MTD 437/637: Teaching & Learning Geometry Fall Semester 2009 Instructor:

Prof. Joanna O. Masingila 201 Carnegie 443-1483, [email protected] Office hours: I am available by appointment, email, and telephone.

Time:

Tuesdays, 4 - 6:45 p.m.

Place:

222 Carnegie and 110 Link (5:15-6:35 p.m.)

Course Description: This course is designed for graduate and upper level undergraduate students in mathematics education and inservice mathematics teachers. The course consists of a blend of (a) theoretical and philosophical readings and discussions about teaching and learning geometry ideas, and (b) pragmatic activities involving exploring some geometry concepts and developing ideas for teaching geometry. Objectives: There are three objectives for this course. I. Broaden students' perspectives about the philosophical and theoretical underpinnings of teaching geometry. II. Use these perspectives to examine and identify key issues related to helping all students learn geometry ideas. III.

Develop new insight into geometry ideas through mathematical explorations.

Primary References: Articles posted on Blackboard Available at the Orange Student Book Store in Marshall Square Mall Day, R., Kelley, P., Krussel, L., Lott, J. W., & Hirstein, J. (2002). Navigating through geometry in grades 9-12. Reston, VA: National Council of Teachers of Mathematics. Krause, E. F. (1986). Taxicab geometry: An adventure in non-Euclidean geometry. Mineola, NY: Dover Publications.

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Assignments: 1. Study all readings and be prepared to discuss them intelligently. 2. Prepare at least one thoughtful, discussion question each week readings are assigned. These must be sent to me via email by Tuesday noon before the class. These questions will be used to facilitate the class discussions. 3. Complete the taxicab geometry explorations and reflection. Keep these in a three-ring binder and bring them to class. [Chapters 1-3 due September 29, Chapters 4-5 due November 3, Chapters 6, 7 and Appendix due December 1] 4. Participate in your taxicab geometry exploration group. 5. Write a 6-8 page paper on the four big ideas in the Geometry Standard discussing what are the essence of these ideas and how are they evident in the mathematics curriculum at your chosen grade level. [due October 13] 6. Prepare and lead a group exploration of one or several geometry ideas using Geometer’s Sketchpad™ software. [November 17, 24 and December 1] For Undergraduate and Master’s Level Students 7. Develop/adapt a two-week unit (400 instructional minutes) designed to develop students’ geometric reasoning at your chosen grade level. Your lessons should include strategies for a variety of student learning needs. [due December 8] For Doctoral Students 7. Select a research area of particular interest to you, directly related to any of the topics covered in the class readings. Review 12 - 15 papers from the research literature on this topic. You are expected to analyze, synthesize and reflect upon the research findings. Your paper should be 20 - 22 pages in length (excluding references), double-spaced, and use APA style guidelines for all references. [due December 8] Point Distribution: 1. Class participation/group participation/preparing questions/quality of questions 10% 2. Taxicab Geometry Explorations 30% 3. Big Idea Paper 15% 4. Preparing and Leading Group Exploration Using Geometer’s Sketchpad™ 15% 5. Instructional Unit/Research Paper 30%

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Students with Disabilities: If you believe that you need accommodations for a disability, please contact the Office of Disability Services (ODS), http://disabilityservices.syr.edu, located in Room 309 of 804 University Avenue, or call 315-443-4498 for an appointment to discuss your needs and the process for requesting accommodations. ODS is responsible coordinating disability-related accommodations and will issue students with documented disabilities Accommodation Authorization Letters, as appropriate. Since accommodations may require early planning and generally are not provided retroactively, please contact ODS as soon as possible. You are also welcome to contact me privately to discuss your academic needs although I cannot arrange for disability-related accommodations. Academic Integrity: The Syracuse University Academic Integrity Policy holds students accountable for the integrity of the work they submit. Students should be familiar with the Policy and know that it is their responsibility to learn about instructor and general academic expectations with regard to proper citation of sources in written work. The policy also governs the integrity of work submitted in exams and assignments as well as the veracity of signatures on attendance sheets and other verifications of participation in class activities. Serious sanctions can result from academic dishonesty of any sort. For more information and the complete policy, see http://academicintegrity.syr.edu Semester Schedule Sept 1

Topic: Introduction to Geometry 1st part: Discussion—Intro to class; Geometry Standard; Geometric Probability 2nd part: Activity—Hey, Taxi! 3rd part: GSP Activity—getting started on GSP

Sept 8

Topic: Transformations 1st part: Discussion—Introduction and Chapter 1 in NCTM book 2nd part: GSP Activity—Reflections, Translations, Rotations 3rd part: GSP Activity—Transformation Golf Assignment: Chapter 1 in Krause

Sept 15

Topic: Location 1st part: Discussion—Chapter 2 in NCTM book 2nd part: Activity— Spherical geometry activity 3rd part: GSP Activity—Constructions Assignment: Chapter 2 in Krause

Sept 22

Topic: Shape 1st part: Discussion—Chapter 3 in NCTM book 2nd part: Activity—Taxicab and Other Geometry Explorations 3rd part: GSP Activity—Taxicab problems from Chp 1 & 3 Using Geometer’s Sketchpad™ Assignment: Chapter 3 in Krause

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Sept 29

Topic: Visualization 1st part: Discussion—Chapter 4 and p. 75 in NCTM book 2nd part: Activity—Quadrilateral Relationships 3rd part: GSP Activity—Fractal Geometry Assignment: Chapter 4 in Krause; Chapters 1-3 in Krause due

Oct 6

Topic: Geometry in General Education 1st part: Discussion— Chapter 1 in reader 2nd part: Activity—Constructing Conic Sections with Patty Paper 3rd part: GSP Activity—Paper Folding and Conic Sections Assignment: Chapter 4 in Krause

Oct 13

Topic: Building on Students’ Informal Knowledge about Geometry 1st part: Discussion— Chapter 2 in reader 2nd part: Activity—Tessellations using Tessellation Creator™ 3rd part: GSP Activity—Tessellations Assignment: Chapter 5 in Krause; Big Idea paper due

Oct 20

Topic: Geometry in Secondary School 1st part: Discussion— Chapter 3 & Masingila article in reader 2nd part: Activity—Billiard Ball exploration 3rd part: GSP Activity—Taxicab Extensions Assignment: Chapter 6 in Krause

Oct 27

Colloquium: Jim Hiebert, University of Delaware

Nov 3

Topic: van Hiele Model of the Development of Geometric Thinking 1st part: Discussion—Crowley & Malloy articles in reader 2nd part: Activity—Geometric Conjectures 3rd part: GSP Activity—Geometric Conjectures using Geometer’s Sketchpad™ Assignment: Chapter 6 in Krause; Chapters 4-5 in Krause due

Nov 10

Topic: Student Understanding in Geometry 1st part: Discussion—Chapter 5 in reader 2nd part: Activity—Angle Bisector Problem 3rd part: GSP Activity— Taxicab problems from Chp 5 & 7 Using Geometer’s Sketchpad™ Assignment: Chapter 7 in Krause

Nov 17

Topic: Children’s Geometric Reasoning 1st part: Discussion—Chapter 6 in reader 2nd part: Geometer’s Sketchpad explorations 3rd part: Geometer’s Sketchpad explorations Assignment: Appendix in Krause

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Nov 24

Topic: Developing Geometric Understanding 1st part: Discussion—Chapter 7 in reader 2nd part: Geometer’s Sketchpad explorations 3rd part: Geometer’s Sketchpad explorations

Dec 1

Topic: Conjecturing and Argumentation 1st part: Discussion—Chapter 13 & Keiser article in reader 2nd part: Geometer’s Sketchpad explorations 3rd part: Geometer’s Sketchpad explorations Assignment: Chapters 6, 7 and Appendix in Krause due

Dec 8

Topic: Dynamic Geometry and Proof in Dynamic Geometry 1st part: Discussion—Chapters 14, 15 & 16 in reader 2nd part: Activity— presentation of instructional units and research papers Assignment: Instructional unit/Research paper due

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