Chin, Kin Eng (2013) Making sense of mathematics : supportive and problematic conceptions with special reference to trigonometry. PhD thesis, University of Warwick.

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Abstract

This thesis is concerned with how a group of student teachers make sense of
trigonometry. There are three main ideas in this study. This first idea is
about the theoretical framework which focusses on the growth of
mathematical thinking based on human perception, operation and reason.
This framework evolves from the work of Piaget, Bruner, Skemp, Dienes,
Van Hiele and others. Although the study focusses on trigonometry, the
theory constructed is applicable to a wide range of mathematics topics.
The second idea is about three distinct contexts of trigonometry namely
triangle trigonometry, circle trigonometry and analytic trigonometry.
Triangle trigonometry is based on right angled triangles with positive sides
and angles bigger than 0 [degrees] and less than 90 [degrees]. Circle trigonometry involves
dynamic angles of any size and sign with trigonometric ratios involving
signed numbers and the properties of trigonometric functions represented
as graphs. Analytic trigonometry involves trigonometric functions expressed
as power series and the use of complex numbers to relate exponential and
trigonometric functions.
The third idea is about supportive and problematic conceptions in making
sense of mathematics. This idea evolves from the idea of met‐before as
proposed in Tall (2004). In this case, the concept of ‘met‐before’ is given a
working definition as ‘a trace that it leaves in the mind that affects our
current thinking’. Supportive conception supports generalization in a new
contexts whereas problematic conception impedes generalization.
Furthermore, a supportive conception might contain problematic aspects in
it and a problematic conception might contain supportive aspects in it. In
general, supportive conceptions will give the learner a sense of confidence
whereas problematic conceptions will give the learner of sense of anxiety.
Supportive conceptions may occur in different ways. Some learners might
know how to perform an algorithm without a grasp of how it can be related
to different mathematical concepts and the underlying reasons for using
such an algorithm.

Item Type:	Thesis or Dissertation (PhD)
Subjects:	L Education > LB Theory and practice of education Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Trigonometry -- Study and teaching, Mathematics -- Study and teaching, Mathematics teachers -- Training of
Official Date:	June 2013
Institution:	University of Warwick
Theses Department:	Institute of Education
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Tall, David Orme; Hammond, Michael, 1956-
Sponsors:	Malaysia. Kementerian Pengajian Tinggi [Malaysia. Ministry of Higher Education]; Universiti Malaysia Sabah
Extent:	xii, 344 leaves.
Language:	eng

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