| Description |
1 online resource (xvi, 104 pages) : illustrations |
| Series |
Research in mathematics education |
|
Research in mathematics education series.
|
| Contents |
Definitions in mathematics -- An introductory example-isosceles triangles -- Hierarchies, hierarchical chains, and partitions -- Quadrilaterals -- Quadrilaterals and quadrangles -- Quadrilaterals as polygons -- Types of quadrilaterals -- Quadrilaterals in Euclid -- Parallelograms -- Showing that definitions are equivalent -- The hierarchy underneath parallelograms -- Trapezoids -- Choosing between exclusive and inclusive definitions -- Trapezoids on the coordinate plane -- Rectangles -- Analysis of defining conditions for rectangles -- Why are so many different defining conditions in use? -- possible influence of non-Euclidean geometries -- Isosceles Trapezoids -- Symmetry as a defining condition -- Should rectangles be isosceles trapezoids? -- Kites -- Equivalent defining conditions for kites -- Isosceles triangles as degenerate kites -- Rhombuses (Rhombi) -- Squares -- Defining quadrilaterals using only the hierarchy -- Cyclic quadrilaterals -- Properties of quadrilaterals exhibited in hierarchies -- Types of quadrilaterals as intersections of other types -- Hierarchical properties of angles -- Hierarchical properties of sides -- Hierarchical properties of diagonals -- Hierarchical properties of symmetry -- Hierarchical positions on the coordinate plane |
| Summary |
"This monograph reports on an analysis of a small part of the mathematics curriculum, the definitions given to quadrilaterals. This kind of research, which the authors 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." "The authors have chosen in this monograph to examine a bit of mathematics for its definitions: the quadrilaterals. They 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 the authors chose this specific area of definition in mathematics because it demonstrates how broad mathematical issues revolving around definitions become reflected in curricular materials. While the authors were undertaking this research, they found that the area of quadrilaterals supplied grist for broader and richer discussions than was first anticipated." "The intended audience includes curriculum developers, researchers, teachers, teacher trainers, and anyone interested in language and its use."--Jacket |
| Bibliography |
Includes bibliographical references (pages 83-84) |
| Notes |
Print version record |
| Subject |
Quadrilaterals.
|
|
Geometry, Plane.
|
|
quadrilaterals (polygons)
|
|
MATHEMATICS -- Measurement.
|
|
Geometry, Plane
|
|
Quadrilaterals
|
| Form |
Electronic book
|
| Author |
Griffin, Jennifer
|
|
Witonsky, David
|
|
Willmore, Edwin
|
| ISBN |
9781607526001 |
|
160752600X |
|
9781617352683 |
|
1617352683 |
|
