This report outlines the findings from a research project that examined videotapes of six groups of four children participating in the NEMP Farmyard Race task. The videos were analysed using a sociocultural framework. The findings from the analysis highlight that children’s participation in group mathematical tasks has intellectual, physical-spatial, material and social-relational dimensions: The findings suggest:
- a context can be motivating but difficulties can arise when children are expected to engage with a context whilst simultaneously ignoring factors that would be pertinent in a “real-life” situation;
- understanding and expression of mathematical ideas is bound up with language;
- the meaning of ordinal words can be ambiguous in relation to a particular context;
- children make decisions by deferring to an authoritative member, by democratic means and or by the aggregation of information;
- children find it difficult to aggregate information;
- manipulatives can serve as a means of organising a task, a problem space for its solution and a final product that is the outcome of the solution process;
- momentary configurations of manipulatives and children’s talk interlock to form and shape multimodal communication;
- manipulatives can serve as focal artefacts for collaborative problem solving;
- the physical-spatial arrangement of children in relation to a task problem space shapes access to collaborative work;
- group activities rely on children having and deploying a range of social practices;
- a child’s social standing and skills influence access to talk and materials;
- the child/ children who assume leadership responsibility impact on group goals and achievements;
- children’s purposes shift and take form as they interact about a task;
- children’s mathematical goals are interwoven with the context and artefacts of a task.
A sociocultural interpretation of children’s participation in group mathematics assessment tasks highlights several aspects. These are:
- the product of a group deliberation provides a restrictive view of what children know and can do;
- information about the process of reaching a solution provides more insight into children’s thinking;
- tasks do not always constrain children’s thinking in ways that lead them to being able to accomplish the task as it was intended;
- a contrived context relies on children’s appreciation of the nature of school mathematical tasks;
- a contextualised task can introduce language demands to do with the boundary between everyday language and experience and the particular ways language is used in the register of mathematics;
- children’s lack of familiarity with a task structure may obfuscate what they know and can do;
- a task needs to demand that all children contribute to its conceptual and practical outcome to evoke genuine cooperation.