‘Can’t you just tell us the rule?’: teaching procedures relationally
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 researc...
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| Format: | Conference or Workshop Item |
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2014
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| Online Access: | https://eprints.nottingham.ac.uk/32205/ |
| _version_ | 1848794357907324928 |
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| author | Foster, Colin |
| author_facet | Foster, Colin |
| author_sort | Foster, Colin |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T19:14:55Z |
| format | Conference or Workshop Item |
| id | nottingham-32205 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:14:55Z |
| publishDate | 2014 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-322052020-05-04T20:16:37Z https://eprints.nottingham.ac.uk/32205/ ‘Can’t you just tell us the rule?’: teaching procedures relationally Foster, Colin 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. 2014 Conference or Workshop Item NonPeerReviewed Foster, Colin (2014) ‘Can’t you just tell us the rule?’: teaching procedures relationally. In: 8th British Congress of Mathematics Education, 14 - 17 April 2014, University of Nottingham. Algorithms; Conceptual knowledge; Instrumental understanding; Procedural knowledge; Quadratic equations; Relational understanding; Student autonomy http://www.bsrlm.org.uk/BCME8/BCME8-20.pdf |
| spellingShingle | Algorithms; Conceptual knowledge; Instrumental understanding; Procedural knowledge; Quadratic equations; Relational understanding; Student autonomy Foster, Colin ‘Can’t you just tell us the rule?’: teaching procedures relationally |
| title | ‘Can’t you just tell us the rule?’: teaching procedures relationally |
| title_full | ‘Can’t you just tell us the rule?’: teaching procedures relationally |
| title_fullStr | ‘Can’t you just tell us the rule?’: teaching procedures relationally |
| title_full_unstemmed | ‘Can’t you just tell us the rule?’: teaching procedures relationally |
| title_short | ‘Can’t you just tell us the rule?’: teaching procedures relationally |
| title_sort | ‘can’t you just tell us the rule?’: teaching procedures relationally |
| topic | Algorithms; Conceptual knowledge; Instrumental understanding; Procedural knowledge; Quadratic equations; Relational understanding; Student autonomy |
| url | https://eprints.nottingham.ac.uk/32205/ https://eprints.nottingham.ac.uk/32205/ |