McGowen, Mercedes A. (1998) Cognitive units, concept images, and cognitive collages : an examination of the processes of knowledge construction. PhD thesis, University of Warwick.

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Abstract

The fragmentation of strategies that distinguishes the more successful elementary
grade students from those least successful has been documented previously. This
study investigated whether this phenomenon of divergence and fragmentation of strategies
would occur among undergraduate students enrolled in a remedial algebra
course. Twenty-six undergraduate students enrolled in a remedial algebra course used
a reform curriculum, with the concept of function as an organizing lens and graphing
calculators during the 1997 fall semester. These students could be characterized as
"victims of the proceptual divide," constrained by inflexible strategies and by prior
procedural learning and/or teaching. In addition to investigating whether divergence
and fragmentation of strategies would occur among a population assumed to be relatively
homogeneous, the other major focus of this study was to investigate whether students
who are more successful construct, organize, and restructure knowledge in ways
that are qualitatively different from the processes utilized by those who are least successful.
It was assumed that, though these cognitive structures are not directly knowable,
it would be possible to document the ways in which students construct
knowledge and reorganize their existing cognitive structures.
Data reported in this study were interpreted within a multi-dimensional framework
based on cognitive, sociocultural, and biological theories of conceptual development,
using selected insights representative of the overall results of the broad data
collection. In an effort to minimize the extent of researcher inferences concerning cognitive
processes and to support the validity of the findings, several types of triangulation
were used, including data, method, and theoretical triangulation. Profiles of the
students characterized as most successful and least successful were developed.Analyses
of the triangulated data revealed a divergence in performance and qualitatively different
strategies used by students who were most successful compared with students
who were least successful.
The most successful students demonstrated significant improvement and
growth in their ability to think flexibly to interpret ambiguous notation, switch their
train of thought from a direct process to the reverse process, and to translate among
various representations. They also curtailed their reasoning in a relatively short Period
of time. Students who were least successful showed little, if any, improvement during
the semester. They demonstrated less flexible strategies, few changes in attitudes, and
almost no difference in their choice of tools. Despite many opportunities for additional
practice, the least successful were unable to reconstruct previously learned inappropriate
schemas. Students' concept maps and schematic diagrams of those maps revealed
that most successful students organized the bits and pieces of new knowledge into a
basic cognitive structure that remained relatively stable over time. New knowledge
was assimilated into or added onto this basic structure, which gradually increased in
complexity and richness. Students who are least successful constructed cognitive
structures which were subsequently replaced by new, differently organized structures
which lacked complexity and essential linkages to other related concepts and procedures.
The bits and pieces of knowledge previously assembled were generally discarded
and replaced with new bits and pieces in a new, differently organized structure.

Item Type:	Thesis (PhD)
Subjects:	L Education > LB Theory and practice of education Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Teaching -- Methodology, Mathematics -- Study and teaching, Mathematics -- Study and teaching -- Psychological aspects, Education, Higher -- Study and teaching , Mathematics -- Remedial teaching
Official Date:	April 1998
Dates:	Date Event April 1998 Submitted
Institution:	University of Warwick
Theses Department:	Institute of Education
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Tall, David Orme
Extent:	xi, 245 leaves : illustrations
Language:	eng

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