Akkoç, Hatice (2003) Students' understanding of the core concept of function. Other thesis, University of Warwick.

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Abstract

This thesis is concerned with students' understanding of the core concept of function
which cannot be represented by what is commonly called the multiple representations of
functions. The function topic is taught to be the central idea of the whole of mathematics.
In that sense, it is a model of mathematical simplicity. At the same time it has a richness
and has mathematical complexity. Because of this nature, for students it is so difficult to
grasp. The complexity of the function concept reveals itself as cognitive complications for
weak students. This thesis investigates why the function concept is so difficult for students.
In the Turkish context, students in high school are introduced to a colloquial definition and
are presented with four different aspects of functions, set-correspondence diagrams, sets of
ordered pairs, graphs and expressions. The coherency in recognizing these different aspects
of functions by focusing on the definitional properties is considered as an indication of an
understanding of the core concept of function. Focusing on a sample of a hundred and
fourteen students, their responses in the questionnaires are considered to select nine
students for individual interviews. The responses from these nine students in the interviews
are categorized as they deal with different aspects of functions. The data indicates that
there is a spectrum of performance of students. In this spectrum, responses range from the
responses which handle the flexibility of the mathematical simplicity and complexity to the
responses which are cognitively complicated. Successful students could focus on the
definitional properties by using the colloquial definition for all different aspects of
functions. Less successful students could use the colloquial definition for only set-correspondence
diagrams and sets of ordered pairs and gave complicated responses for the
graphs and expressions. Weaker students could not focus on the definitional properties for
any aspect of functions.

Item Type:	Thesis or Dissertation (Other)
Subjects:	L Education > LB Theory and practice of education Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Functions -- Study and teaching -- Turkey
Official Date:	May 2003
Dates:	Date Event May 2003 Submitted
Institution:	University of Warwick
Theses Department:	Institute of Education
Thesis Type:	Other
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Tall, David Orme
Sponsors:	Turkey. Millí Eğitim Bakanlığı
Extent:	xii, 284 p.
Language:	eng

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