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Title: Finding meaning in mathematics through its philosophy : an empirical study with 17-year-old Greek students
Author: Charlampous, Eleni
ISNI:       0000 0004 7225 6697
Awarding Body: University of Cambridge
Current Institution: University of Cambridge
Date of Award: 2017
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Through philosophical means, this thesis investigates the question: What mathematics can mean to students philosophically and psychologically? It is reasonable to assume that students may touch upon philosophical issues in trying to make sense of mathematics, since, in a sense, all individuals philosophise while searching for meaning in their own activities. Moreover, the existing literature indicates a substantial gap in our understanding of the meaning of mathematics and its philosophy in education. The thesis is based on a hermeneutical perspective. In this context, in-depth interviews were conducted with 17-year-old students in a Greek school. This method allowed me to obtain data which illuminated the objective meaning of students’ philosophical beliefs by way of the subjective, psychological meaning that they attributed to mathematics. The sample consisted of 28 students comprising both sexes and all levels of engagement with mathematics. The main issues that were examined were: whether mathematics exists; whether mathematical knowledge is certain, objective, true and immutable; whether mathematics consists of rules; and whether mathematical knowledge is based on logic or on experience. A thematic analysis helped me to move within the hermeneutical circle of understanding. As well as organising the objective meaning of students’ philosophical beliefs into themes and subthemes, analysis showed how for each student, there was an emergent a story which illustrating how they could combine such beliefs in order to find subjective meaning in mathematics. The most important finding of the study suggests that the students’ beliefs were influenced by common sense, and that students were able to find positive subjective meaning in mathematics when they were able to relate aspects of mathematical reasoning (e.g. certainty, subjectivity, rules, experience) to the operation of their everyday common sense. The study therefore shows that discussing philosophical issues, and in particular mathematical reasoning, could be of considerable benefit for students learning mathematics.
Supervisor: Gardner, Philip ; Andrews, Paul Sponsor: Academy of Athens
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
Keywords: mathematics education ; philosophy of mathematics ; meaning