The development of geometric reasoning: middle years students’ understanding of 2-dimensional shapes

Berenger, A 2017, The development of geometric reasoning: middle years students’ understanding of 2-dimensional shapes, Masters by Research, Education, RMIT University.

Document type: Thesis
Collection: Theses

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Title The development of geometric reasoning: middle years students’ understanding of 2-dimensional shapes
Author(s) Berenger, A
Year 2017
Abstract Visualisation plays a critical role in geometric reasoning. An ‘image in the mind’ provides students with the necessary structures of a shape in order to define and classify them and then deduce other properties from them. Convincing others through a common mathematical discourse is seen as a necessary component in the meaning-making process of geometry. It is necessary for teachers to have the pedagogical content knowledge necessary to develop and support geometric argument in the classroom.

This study used a design-based research methodology to examine the geometric thinking of students in Years 7 and 8 at two inner-suburban schools in Melbourne, Victoria, Australia. Student written work samples, classroom observations and video-recorded teaching episodes were used to collect data about how students and teachers communicated their understanding of geometric concepts relating to 2-dimensional shapes. A series of geometric reasoning tasks were developed to provide opportunities for students to learn through group work activities.

Students’ use of keywords, visual mediators, narratives and discourse routines were interpreted using Sfard’s (2008) interpretive framework of mathematical discourse. The results of the research from the preliminary tasks show that students do not readily use diagrams to describe shapes, and instead, produce exhaustive lists of known properties of common shapes. This is defined as analysis by the van Hiele levels of geometric thought. The results also demonstrated that students do not engage in mathematical discussion in the absence of clearly defined classroom norms for group work. Student work samples from supplementary tasks revealed a growth in the sophistication of keywords and visual mediators used to describe shapes yet raised questions about the teachers’ readiness to provide appropriate intervention and instruction in geometry.

The main conclusion that can be drawn from this study was that students’ progress in geometric reasoning was hampered by misconceptions by both students and teachers. The role of the teacher was consequential to engendering group work skills in their students because geometric argument necessitates the communication of ideas in constructing endorsed narratives of new knowledge from familiar geometric concepts.
Degree Masters by Research
Institution RMIT University
School, Department or Centre Education
Subjects Mathematics and Numeracy Curriculum and Pedagogy
Keyword(s) geometric thinking
2-dimensional shapes
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Created: Fri, 04 Aug 2017, 09:48:02 EST by Denise Paciocco
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