The Role of Crafting in the Development of Mathematical Concepts

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dc.contributor.authorGrant, Tessa
dc.date.accessioned2023-07-23T22:34:07Z
dc.date.available2023-07-23T22:34:07Z
dc.date.issued2023en
dc.description.abstractThe core of mathematics education is the objective to introduce and strengthen students understanding of mathematical concepts. The use of props, and sometimes craft to achieve this is common. However, these practices are often relegated to earlier years of teaching, and not utilised very often in higher education. This thesis will analyse how the crafting process aids students in developing mathematical concepts at a third year university level, specifically analysing the MATH380 course offered at the University of Canterbury. We will break down the development of the crafting process’s affect on the development of mathematical concepts using the following three frameworks. Firstly, an altered version of the CRA model of learning. Where the CRA model typically focuses on a linear progression from concrete to relational to abstract, we challenge this based on the justification that often mathematical concepts naturally lend themselves to abstract representations, not concrete ones. As such we propose an altered model that focuses not only on concrete to abstract understandings, but also abstract to concrete understandings. Our second framework, Inclusive Materialism, is a variation of the traditional philosophical school of thought, materialism. Inclusive Materialism focuses on the breaking down of barriers between the human body and external matter, and how the entanglements that form between the body and external matter may affect learning. Inclusive Materialism also emphasises the affect of gestures, something that is particularly relevant when considering the crafting process. Finally, we also use a selfdeveloped framework referred to as the phases of the crafting process. This framework allows us to divide the overall crafting process into three phases. The design phase, the crafting phase, and the craft-prop phase. This framework will be used to analyse where in the crafting process a specific craft has its closest ties to the related mathematical concepts. We analysed both the in-class craft activities and the self-led student projects which involved craft that took place in the MATH380 course. We found that different crafts leant themselves naturally to different aspects of our framework, and were able to develop an understanding of how each case study lead to the development of mathematical concepts. Our analysis also re-affirmed the need to use the altered CRA model, as we found the traditional CRA model to be lacking when attempting to analyse the case studies. We concluded that the craft process interacts with the development of mathematical concepts in a significant way. The inclusion of crafting activities appeared to aid in the development of mathematical concepts and we developed a considerable understanding of these processes. We were not able to answer the question of whether teaching certain mathematical concepts through craft is more affective than traditional teaching methods as we did not have sufficient data to make such conclusions. However, we still suggest that the inclusion of craft activities has a place in mathematics education, and at a much higher level than it is currently applied.en
dc.identifier.urihttps://hdl.handle.net/10092/105732
dc.identifier.urihttp://dx.doi.org/10.26021/14826
dc.languageEnglish
dc.language.isoenen
dc.rightsAll Right Reserveden
dc.rights.urihttps://canterbury.libguides.com/rights/thesesen
dc.titleThe Role of Crafting in the Development of Mathematical Conceptsen
dc.typeTheses / Dissertationsen
thesis.degree.disciplineMathmaticsen
thesis.degree.grantorUniversity of Canterburyen
thesis.degree.levelBachelors with Honoursen
thesis.degree.nameOtheren
uc.collegeFaculty of Engineeringen
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