The Classification of Quadrilaterals
The Classification of Quadrilaterals

Author: Zalman Usiskin

Publisher: IAP

Published: 2008-01-01

Total Pages: 120

ISBN-13: 160752600X

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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.

The Words of Mathematics
The Words of Mathematics

Author: Steven Schwartzman

Publisher: MAA

Published: 1994

Total Pages: 276

ISBN-13: 9780883855119

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This book explains the origins of over 1500 mathematical terms used in English.

If You Were a Quadrilateral
If You Were a Quadrilateral

Author: Molly Blaisdell

Publisher: Capstone

Published: 2010

Total Pages: 14

ISBN-13: 1404855114

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The creative examples, simple text, and art in this series help students learn primary math concepts.

The Second Handbook of Research on the Psychology of Mathematics Education
The Second Handbook of Research on the Psychology of Mathematics Education

Author: Ángel Gutiérrez

Publisher: Springer

Published: 2016-07-23

Total Pages: 571

ISBN-13: 9463005617

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Since its establishment in 1976, PME (The International Group for the Psychology of Mathematics Education) is serving as a much sought after venue for scientific debate among those at the cutting edge of the field, as well as an engine for the development of research in mathematics education. A wide range of research activities conducted over the last ten years by PME members and their colleagues are documented and critically reviewed in this handbook, released to celebrate the Group’s 40 year anniversary milestone. The book is divided into four main sections: Cognitive aspects of learning and teaching content areas; Cognitive aspects of learning and teaching transverse areas; Social aspects of learning and teaching mathematics; and Professional aspects of teaching mathematics. The selection for each chapter of a team of at least two authors, mostly located in different parts of the world, ensured effective coverage of each field. High quality was further enhanced by the scrupulous review of early chapter drafts by two leaders in the relevant field. The resulting volume with its compilation of the most relevant aspects of research in the field, and its emphasis on trends and future developments, will be a rich and welcome resource for both mature and emerging researchers in mathematics education.

Some Adventures in Euclidean Geometry
Some Adventures in Euclidean Geometry

Author: Michael de Villiers

Publisher: Dynamic Mathematics Learning

Published: 2009-09-08

Total Pages: 221

ISBN-13: 0557102952

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This book seeks to actively involve the reader in the heuristic processes of conjecturing, discovering, formulating, classifying, defining, refuting, proving, etc. within the context of Euclidean geometry. The book deals with many interesting and beautiful geometric results, which have only been discovered during the past 300 years such as the Euler line, the theorems of Ceva, Napoleon, Morley, Miquel, Varignon, etc. Extensive attention is also given to the classification of the quadrilaterals from the symmetry of a side-angle duality. Many examples lend themselves excellently for exploration on computer with dynamic geometry programs such as Sketchpad. The book is addressed primarily to university or college lecturers involved in the under-graduate or in-service training of high school mathematics teachers, but may also interest teachers who are looking for enrichment material, and gifted high school mathematics pupils.

Early Childhood Mathematics Education Research
Early Childhood Mathematics Education Research

Author: Julie Sarama

Publisher: Routledge

Published: 2009-04-01

Total Pages: 440

ISBN-13: 1135592497

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This important new book synthesizes relevant research on the learning of mathematics from birth into the primary grades from the full range of these complementary perspectives. At the core of early math experts Julie Sarama and Douglas Clements's theoretical and empirical frameworks are learning trajectories—detailed descriptions of children’s thinking as they learn to achieve specific goals in a mathematical domain, alongside a related set of instructional tasks designed to engender those mental processes and move children through a developmental progression of levels of thinking. Rooted in basic issues of thinking, learning, and teaching, this groundbreaking body of research illuminates foundational topics on the learning of mathematics with practical and theoretical implications for all ages. Those implications are especially important in addressing equity concerns, as understanding the level of thinking of the class and the individuals within it, is key in serving the needs of all children.

The Math Teacher's Book Of Lists
The Math Teacher's Book Of Lists

Author: Judith A. Muschla

Publisher: John Wiley & Sons

Published: 2005-04-11

Total Pages: 436

ISBN-13: 078797398X

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This is the second edition of the bestselling resource for mathematics teachers. This time-saving reference provides over 300 useful lists for developing instructional materials and planning lessons for middle school and secondary students. Some of the lists supply teacher background; others are to copy for student use, and many offer new twists to traditional classroom topics. For quick access and easy use, the lists are numbered consecutively, organized into sections focusing on the different areas of math, and printed in a large 8-1/2" x 11" lay-flat format for easy photocopying. Here's an overview of the ready-to-use lists you'll find in each section: I. NUMBERS: THEORY AND OPERATIONS presents 40 lists including classification of real numbers, types of fractions, types of decimals, rules for various operations, big numbers, and mathematical signs and symbols. II. MEASUREMENT contains over 30 lists including, things that measure, measurement abbreviations, the English and Metric Systems, and U.S. money3⁄4coins and bills. III. GEOMETRY offers more than 50 lists covering topics such as lines and planes, types of polygons, types of quadrilaterals, circles, Pythagorean triples, and formulas for finding area and volume. IV. ALGEBRA gives you over 40 lists including how to express operations algebraically, powers and roots, common factoring formulas, quadratic functions, and types of matrices. V. TRIGONOMETRY AND CALCULUS provides more than 30 lists including the quadrant signs of the functions, reduction formulas, integration rules, and natural logarithmic functions. VI. MATH IN OTHER AREAS offers more than 30 lists that tie math to other content areas, such as descriptive statistics, probability and odds, numbers in popular sports, and some mathematical facts about space. VII. POTPOURRI features 16 lists that explore the various aspects of math including, famous mathematicians through history, world firsts, math and superstition, and the Greek alphabet. VIII. SPECIAL REFERENCE LISTS FOR STUDENTS provides 10 lists of interest to students such as overcoming math anxiety, steps for solving word problems, and math web sites for students. IX. LISTS FOR TEACHERS’ REFERENCE contains 25 lists such as how to manage a cooperative math class, sources of problems-of-the-day, how to have a parents’ math night, and math web sites for teachers. X. REPRODUCIBLE TECHING AIDS contains an assortment of helpful reproducibles including number lines, fraction strips, algebra tiles, and various nets for making 3-D geometric shapes.