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Author: Zalman Usiskin
Publisher: IAP
ISBN: 160752600X
Category : Education
Languages : en
Pages : 120
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Book Description
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.
Author: Zalman Usiskin
Publisher: IAP
ISBN: 160752600X
Category : Education
Languages : en
Pages : 120
Get Book Here
Book Description
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.
Author: Zalman Usiskin
Publisher:
ISBN: 9781617352683
Category : Geometry, Plane
Languages : en
Pages : 104
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Book Description
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 (Edwards and Ward 2004). 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 (see, for example, Craine and Rubenstein 1993; Mendoza 1993; Prevost 1985; Keedy 1966,1980; Maraldo 1980; the Math Forum internet site, definitions and classification of quadrilaterals; and the Numericana internet site). 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 would include curriculum developers, researchers, teachers, and teacher trainers.
Author: Molly Blaisdell
Publisher: Capstone
ISBN: 1404855114
Category : Juvenile Nonfiction
Languages : en
Pages : 14
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Book Description
The creative examples, simple text, and art in this series help students learn primary math concepts.
Author: Steven Schwartzman
Publisher: MAA
ISBN: 9780883855119
Category : Mathematics
Languages : en
Pages : 276
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Book Description
This book explains the origins of over 1500 mathematical terms used in English.
Author: Bonnie Coulter-Leech
Publisher: The Rosen Publishing Group, Inc
ISBN: 9781404234963
Category : Juvenile Nonfiction
Languages : en
Pages : 36
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Book Description
Explains what quadrilaterals are, describes how to measure their perimeter and area, and further explores named quadrilaterals such as rectangles, kites, and rhombi.
Author: Ángel Gutiérrez
Publisher: Springer
ISBN: 9463005617
Category : Education
Languages : en
Pages : 571
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Book Description
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.
Author: J. Richard Dennis
Publisher:
ISBN:
Category : Computer-assisted instruction
Languages : en
Pages : 13
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Book Description
Author: Michael de Villiers
Publisher: Dynamic Mathematics Learning
ISBN: 0557102952
Category : Euclid's Elements
Languages : en
Pages : 221
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Book Description
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.
Author: LuAnn S. Crosby
Publisher:
ISBN:
Category : Quadrilaterals
Languages : en
Pages : 8
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Book Description
Author: Brainard Braimah
Publisher: Xulon Press
ISBN: 160477360X
Category : Mathematics
Languages : en
Pages : 258
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Book Description
These definitions are essential to the study of Mathematics at the target age range. The book provides clear and simple definitions supported by examples and diagrams. Nearly 1000 mathematical terms are defined. The book is a reference for pupils, parents and mathematics teachers who are not mathematics specialists. The publication is an important resource for classroom practitioners for Mathematics. It is intended for teachers to explain clearly most of the Mathematical concepts learners will encounter. This has been done, with the needs of teachers and learners in mind, in a simple way and with examples to illustrate and enhance the meaning and application of key concepts. It is a must have publication. A great resource in the classroom, library and home. The Author has used his extensive experience to highlight the need for such a publication and has undertaken a remarkable task in producing this for practitioners in the classroom. Mr. Braimah is a village boy from Ghana who does not even know his correct age. An experienced Mathematics teacher, founder of after-school classes now in their 19th year, and possessor of an MBE, he is echoing the government's concern about the paucity of black role models for teenagers teetering on the edge of disillusion. "It's not just individual role models either," he said. Brainard Braimah, who has established and maintained a number of charities to improve employment and prospects for young people, won the Lifetime Difference Award in 2005. I am or have been a member of the following committees: CHEL, Education 2000 (Learning Partnership) Leeds West Indian Carnival, Leeds West Indian Centre and F1 Business Support. Trustee for Wade Charity, Regional Committee Member for Children in Need, Regional panel member for NCH - Action for Children (Family Finders) and a School Governor.
