Geometry connections : mathematics for middle school teachers
著者
書誌事項
Geometry connections : mathematics for middle school teachers
(Connections in mathematics courses for teachers)
Pearson Prentice Hall, c2006
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注記
At head of title: Connecting Middle School and College Mathematics (CM)2
Includes bibliographical references and index
内容説明・目次
内容説明
For one-semester undergraduate courses in geometry for the middle school teachers.
With exciting new standards-based middle school mathematics curricula now in place, future teachers need college-level mathematics courses that better prepare them for their professional careers. Throughout the text, students will find problems and activities that demonstrate the presentation and use of geometry in the middle school by using activities currently found in middle schools textbooks. These problems and activities serve to connect many of the concepts covered in this book to future teaching experiences that the students will encounter as they embark on their teaching careers. Additionally, this will motivate future teachers to learn more mathematical content. The student will realize what they are learning is closely related to what they will be teaching. This will help to build the student's skills so when they are in the classroom, they will have the confidence to teach these concepts.
This text presents an insightful review of geometry so that future middle grade mathematics teachers are equipped with the skills needed for teaching NCTM (National Council of Teachers of Mathematics) Standards-based curricula. Included in this text are a variety of classroom connections and classroom discussions designed to deepen the connections between the geometry students are studying now and the geometry they will teach later. The classroom connections consist of activities which teachers might use in the middle school classroom. In contrast, the classroom discussions are explorations that are somewhat more central to the purpose of the book to build the student's understanding of the concepts that they may pass along this knowledge when they teach.
Other titles in the Prentice Hall Connections in Mathematics Courses for Teachers include:
Geometry Connections: Mathematics for Middle School Teachers
Algebra Connections: Mathematics for Middle School Teachers
Data and Probability Connections: Mathematics for Middle School Teachers
Calculus Connections: Mathematics for Middle School Teachers
目次
CONTENTS
Note: All chapters end with a Chapter Review.
Preface
List of Numbered Figures
List of Classroom Connections
List of Classroom Discussions
Chapter 1: Euclid's Geometry Euclid's postulates and common notions
Using logic
Notation and measurement
Polygons and solids
Measuring the earth's radius
Chapter 2: Congruent Figures, Areas and Volumes Congruent triangles
Parallel lines
Quadrilaterals
Areas of figures
Circles
Volumes and surface areas
Chapter 3: Similarity Similar Polygons
Applications of similar triangles
Pythagorean Theorem
Area and perimeter of similar figures
Similarity for more general figures
Chapter 4. Rigid Motions and Symmetry
Reflections over lines and orientation
Translations, rotations, and glide-reflections
Symmetries
Isometries in space
Chapter 5. Vectors and Transformations
Vectors as oriented line segments
Representing vectors with coordinates
Matrices
Transformations using matrices
Isometries and orthogonal matrices
Isometries and complex numbers
Chapter 6. Three Other Geometries Taxicab Geometry
Spherical Geometry
Hyperbolic Geometry
Appendix I Geometer's Sketchpad
Appendix II Euclid's Assumptions
Appendix III Selected Geometry Formulas
Glossary
Answers and hints for odd exercises
Index
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