Types and levels of data arrangement and representation in statistics as modeled by grade 4 - 7 learners

Abstract

The crucial role of representation in mathematical and statistical modeling and problem solving as evident in learners' arrangement and representation of statistical data were investigated with focus points data arrangement, data representation and statistical thinking levels. The representation tasks required learners to arrange and represent data through modeling, focusing on spontaneous representations. Successful transnumeration determine the ultimate success of a representation and the ability to organise data is regarded as critical. Arrangement types increased in sophistication with increased grade level and the hierarchical nature of arrangement types became apparent when regarded in the context of an adapted SOLO Taxonomy framework. A higher level arrangement strategy pointed to a higher SOLO level of statistical thinking. Learners in the two tasks produced a rich variety of representations which included idiosyncratic, unsophisticated responses as well as standard statistical representations. The context of the two tasks, the quantitative versus qualitative nature of the data in the tasks, and the statistical tools or representational skills learners have at their disposal, played an important role in their representations. Well-planned data handling activities develop representational and higher order thinking skills. The variety of responses and different response levels elicited in the two tasks indicate that the nature of the tasks rather than the size of the data set play a conclusive role in data tasks. Multiple representations by an individual were an indication of successful modeling, are effective in problem solving and are associated with good performance. The SOLO model which incorporates a structural approach as well as a multimodal component proved valuable in the analysis of responses. Using this model with accompanying acknowledgement of different problem solving paths and the contribution of ikonic support in the concrete symbolic mode, promote the in-depth analysis of responses.

This study contributes to the research in the field of data representation and statistical thinking. The analysis and results led to an integrated picture of Grade 4-7 learners' representation of statistical data and of the statistical thinking levels evident in their representations.