DeMarois, Phil (1998) Facets and layers of function for college students in beginning algebra. PhD thesis, University of Warwick.

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Abstract

The first mathematics course for approximately 53 percent of U.S. community college
students is a developmental algebra course. Many such students appear to be severely
debilitated by their previous encounters with mathematics. Due to numerous misconceptions
that dictate against a traditional course, a "reform" beginning algebra course,
with function as the unifying concept, was designed. Since there is little research on
this population to justify such a approach, the key research question for this thesis
becomes: Can adult students who arrive at college having had debilitating prior experiences
with algebra acquire at least a process level understanding of function through
appropriate instructional treatment? Answering this question provides crucial information
for future curricular design in the area of developmental mathematics at the college
level.
The theoretical framework considers different aspects that make up the function concept,
taking critical account of several current theories of multiple representations and
encapsulation of process as object to build a view of function in terms of different facets
(representations) and different layers (of development via procedure, process,
object, and procept).
Ninety-two students at four community colleges completed written function surveys
before and after a "reform" beginning algebra course. Twelve students, representing all
four sites, participated in task-based interviews. Comparison of pre- and post-course
surveys provided data indicating statistically significant improvement in student abilities
to correctly interpret and manipulate function machines, two-variable equations,
two-column tables, two-dimensional graphs, written definitions and function notation.
The students were divided into three categories (highly capable, capable, and incapable)
based on their demonstrated understanding of function. Using the interviews, visual
profiles for students in each category were developed. The profiles indicate that the
development of the concept image of function in such students is complex and uneven.
The cognitive links between facets is sometimes nonexistent, sometimes tenuous, and
often unidirectional. The highly capable demonstrated some understanding across all
facets while the incapable indicated understanding of the more primitive facets, such
as colloquial and numeric, only. Profound differences were noted particularly in the
geometric, written, verbal, and notation facets. Overall, the target population appeared
able to develop a process layer understanding of function, but this development was far
from uniform across facets and across students.

Item Type:	Thesis (PhD)
Subjects:	L Education > LB Theory and practice of education Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Algebra -- Study and teaching -- United States, Functions -- Study and teaching -- United States, Community colleges -- Curricula -- United States
Official Date:	January 1998
Dates:	Date Event January 1998 Submitted
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Tall, David Orme
Extent:	266 p.
Language:	eng

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