Panorkou, Nicole; (2011) A phenomenographic study of students experiences of dimension. Doctoral thesis , Institute of Education, University of London.

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Abstract

This study explored the experiences of dimension among young school children. Dimension is a powerful mathematical construct that is rarely taught or researched explicitly and not normally construed as something that is 'experienced'. The existing literature showed that the notion of dimension could be investigated through various perspectives: everyday life, scientific discourse, psychology, school curriculum and teaching. From this exploration, I developed an orientation of what I might consider to be an experience of dimension. A phenomenographic approach was followed, and meanings of dimension were generated from 24 students during four situations. Data were collected using clinical interviews accompanied with the design of tasks using the software Elica, physical objects, the film Flatland, and the software Google SketchUp in each of the situations respectively. The meanings generated from the first three situations were compared and grouped into theme categories. The aim of the fourth situation was to design an environment in which we might witness experiences of dimension not observed before, by building on preceding research on how modelling can foster the utility of mathematical concepts. SketchUp and its dimensional tools helped the students to form situated experiences about mathematical ideas relating to vectors and capacity. Dimensional experience was categorised as Dimension as Action, Dimension as Material, Dimension as Vector and Dimension as Capacity. An analysis of the relationship between the categories pointed to the duality of the passive or the dynamic way of experiencing dimension as well as looking within and between dimensions. These characteristics of the dimensional experiences informed the notion of dimension in general as incorporating a dual nature, as an object but also as a process. Conclusively, an examination of the four situations gave an insight into what makes a window expressive both for the student as a means of 'seeing' the phenomenon of dimension and for the researcher to 'see' how the student experiences that phenomenon.

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