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Saralar, Ipek (2020) Designing Lessons to Help Turkish Middle School Students Learn about Orthogonal and Isometric Drawings of Three-dimensional Shapes. PhD thesis, University of Nottingham.

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Abstract

This thesis describes a design-based research project to develop, implement and evaluate lessons intended to help middle school students learn about three-dimensional shapes and in particular orthogonal and isometric drawings of polycubes.



In an initial study, four classes from two schools in Turkey were observed during the regular teaching of three-dimensional shapes, and then students were asked to complete a worksheet to examine the outcomes of this teaching. The study found that students’ performance on orthogonal and isometric questions of the types asked in national exams were lower than desired. It also analysed the types of mistakes students made and noted the difficulties which may have led to these. Informed by these findings and the wider literature, a model was developed which suggests that teaching of three-dimensional shapes can be: realistic, exploratory, technology-enhanced and active, hence the RETA principles. These principles informed the design of four lessons on orthogonal and isometric drawings of polycubes, which were researched in the remaining studies of this thesis.

The second, third and fourth study aimed to see whether the RETA-based lessons were engaging and effective and improve them if they were found not to be. Each cycle reported how the RETA-based lessons were experienced by participants and the outcomes they achieved.

Specifically, the second study explored eight students’ experiences of the RETA-based lessons in an after-school mathematics course. In general, the results showed that students mostly experienced the lessons positively, and the lessons had the potential to improve their drawings. The third study focused on a teacher’s experiences of teaching with the RETA-based lessons in a class of 30 students and its outcomes. The teacher was a typical Turkish maths teacher, having a very different pedagogical approach and background to that of the researcher. This study explored her experiences in teaching in this way and found statistically significant improvement in students’ orthogonal and isometric drawing performance with the RETA-based lessons. The final study was a quasi-experiment with 205 students and four teachers where the RETA classrooms were compared to business as usual classes. The results showed that RETA-based lessons were significantly more effective than traditional methods.

This thesis offers insights and contributions into both the theory and the practice as expected from a design-based research project. The first of these is the RETA principles, which provide a basis for designing lessons on how three-dimensional shapes can be taught. The second contribution is the designed lessons on orthogonal and isometric drawings of polycubes, which are complete and detailed lesson plans that can be reused and adapted by mathematic teachers and researchers. These lesson plans were iteratively improved through three cycles, and by providing accounts of the design changes after each study together with the process involved, the outcomes of the lessons, and what worked and what did not, they are intended to offer detailed information to inform future research and practice.

Item Type:	Thesis (University of Nottingham only) (PhD)
Supervisors:	Ainsworth, Shaaron Wake, Geoffrey
Keywords:	middle school, 3D shapes, drawings, polycubes, RETA model, Turkey
Subjects:	L Education > LB Theory and practice of education > LB1501 Primary education Q Science > QA Mathematics
Faculties/Schools:	UK Campuses > Faculty of Social Sciences, Law and Education > School of Education
Item ID:	60288
Depositing User:	Saralar, Ipek
Date Deposited:	08 May 2025 12:57
Last Modified:	08 May 2025 12:57
URI:	https://eprints.nottingham.ac.uk/id/eprint/60288

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