Geometric Structures An Inquiry-Based

This text provides a creative, inquiry-based experience with geometry that is appropriate for prospective elementary and middle school teachers. The coherent series of text activities supports each studentrs"s growth toward being a confident, independent learner empowered with the help of peers to make sense of the geometric world. This curriculum is explicitly developed to provide future elementary and middle school teachers.

John Wolfe, Oklahoma State University: John recently was promoted to professor emeritus at Oklahoma State University. After graduating from the University of California at Berkeley in 1971 he was active in mathematics research including several publications and National Science Foundation research grants in Banach Space Theory. His enthusiasm for teaching has been recognized by awards from both the Mathematical Association of America and the Regents of Oklahoma State University. Over the past several years educational issues with a special passion for geometry have been the focus of his professional life. Woodworking, travel, camping and grandkids are becoming increasingly important in his life.

Douglas B. Aichele, Oklahoma State University: Douglas grew up in Great Neck, NY. He received his undergraduate and graduate education in mathematics at the University of Missouri-Columbia. He has been a faculty member at Oklahoma State University for many years and was appointed Regents Professor in 1989. He is currently serving as Associate Head of the Department of Mathematics. Good teaching of mathematics has always been important to him and he has been recognized over the years by such institutions/organizations as the OSU Blue Key Alumni Association, Mathematical Association of America, and the University of Missouri-Columbia.His other interests reside mainly in the outdoors - particularly spending time with his family in the mountains of Colorado at a log cabin that he built by hand. He is an avid backpacker and hiker; he has climbed most of Colorado's Fourteeners (mountains with elevations greater then 14,000 ft.) and several mountains and glaciers near Juneau, Alaska.

Paper Folding
Warm Up Activities
Introduction
Folding Polygons from a Circle
Making Squares
Two Congruent Halves
Dissecting Figures
Polygons and the Angle Relationships
Introduction
Parallel Line Grid - Triangle Angle Sum
Envelope Fold - Triangle Angle Sum
Triangle and Quadrilateral Angle Sums by Tearing
Polygon Angle Sums: How many Triangles?
The Angles of a Polygon
When Does Erika's Idea Work?
The Greedy Triangle
Problems: Angle Sums and Angle Relationships
Four Kinds of Related Angles
Figuring Angles and Checking by Measurement
Parallel Lines: How to Recognize Them
Measuring Sides and Angles of Triangles
Convex: Different Ways to Make Sense of It
Angle Problems - Version A
Angle Problems - Version B
Angle Probems - More
How Do I Know if I Understand?
Conjecturing ABout Quadrilaterals
Possible or Not?
True or False (with Example)
Under What Conditions?
Quadrilaterals and Their Definitions
Introduction
Checking Properties of Quadrilaterals
Properties of Quadrilaterals
Marking Quadrilateral Properties
Properties of Diagonals of Quadrilaterals
Checking Quadrilaterals by Folding
Read Carefully: Every Word Counts!
Checking Examples Visually or Physically
Exploring Medial Quadrilaterals
Problems: Properties of Quadrilaterals, Version A
Problems: Properties of Quadrilaterals, Version B
More Problems: Properties of Quadrilaterals
A Deeper Understanding of Definitions
Special Cases of Quadrilaterals
Definitions: Inclusive or Exclusive
Problems: Inclusive and Exclusive Definitions
What Is a Kite? Equivalent Definitions
Problems: Definitions of Quadrilaterals, Version A
Problems: Definitions of Quadrilaterals, Version B
More Problems: Definitions of Quadrilaterals
How Do I Know if I Understand? Prologue: Four Contexts for Geometric Constructions Prologue to Chapters 3, 10, 12, and 14
Constructions by Paper Folding
Introduction
Introducing CDs: Two Basic Constructions
CD Problem: A Parallel Line
CD Problem: The Median
CD Problem: An Equilateral Triangle
CD Problem: A Square
Circumscribing Circle
Inscribed Circle
Balance Point of a Triangle
Additional CD Problems Using Basic Construction Steps
Group Problem: Inscribed Circles
Folding a Six-Pointed Star or a "Snowflake"
Problems Involving Paper Folding
How Do I Know if I Understand?
Explorations in Three-dimensional Geometry
Introduction
Polyhedra (Solids) from an Envelope
Roll-and-Fold Prism and Pyramid Activities
Net Project A: Prisms
Prisms
Makiing Sense of Volume: A Basic Relationship
Net Project B: Pyramids
Pyramids
Edges, Faces, and Vertices of Polyhedra
Special Kinds of Polyhedra
Riddles with Solids
Volumes Prisms, Pyramids, and Spheres
Volume of a Pyramid
What Does Volume Really Mean?
Volume of Solids: First Try
Solid-Geometry Problems, Version A
Solid-Geometry Problems, Version B
More Solid-Geometry Problems Addendum: Unit Origami: An Introduction
Instructions for the Basic Parallelogram Unit
Project for the Whole Class: Monster Stellated Icosahedron
Uni
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Geometric Structures An Inquiry-Based Approach for Prospective Elementary and Middle School Teachers

Summary

Author Biography

Table of Contents

Supplemental Materials