Crisan, C; (2014) The case of the square root: ambiguous treatment and pedagogical implications for prospective mathematics teachers. In: Pope, S, (ed.) Edited proceedings of BCME 8, University of Nottingham, Apr 2014. (pp. pp. 75-82). British Society for Research into Learning Mathematics: Nottingham, UK.

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Abstract

I report on a small-scale study rooted in the UK context that was conducted with eight volunteers from a cohort of PGCE secondary mathematics students (participants). The participants? own understanding of the square root concept and use of the associated symbol were explored and the findings revealed that they may not possess adequate subject knowledge about and for teaching this concept. Access to instructional materials, mainly textbooks and discussions with other more experienced teachers were identified as the main external sources consulted by the participants in order to refresh their knowledge of the square root concept. During this study, those participants who became aware of the shortcomings of their conceptual understanding of the square root felt, at first, uncomfortable with modifying their personal knowledge and their long held beliefs about this concept. Group discussion helped most of the participants become aware of connections between their more advanced knowledge of mathematics and the square root concept. Such awareness empowered the participants to clarify this concept for themselves and critically scrutinise the (re)sources available. A tension between employing their modified knowledge about the square root and adherence to the widely accepted view about this topic in school mathematics has also been identified.

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