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Summer Workshop Plans


Summer Workshop Agenda

submitter: Creating A Community of Mathematics Learners
published: 07/30/1998
posted to site: 07/30/1998
Creating a Community of Mathematics Learners presents

The Glorious Features of Geometry

Eckstein Middle School, Seattle School District
June 24 -- June 30, 1998
8 a.m. -- 3 p.m.
Coffee, tea and pastries at 7:30 each day

Opening Session: Cafeteria

ArchimedesRoom 124Room 124Gini Stimpson, Jeff Jacobs
HypatiaRoom 124Room 124a
GaussRoom 129Room 129Christopher Fraley, Michael Keynes, Beckie Nagy
GermainRoom 129Room 127
NapoleonRoom 125Room 125Jack Beal, Maureen Doyle, Allison Harris
NightingaleRoom 125Room 128
NapierRoom 132Room 132Ramesh Gangolli, Rosalind Wise
RussellRoom 132Room 132
Sun ZiRoom 130Room 130Ginger Warfield, Anita Lenges
SekiRoom 130Hearing Room

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

Overview of the Institute

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

Daily Schedules for June 24 - 30, 1998

Wednesday - June 24


  • 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


  • 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.
8:00 - 10:15 a.m.Similarity and perspective (classrooms)
10:15 - 10:30 a.m.Break
10:30 a.m. - 12 p.m.Team Planning (Focus rooms)

Understanding Student Thinking about Mathematics (132)
Thinking about Effective Mathematics Curriculum, Instruction and Assessment (125)
Deepening Our Own Understanding of Mathematics (130)
Developing Ways to Use Technology in Mathematics (124a)
Using Problem/Project-Based Learning to Teach Mathematics (124)

12:00 - 12:45 p.m.Lunch (hallway by classrooms)
12:45 - 2:00 p.m.Similarity and Perspective (classrooms)
2:00 - 3:00 p.m.Coordinate Geometry
3:00 p.m.Adjourn
Evening Assignment:Coordinate systems
Focus group reading

Friday - June 26


  • 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.
8:00 - 8:30 a.m.Community Building in Groups (breakouts)
8:30 - 10:00 a.m.Team planning (focus rooms)
10:00 - 10:15 a.m.Break
10:15 - 12:15 a.m.Tessellations
12:15 - 1:00 p.m.Lunch
1:00 - 3:00 p.m.From Tessellations to Platonic Solids
3:00 p.m.Adjourn

Monday - June 29


  • 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.
8:00 - 9:30 a.m.Finalize team plans (focus rooms)
9:30 - 9:45 a.m.Break
9:45 - 10:40 a.m.Transformations (classrooms)
10:40 - 10:50 a.m.Break
10:50 a.m. - 12 p.m.Transformations (classrooms)
12:00 - 12:45 p.m.Lunch
12:45 p.m. - 1:15 p.m.Debrief homework from day two (classrooms)
1:15 - 3:00 p.m.Coordinate systems
3:00 p.m.Adjourn

Tuesday - June 30


  • 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.
8:00 - 11:30 a.m.Team presentations
11:30 a.m. - 1:00 p.m.Lunch
1:00 - 2:45 p.m.An outdoor coordinate geometry experience
2:45 - 3:00 p.m.Evaluations and clock hour forms
3:00 p.m.Adjourn

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.