# Doctoral Dissertation

**Supervisor:**Professor Dave Pratt**Examiners:**Professor Richard Noss and Professor John Mason

## 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.

## Publications

**Panorkou, N.**and Pratt, D. (2016).*Using Google SketchUp to research students’ experiences of dimension in geometry*. Digital Experiences in Mathematics Education, 2 (3), pp. 199-227.**Panorkou, N**& Pratt, D (2011)*Using Google SketchUp to research children’s experience of dimension.*In B. Ubuz (Eds) Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education, Vol. 3, pp. 337-344. Ankara, Turkey: PME.**Panorkou, N**& Pratt, D (2011)*Designing windows for researching children’s experiences of dimension.*In Joubert M., Clark-Wilson A. and McCab M. (Eds) Proceedings of the International conference of technology in mathematics teaching, Portsmouth: ICTMT’10.**Panorkou, N**(2011)*A phenomenographic study on students’ experiences of dimension.*Proceedings of the International symposium Elementary Mathematics Teaching. Prague: SEMT’ 11**Panorkou, N**(2011)*A phenomenographic study of students’ experiences of dimension.*Doctoral thesis. British Library: Electornic Theses Online Service (EThos)**Panorkou, N**& Pratt, D. (2009)*Mapping experience of dimension.*In Tzekaki, M., Kaldrimidou, M. & Sakonidis, C. (Eds.). Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education, Vol. 4, pp. 281-288. Thessaloniki, Greece: PME.**Panorkou, N**(2009),*Thinking about dimension.*In Tzekaki, M., Kaldrimidou, M. &Sakonidis, C. (Eds.). Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education, Vol. 5, pp. 481.Thessaloniki, Greece: PME.

## Conference Presentations

**Panorkou, N.**(2011)*A phenomenographic study on students’ experiences of dimension*, paper presented at the Proceedings of the International symposium Elementary Mathematics Teaching, August 2011.**Panorkou, N.**and Pratt, D. (2011)*Using Google SketchUp to research children’s experience of dimension*, paper presented at the 35th Conference of the International Group for the Psychology of Mathematics Education, July 2011.**Panorkou, N.**(2011)*Designing windows for researching children’s experiences of dimension*, paper presented at the International conference of technology in mathematics teaching, July 2011.**Panorkou, N.**(2009)*Changes of thinking about dimension, paper presented at the BERA Annual conference*, University of Manchester, September 2009.**Panorkou, N.**(2009)*Thinking about dimension, seminar given at the PME conference*, Aristotle University of Thessaloniki, July 2009. Panorkou, N. and Pratt, D. (2009) Mapping experience of dimension, seminar given at the PME conference, Aristotle University of Thessaloniki, July 2009. Panorkou, N. (2009) Mapping experience of dimension: Characterising dimensional thinking, seminar given at the BSRLM Day Conference, University of Cambridge, February 2009.**Panorkou, N.**(2007)*Embracing two-dimensional and three-dimensional geometry*, seminar given at the Institute of Education Doctoral School Conference, June 2007.