The Classification of Quadrilaterals

A Study in Definition

Nonfiction, Science & Nature, Mathematics, Research, Geometry, Reference & Language, Education & Teaching
Cover of the book The Classification of Quadrilaterals by Zalman Usiskin, Information Age Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Zalman Usiskin ISBN: 9781607526001
Publisher: Information Age Publishing Publication: January 1, 2008
Imprint: Information Age Publishing Language: English
Author: Zalman Usiskin
ISBN: 9781607526001
Publisher: Information Age Publishing
Publication: January 1, 2008
Imprint: Information Age Publishing
Language: English

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 microcurricular 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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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 microcurricular 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.

More books from Information Age Publishing

Cover of the book Great Expectations by Zalman Usiskin
Cover of the book Lives And Relationships by Zalman Usiskin
Cover of the book Pedagogies of Deveiling by Zalman Usiskin
Cover of the book Encyclopedia of Sports & Recreation for People with Visual Impairments by Zalman Usiskin
Cover of the book New Frontiers for Self Research by Zalman Usiskin
Cover of the book Educational Reform in Europe by Zalman Usiskin
Cover of the book History Education 101 by Zalman Usiskin
Cover of the book Globalizing Minds by Zalman Usiskin
Cover of the book Schools as Radical Sanctuaries by Zalman Usiskin
Cover of the book Teaching Social Issues with Film by Zalman Usiskin
Cover of the book Learning from Television by Zalman Usiskin
Cover of the book Spark the Brain, Ignite the Pen (FIRST EDITION) by Zalman Usiskin
Cover of the book Online Learning Communities by Zalman Usiskin
Cover of the book Culture as the Core by Zalman Usiskin
Cover of the book Queering Classrooms by Zalman Usiskin
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy