Primary pre-service teachers: reasoning and generalisation

Research output: Chapter in Book/Report/Conference proceedingConference contribution


  • Tim Rowland
  • Gwen Ineson
  • Julie Alderton
  • Gina Donaldson
  • Chronoula Voutsina

Colleges, School and Institutes


Generalising tasks, in the context of mathematical reasoning, have featured in our work with primary pre-service teachers (PSTs). We used two particular problems - 'matchstick squares' and 'flower beds' - to explore the generalisation approaches taken by PSTs. In this paper, we analyse the ways in which one of them, Terry, uses recursive or functional approaches to generalisation, and how he attends to looking for a relationship and seeing sameness and difference between figures in a sequence. We consider what motivates shifts in attention, the significance of the PST's prior experience and of PST-collaboration in our teaching sessions. We conclude with a discussion about the significance of this activity in the PST’s preparation for teaching, with reference to Mason's (2010) notions of pro- spection and retro-spection.


Original languageEnglish
Title of host publicationResearch Proceedings of the 9th British Congress on Mathematics Education
Subtitle of host publication3-6 April, University of Warwick, UK
EditorsJennie Golding, Nicola Bretscher, Cosette Crisan, Eirini Geraniou, Jeremy Hodgen, Candia Morgan
Publication statusPublished - 3 Apr 2018
EventProceedings of the 9th British Congress of Mathematics Education (BCME9) 2018 - University of Warwick, Warwick, United Kingdom
Duration: 3 Apr 20186 Apr 2018

Publication series

NameBCME Conference Proceedings


ConferenceProceedings of the 9th British Congress of Mathematics Education (BCME9) 2018
Abbreviated titleBCME9
CountryUnited Kingdom