Ali, Maselan Bin (1996) Symbolic manipulations related to certain aspects such as interpretations of graphs. PhD thesis, University of Warwick.

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Abstract

This thesis describes an investigation into university students' manipulation of
symbols in solving calculus problems, and relates this to other aspects such as
drawing and interpretation of graphs. It is concerned with identifying differences
between students who are successful with symbol manipUlation and those who are
less successful.
It was initially expected that the more successful would have flexible and efficient
symbolic methods whilst the less successful would tend to have single procedures
which would be more likely to break down. Krutetskii (1976) noted that more
successful problem-solvers curtail their solutions whilst the less able are less likely to
acquire that ability even after a long practice. This suggested a possible correlation
between success and curtailment. An initial pilot study with mathematics education
students at a British University showed that in carrying out the algorithms of the
calculus, successful students would often work steadily in great detail, however, they
were more likely to have a variety of approaches available and were more likely to
use conceptual ideas to simplify their task. However, the efficiency in handling
symbolic manipulation may not be an indication that the students are able to relate
their computational outcome to graphical ideas.
A modified pilot test was trialed at the Universiti Teknologi Malaysia before a main
study at the same university in which 36 second year students were investigated in
three groups of twelve, having grades A, B, C respectively in their first year
examination.
The findings of this research indicate that there is no significant correlation between
ability and curtailment, but ability correlates with conceptual preparation of
procedures where there is an appropriate simplification to make the application of the
algorithm simpler. The more able students may have several flexible strategies and
meaningful symbolic mathematical representations but these may not always relate to
visual and graphical ideas. On the other hand the less able students are less likely to
break away from the security of a single procedure and liable to breakdown in getting
the solutions for the calculus problems.

Item Type:	Thesis (PhD)
Subjects:	L Education > LB Theory and practice of education > LB2300 Higher Education Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Education, Higher -- Study and teaching, Mathematics -- Study and teaching, Algorithms -- study and teaching
Official Date:	1996
Dates:	Date Event 1996 Submitted
Institution:	University of Warwick
Theses Department:	Institute of Education
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Tall, David Orme ; Gray, Edward Martin
Extent:	xvii, 160 leaves : illustrations
Language:	eng

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