The 'algebra as object' analogy: a view from school

Treating algebraic symbols as objects (eg. “‘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.

Secondary school students’ epistemic insight into the relationships between science and religion – a preliminary enquiry

A number of previous studies have shown that there is a widespread view among young people that science and religion are opposed. In this paper, we suggest that it requires a significant level of what can be termed ‘epistemic insight’ to access the idea that some people see science and religion as compatible while others do not. To explore this further, we draw on previous work to devise a methodology to discover students’ thinking about apparent contradictions between scientific and religious explanations of the origins of the universe. In our discussion of the findings, we highlight that students’ epistemic insight in this context does seem in many cases to be limited and we outline some of the issues emerging from the study that seem to boost or limit students’ progress in this area.