Papademetri, Chrystalla; (2007) Structural knowledge about shapes :a case study of young children describing constructing and reflecting on squares. Doctoral thesis , Institute of Education, University of London.

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Abstract

The consensus in existing literature is that children's limited, and often appearance-based descriptions of shapes indicate that children view shapes as a whole and lack understanding of shape structure. This study approaches children's understandings of shapes from a different perspective, based on an alternative and more dynamic interpretation of the van Hiele model and with the acknowledgement that there might be multiple ways of knowing and expressing mathematical knowledge. This study examines the understandings young children have about the structure of shapes. It studies how this knowledge is expressed, and how it can be used in the process of constructing squares. Fifty-two children were engaged in three phase naturalistic task-based interviews. In Phase A (Description Task) the children were involved in classification and shape recognition activities. In Phase B (Construction Task) the children were asked to construct squares with the use of sticks and, in Phase C (Reflection Task) the children were asked to reflect on the construction process of Phase B. Even though during Phase A, the children, as supported by existing research, exhibited limited understanding about the structure of squares, through their involvement in Phase B, they exhibited much richer intuitive structural understandings. In Phase C, children tended to express structural understandings about squares. However the structural understanding that they exhibited was expressed in diverse and inventive ways. These findings challenge the view that children's limited verbal descriptions of shapes indicate lack of structural understanding. In the process of the interviews, the children articulated through the 'language' provided, existing intuitive structural knowledge of squares and at the same time they were able to situate their abstractions in the context of construction. Overall the findings indicate that, provided sufficiently sensitive techniques are employed, it is possible for children to express structural knowledge in diverse and often unconventional ways.

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