The Classification of Quadrilaterals

A volume in Research in Mathematics EducationSeries Editor Barbara J. Dougherty, University of MississippiThis monograph reports on an analysis of a small part of the mathematics curriculum, the definitions given toquadrilaterals. This kind of research, which we call micro-curricular analysis, is often undertaken by thosewho 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 isoscelestrapezoid, the formal definitions of the trigonometric functions and absolute value, and implicit definitions ofthe arithmetic operations addition, subtraction, multiplication, and division.Yet many teachers and students do not realize there is a choice of definitions for mathematical terms. Andeven 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 therole 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 somedisagreement in the definitions and, consequently, in the ways in which quadrilaterals are classified and relate to each other. The issues underlyingthese differences have engaged students, teachers, mathematics educators, and mathematicians. There have been several articles and a number ofessays on the definitions and classification of quadrilaterals. But primarily we chose this specific area of definition in mathematics because itdemonstrates how broad mathematical issues revolving around definitions become reflected in curricular materials. While we were undertaking thisresearch, 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.