly about the use of the ‘algebra as object’ analogy, all teachers were aware that it was ‘not recommended’ although one teacher could not articulate why. Reasons given by others included, “You cannot multiply apples”."
And they highlight:
"the need to problematise methods of teaching simplification which do not use ‘algebra as object’: from a learning point of view, is it all that different, for example, to refer to “2 lots of 10 plus 3 lots of 10” rather than apples?"
Is this paper relevant to your current teaching? This could be the stimulus for a discussion in your department about how you work with pupils to overcome difficulties understanding symbols
We think that you will, having read this paper, have a deeper understanding of why some pupils find algebra difficult, and also have some ideas how to respond to this in order to help your pupils develop more secure conceptual understanding and procedural fluency. Let us know what you think.