Geometric Structures An Inquiry-Based Approach for Prospective Elementary and Middle School Teachers

by Aichele, Douglas B.; Wolfe, John

• ISBN13: 9780131483927
• ISBN10: 0131483927
• Edition: 1st
• Format: Paperback
• Copyright: 2007-04-09
• Publisher: Pearson

Summary

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.

Author Biography

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.

 

Table of Contents

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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