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‘Can’t you just tell us the rule?’: teaching procedures relationally

Foster, Colin


Colin Foster


It is now almost 40 years since Skemp’s (1976) seminal division of understanding into ‘instrumental’ and ‘relational’ categories, yet the current political direction of mathematics education in the UK is decidedly towards the traditional teaching of ‘standard algorithms’ (DfE, 2013). In this research paper, I draw on a lively staffroom discussion about different approaches to the teaching of quadratic equations, in which one method used was derided as ‘a trick’. From this, I discuss reasons why certain mathematical processes are often regarded as inherently and irretrievably ‘procedural’. Informed by recent theoretical interpretations of procedural and conceptual learning in mathematics, which increasingly stress their intertwining and iterative relationship(Star, 2005; Baroody, Feil and Johnson, 2007; Star, 2007; Kieran, 2013), I make a case that stigmatising particular methods and censoring their use may deny students valuable opportunities to make sense of mathematics. I argue instead that encouraging students to take a critical stance regarding the details and the value of the procedures that they encounter can cultivate in them a deeper awareness of mathematical connections and a more empowered sense of ownership over their mathematics.


Foster, C. (2014). ‘Can’t you just tell us the rule?’: teaching procedures relationally.

Conference Name 8th British Congress of Mathematics Education
End Date Apr 1, 2014
Publication Date Jan 1, 2014
Deposit Date Mar 14, 2016
Publicly Available Date Mar 14, 2016
Peer Reviewed Not Peer Reviewed
Keywords Algorithms; Conceptual knowledge; Instrumental
understanding; Procedural knowledge; Quadratic equations; Relational
understanding; Student autonomy
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