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Expanding Visions of Geometry: Learning and Teaching Approaches, Lecture notes of Geometry

Ohio State University (OSU) - Wooster Geometry

A collection of articles and research papers on geometry, exploring different approaches to learning and teaching geometry. The first section focuses on expanding visions of geometry, including topics such as symmetry, curvature, and fractals. The second section discusses learning geometry, highlighting research on how children learn and develop spatial reasoning skills. The document also includes a CD-ROM with blackline masters and templates for hands-on activities. University topics related to this document include geometry, mathematics education, and spatial reasoning. The most important US university that most likely has courses related to them is Ohio State University. Correlated university topics include education, cognitive science, and STEM education. The document could be useful as study notes or summaries with a rate of 8 out of 10. The typology associated with this document is 'lecture notes'. A possible academic course which the document might belong to is 'Geometry and Spa

Typology: Lecture notes

2021/2022

Uploaded on 05/11/2023

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Contents

Preface ................................................................................................xi

I. Expanding Visions of Geometry ..................................................1

1. What Is Geometry? ..............................................................................3

Joseph Malkevitch

City College of New York—York College, Jamaica, New York

2. Enumerating Symmetry Types of Rectangle and Frieze Patterns:

How Sherlock Might Have Done It ....................................................17

Doris Schattschneider

Moravian College (Emerita), Bethlehem. Pennsylvania

3. Möbius Concepts: Strips and Tori ......................................................33

Yuichi Handa

California State University—Chico, Chico, California

David A. James

University of Michigan—Dearborn, Dearborn, Michigan

Thomas Mattman

California State University—Chico, Chico. California

4. Exploring Curvature with Paper Models ...........................................49

Howard T. Iseri

Mansfield University of Pennsylvania, Mansfield, Pennsylvania

5. Prairie Plants: Exploring Fractals in Nature .....................................63

Dane Camp

New Trier Township High School—Winnetka Campus, Winnetka,

Illinois

Erich Hauenstein

College of DuPage, Glen Ellyn, Illinois

6. Folding Polygons to Convex Polyhedra .............................................77

Joseph O’Rourke

Smith College, Northampton, Massachusetts

II. Learning Geometry ....................................................................89

7. Highlights of Research on Learning School Geometry .......................91

Michael T. Battista

Ohio State University, Columbus, Ohio

Partial preview of the text

Download Expanding Visions of Geometry: Learning and Teaching Approaches and more Lecture notes Geometry in PDF only on Docsity!

What Is Geometry? .............................................................................. Joseph Malkevitch City College of New York—York College, Jamaica, New York
Enumerating Symmetry Types of Rectangle and Frieze Patterns: How Sherlock Might Have Done It.................................................... Doris Schattschneider Moravian College (Emerita), Bethlehem. Pennsylvania
Möbius Concepts: Strips and Tori ...................................................... Yuichi Handa California State University—Chico, Chico, California David A. James University of Michigan—Dearborn, Dearborn, Michigan Thomas Mattman California State University—Chico, Chico. California
Exploring Curvature with Paper Models ........................................... Howard T. Iseri Mansfield University of Pennsylvania, Mansfield, Pennsylvania
Prairie Plants: Exploring Fractals in Nature ..................................... Dane Camp New Trier Township High School—Winnetka Campus, Winnetka, Illinois Erich Hauenstein College of DuPage, Glen Ellyn, Illinois
Folding Polygons to Convex Polyhedra ............................................. Joseph O’Rourke Smith College, Northampton, Massachusetts

II. Learning Geometry ....................................................................

Highlights of Research on Learning School Geometry ....................... Michael T. Battista Ohio State University, Columbus, Ohio

vi Contents

Prototypes and Categorical Reasoning: A Perspective to Explain How Children Learn about Interactive Geometry Objects ............................................................................................. Paul Yu Grand Valley State University, Allendale, Michigan Jeffrey Barrett Illinois State University, Normal, Illinois Norma Presmeg Illinois State University, Normal, Illinois
Conceptions of Angle: Implications for Middle School Mathematics and Beyond ................................................................. Christine Browning Western Michigan University, Kalamazoo, Michigan Gina Garza-Kling Western Michigan University, Kalamazoo, Michigan
Developing the Spatial Operational Capacity of Young Children Using Wooden Cubes and Dynamic Simulation Software ........................................................................................... Jacqueline Sack Rice University, Houston, Texas Retha van Niekerk University of the Witwatersrand, Johannesburg, Johannesburg, South Africa
Fostering Geometric Thinking in the Middle Grades: Professional Development for Teachers in Grades 5–10 ..................................................................................... Mark Driscoll Education Development Center, Inc., Newton, Massachusetts Michael Egan Augustana College, Rock Island, Illinois Rachel Wing DiMatteo Education Development Center, Inc., Newton, Massachusetts Johannah Nikula Education Development Center, Inc., Newton, Massachusetts

viii Contents

Theorems Discovered by Students Inspire Teachers’ Development .................................................................................... Antonio Quesada University of Akron, Akron, Ohio
Using Circle-and-Square Intersections to Engage Students in the Process of Doing Geometry ............................................................. Stephen Blair Eastern Michigan University, Ypsilanti, Michigan Daniel Canada Eastern Washington University, Cheney, Washington
Area Formulas with Hinged Figures ................................................ Alfinio Flores University of Delaware, Newark, Delaware
An Integrated Approach to Teaching and Learning Geometry ........ David Wilson State University of New York, Buffalo State College, Buffalo, New York
Redesigning a Traditional Geometry Lesson as an Investigative Activity............................................................................................. Jon Davis Western Michigan University, Kalamazoo, Michigan
Looking Forward to Interactive Symbolic Geometry ...................... Philip H. Todd Saltire Software, Tigard, Oregon

Contents of the CD-ROM

Section I: Expanding Visions of Geometry

What Is Geometry?
- Art Gallery Problem (Blackline master)
- Folding Boxes (Blackline master)
Enumerating Symmetry Types of Rectangle and Frieze Patterns: HowSherlock Might Have Done It - Frieze pattern worksheet 1 (Blackline master) - Frieze pattern worksheet 2 (Blackline master)
Exploring Curvature with Paper Models
- Curvature template for figure 4.4 (Blackline master)
- Curvature template for figure 4.6 (Blackline master)
- Curvature template for figure 4.7 (Blackline master)
- Curvature template for figure 4.9 (Blackline master)
- Curvature template for figure 4.10 (Blackline master)
Folding Polygons to Convex Polyhedra
- Folding a Latin cross to make a tetrahedron (Blackline master)
- Folding a square into an octahedron (Blackline master)
- Folding a triangle into a tetrahedron (Blackline master)

Section II: Learning Geometry

Conceptions of Angle: Implications for Middle School Mathematics and Beyond - Link to Smile Math and Logo Light
Developing The Spatial Operational Capacity of Young Children Using Wooden Cubes and Dynamic Simulation Software

Construction box (Video clip)
Extended construction box (Video clip)
Geocadabra installation

Fostering Geometric Thinking in the Middle Grades: Professional Development for Teachers in Grades 5–

Link to Web site
Do Math sessions 4 and 5 — Session 4: Dissecting Shapes (PDF) — Session 5: Analyze Student Work (PDF)