Abstract
We report an innovative assessment feedback tool – we call it a mathsmap – and describe how two pre-service teachers in the UK made sense of this personalised diagnostic map to reflect on their own subject knowledge in mathematics. The mathsmap provides both a summative and a diagnostic profile of their attainment and errors across the mathematics curriculum. The use of the mathsmap to reflect on learning on a personal level is also seen to provoke ‘accounts’ or ‘stories’ that might inform pedagogical content knowledge: in making their mathsmap comprehensible to themselves, the teachers needed to account for their own ‘knowledge-troubles’, that is to narrate their metacognition.
This chapter draws on our earlier work reported in Ryan and Williams (2007b) extending the analysis of Lorna and Charlene’s accounts of their learning – in particular in ‘accounting for the unexpected’ as an opportunity for learning and development of pedagogical content knowledge.
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Notes
- 1.
Lorna and Charlene are pseudonyms.
- 2.
GCSE is the General Certificate of Secondary Education in England which assesses children’s attainment at the end of current compulsory schooling, usually at 16 years of age.
- 3.
Lorna’s ‘ability’ is located at 0.91 logits on the scale which indicates that she is nearly one standard deviation above the mean of the item difficulties. We can therefore compute the probability of her correctly answering an item of difficulty ‘d’ as being approximately exp(0.91–d)/ [1 + exp(0.91–d)]; thus, for the average item with d = 0, this is approximately 70% for Lorna.
- 4.
O-level was the pre-1988 forerunner of the national GCSE examination.
- 5.
AS is the first year of the Advanced level which constitutes the final 2 years (called AS and A2) of post-compulsory schooling in England.
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Ryan, J., Williams, J. (2011). Teachers’ Stories of Mathematical Subject Knowledge: Accounting for the Unexpected. In: Rowland, T., Ruthven, K. (eds) Mathematical Knowledge in Teaching. Mathematics Education Library, vol 50. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9766-8_15
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