"Squash, tilt, drag, split, turn..." An intervention study examining children's collaborative talk and reasoning about shape, space and measure
The aim of this thesis is to evaluate the effect of collaborative work on primary-age children’s reasoning about shape, space and measure. Children’s early development in these areas of mathematics has been well researched but the difficulties older children experience are less well charted. Method: An intervention study was carried out with two Year 5 classes in a South London primary school using a naturalistic experimental design with two parallel classes as the intervention and control groups. The intervention class undertook two iterations of group work while the control class worked individually across the two sessions. An innovative pre- to post-test measure was developed using the Rasch Analysis partial credit model. This consisted of two sets of six similar and overlapping think-aloud tasks. The design of the group work was informed by both sociocultural and socio-cognitive conflict theory: ground rules for talk were used in the intervention class and the children were grouped in triads with differing ideas (elicited from their pre-test responses). Novel features were included to increase the likelihood of all children encountering challenge to their initial ideas: a) the children were prompted to reflect on the certainty of their joint or individual answers at the end of the first session; b) the children all had the chance to consult written clues in the second session, at the cost of a point per clue. Analysis: Quantitative comparison of the children’s progress from pre- to post-test was complemented with qualitative analysis of the children’s use of language across the study. Transcripts of the children talking about the shape, space and measurement tasks were coded for imaginative expressions to explore whether imaginative forms were associated with more sophisticated reasoning about shape, space and measure. The children’s group talk was coded for exploratory features of language to evaluate the impact on the children’s reasoning of the prompt to reflect on the certainty of their joint responses. Findings: The children working in groups made significantly more progress than the children working alone from pre- to post-test, as hypothesised, and they were more effective in their decisions about whether to seek help in the form of written clues than children working alone. Following the prompt to reflect on their group answers, there were changes in the observed language of the intervention groups. While the overall use of exploratory features: “because”, “I think”, “I agree/disagree” and modal verbs remained similar from session one to session two, there was a significant increase in the use of modal verbs following the prompt (p < .05). Swift surface-level agreements were probed further after a group consensus had been reached. Using a grounded approach, the children’s imaginative expressions across the study were coded and three categories identified: movement, manipulation or decomposition. Children working with peers made more progress and increased their use of imaginative expressions from pre- to post-test by comparison with the children working alone. Temporal analysis of the children’s talk across the study revealed common examples of imaginative work that supported the development of more sophisticated reasoning. For example, imagining “splitting” and “halving” objects served as a heuristic bridge towards inferring length and finding the difference. Similarly, by imagining “turning” and “squashing” familiar shapes, children began to create axioms about the properties of shape beyond iconic examples and orientations. The partial credit model used to measure children’s progress in this study increases our knowledge about the incremental steps that children make in their understanding about geometry and measurement in the upper primary years. By revealing the imaginative language tools the children used to probe their existing reasoning models, this study highlights the importance of children articulating their imaginative work in maths with peers.
intervention study, collaborative learning, mathematics education, reasoning, imagination, metaphor, shape, space and measure, geometry, primary education
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