Alcock, Lara (2001) Categories, definitions and mathematics : student reasoning about objects in analysis. PhD thesis, University of Warwick.

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Abstract

This thesis has two integrated components, one theoretical and one investigative.
The theoretical component considers human reason about categories of objects. First, it
proposes that the standards of argumentation in everyday life are variable, with emphasis on
direct generalisation, whereas standards in mathematics are more fixed and require
abstraction of properties. Second, it accounts for the difficulty of the transition to university
mathematics by considering the impact of choosing formal definitions upon the nature of
categories and argumentation. Through this it unifies established theories and observations
regarding student behaviours at this level. Finally, it addresses the question of why Analysis
seems particularly difficult, by considering the relative accessibility of its visual
representations and its formal definitions.
The investigative component is centred on a qualitative study, the main element of which is
a series of interviews with students attending two different first courses in Real Analysis.
One of these courses is a standard lecture course, the other involves a classroom-based,
problem-solving approach. Grounded theory data analysis methods are used to interpret the
data, identifying behaviours exhibited when students reason about specific objects and
whole categories. These behaviours are linked to types of understanding as distinguished in
the mathematics education literature. The student's visual or nonvisual reasoning style and
their sense of authority, whether "internal" or "external" are identified as causal factors in
the types of understanding a student develops. The course attended appears as an
intervening factor. A substantive theory is developed to explain the contributions of these
factors. This leads to improvement of the theory developed in the theoretical component.
Finally, the study is reviewed and the implications of its findings for the teaching and
learning of mathematics at this level are considered.

Item Type:	Thesis (PhD)
Subjects:	L Education > LB Theory and practice of education Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Mathematics -- Research, Mathematics -- Study and teaching -- Great Britain, Mathematics teachers -- Training of -- Great Britain
Official Date:	August 2001
Dates:	Date Event August 2001 Submitted
Institution:	University of Warwick
Theses Department:	Institute of Education
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Simpson, Adrian
Extent:	342 leaves : illustrations
Language:	eng

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