A volume in Research in Mathematics Education Series Editor Barbara J.
Dougherty, University of Mississippi This monograph reports on an
analysis of a small part of the mathematics curriculum, the definitions
given to quadrilaterals. This kind of research, which we call
micro-curricular analysis, is often undertaken by those who create
curriculum, but it is not usually done systematically and it is rarely
published. Many terms in mathematics education can be found to have
different definitions in mathematics books. Among these are "natural
number," "parallel lines" and "congruent triangles," "trapezoid" and
"isosceles trapezoid," the formal definitions of the trigonometric
functions and absolute value, and implicit definitions of the arithmetic
operations addition, subtraction, multiplication, and division. Yet many
teachers and students do not realize there is a choice of definitions
for mathematical terms. And even those who realize there is a choice may
not know who decides which definition of any mathematical term is
better, and under what criteria. Finally, rarely are the mathematical
implications of various choices discussed. As a result, many students
misuse and otherwise do not understand the role of definition in
mathematics. We have chosen in this monograph to examine a bit of
mathematics for its definitions: the quadrilaterals. We do so because
there is some disagreement in the definitions and, consequently, in the
ways in which quadrilaterals are classified and relate to each other.
The issues underlying these differences have engaged students, teachers,
mathematics educators, and mathematicians. There have been several
articles and a number of essays on the definitions and classification of
quadrilaterals. But primarily we chose this specific area of definition
in mathematics because it demonstrates how broad mathematical issues
revolving around definitions become reflected in curricular materials.
While we were undertaking this research, we found that the area of
quadrilaterals supplied grist for broader and richer discussions than we
had first anticipated. The intended audience includes curriculum
developers, researchers, teachers, teacher trainers, and anyone
interested in language and its use.
