Group discussion in primary school mathematical problem-solving provides potentially significant benefits to children’s learning, especially when discussion becomes dialogue, in which students achieve common understanding through cumulative questioning. Arising out of a need to develop talk whilst problem-solving on a primary teacher training programme in the UK, this research employs a think-aloud protocol alongside digital audio technology to promote and capture dialogue in two distinct group problem-solving situations. It explores how thinking-aloud, and the resulting recordings, can be used to support student teachers’ verbalisation of mathematical problem-solving strategies, including via ‘follow-up’ recall opportunities, exploiting connections between thinking-aloud and stimulated recall that are distinct to this work.
In addition to using the recall situation to encourage reflection on performance, a Talk Framework, reflecting mathematical problem-solving stages, has been employed to analyse the participants’ discourse. The Framework has been used to highlight potentially valuable contributions in the initial group situation whilst also identifying aspects to be revisited in the replay situation.
The findings of this work demonstrate that the provision of a think-aloud protocol alone does not guarantee the productive engagement of student teachers. Attitudes to mathematics and the group situation itself may impact on individuals’ expectations of success. The Talk Framework coding, informed by Mercer’s notions of cumulative, exploratory and disputational dialogue, highlights the degree to which exploratory dialogue is perhaps lacking, with a newly proposed category, “supercumulative”, identifying contributions intended to provoke further explanation.
This work highlights techniques that may be of benefit to student teachers and teacher educators when developing mathematical talk. It proposes networking of think-aloud and recall techniques to encourage reflection. It demonstrates that the provision of digitally recorded animated annotations provokes more discussion of the underlying mathematics than audio alone. Ultimately, it proposes a Talk Framework that can be used to identify valuable dialogue in the original problem-solving situation that can then be productively built upon to aid collective understanding of mathematical strategies in the subsequent recall.
