Summer Workshop Plans

Summer Workshop Agenda

Opening Session: Cafeteria

Groups	Classrooms	Breakouts	Facilitators
Archimedes	Room 124	Room 124	Gini Stimpson, Jeff Jacobs
Hypatia	Room 124	Room 124a
Gauss	Room 129	Room 129	Christopher Fraley, Michael Keynes, Beckie Nagy
Germain	Room 129	Room 127
Napoleon	Room 125	Room 125	Jack Beal, Maureen Doyle, Allison Harris
Nightingale	Room 125	Room 128
Napier	Room 132	Room 132	Ramesh Gangolli, Rosalind Wise
Russell	Room 132	Room 132
Sun Zi	Room 130	Room 130	Ginger Warfield, Anita Lenges
Seki	Room 130	Hearing Room

Phone number for emergencies only: (206) 729-3230 (office of Eckstein Middle School).

This summer's institute is designed to enhance your understanding of geometry so that you can better support your students' learning of geometric concepts in middle school curriculum. We will explore connections between visual experimentation, verbal descriptions, computation and algebra, and see how elementary geometric concepts lead to universal and powerful conclusions. We will also participate in opportunities to grow as a learning community as we identify questions of interest related to curriculum, instruction, and assessment in the mathematics classroom and explore strategies for working together to increase our understanding of the selected topics. The overall goals for the institute are:

1. To deepen our understanding of the Glorious Features of Geometry (GFG).

   GFG 1: Geometry is a field in which a small collection of elementary results can lead directly to universal and powerful conclusions.

   GFG 2: Geometry encourages developing the ability to relate two different cognitive functions.

   For example, the interaction between

   • visual experimentation and verbal description of shapes and relations
   • the visual and the computational
   • the visual and the algebraic

2. To learn how to continue to grow as a life-long learner by using study groups to deepen our understanding of three of the following five focus areas:

   Understanding Student Thinking about Mathematics

   • Thinking about Effective Mathematics Curriculum, Instruction & Assessment
   • Deepening Our Own Understanding of Mathematics
   • Developing Ways to Use Technology in Mathematics
   • Using Problem/Project-Based Learning to Teach Mathematics

Wednesday - June 24

Goals:

• To increase understanding of the Pythagorean Theorem and its application. To appreciate how the Pythagorean Theorem illustrates the GFG's.
• To reinforce an appreciation of informal proofs.
• To begin to assume shared/servant leadership for our own and our peers' learning.

8:00 - 8:45 a.m.	Overview of the week (cafeteria) Glorious Features of Geometry
8:45 - 10:00 a.m.	Visual Cues for Proof of the Pythagorean Theorem (classrooms)
10:00 - 10:15 a.m.	Break
10:15 - 11:00 a.m.	The Glorious Features of Growing a Community of Learners (cafeteria)
11:00 a.m.-12:15 p.m.	Group Meetings (breakouts)
12:15 - 1:00 p.m.	Lunch (hallway by classrooms)
1:00 - 3:00 p.m.	Pythagoras Strikes Again (classrooms)
(when appropriate)	Break
3:00 p.m.	Adjourn
Evening assignment:	Construct portable x, y, z system

Thursday - June 25

Goals:

• To increase our understanding of similarity and scaling and the many ways in which we use them in real life whether we work with the formal concept or not.
• To increase our understanding of three dimensional coordinate systems.
• To appreciate how similarity and scaling illustrate the GFG's.
• To develop an understanding of basic study group roles, norms, and processes.

Friday - June 26

Goals:

• To extend two-dimensional reasoning to three-dimensional situations.
• To increase our understanding of the relationship between visual and computational reasoning.
• To appreciate how activities with tessellations and platonic solids illustrate the GFGs.
• To consider two different frames for generating discussion questions for study groups.

Monday - June 29

Goals:

• To continue practicing planning a study group for peers.
• To understand some properties of the basic types of transformations in two-dimensions.
• To understand what transformations in two-dimensions preserve and what they do not.
• To classify transformations by their properties.
• To gain an appreciation of the concept of orientation in 2 and 3 dimensions.

Tuesday - June 30

Goals:

• To experience leading and being led in study groups, reflect on the experiences, and consider future plans.
• To deepen our understanding of issues related to three of the five focus areas.
• To continue to increase our understanding of coordinate systems.
• To increase our understanding of measurement.

Throughout the institute, you will be asked to "Convince the Friendly Skeptic that." This is a signal for you to write an argument in ordinary English to persuade someone that your point of view is correct. The person you are to convince, the Friendly Skeptic, is someone who knows all the geometry that you understand so far. The Skeptic is good at picking holes in arguments and asking tough questions, but the Skeptic also is reasonable and does not argue just for the sake of it. If you imagine that the Skeptic asks "Why?" after everything you write, and that you are able to say " because.," then you are well on the way to developing a convincing argument.