As you arrive, please work on the Geometric Transformation Workout (copies are on your table along with tracing paper if you wish to use it). Warm Up Problem. 2.
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As you arrive, please work on the Geometric Transformation Workout (copies are on your table along with tracing paper if you wish to use it)
Warm Up Problem
Using VideoCases to Develop Teachers’ Conceptual Understanding of MathematicsNanette Seago, WestEdPatrick Callahan, Affiliation?Mark Driscoll, EDCJohannah Nikula, EDCJennifer Jacobs, University of Colorado
Overview of Project
Geometric Transformation Workouts
View and Discuss potential video clips for Definition Module
Using videocases in PD
Q & A
In year four of a 5-year National Science Foundation project
Developing videocase-based, PD materials
1 Foundation Module
4 Extension Modules
Staff: Nanette Seago (PI), Mark Driscoll (Co-PI), Jennifer Jacobs, Johannah Nikula, Patrick Callahan, Hilda Borko
Advisory Board:Harold Asturias, Tom Banchoff, Phil Daro, Megan Franke, Karen Koellner, Glenda Lappan, Hung-Hsi Wu
Evaluation Team: [Horizon Research, Inc.] Dan Heck, Kristen Malzahn, Courtney Nelson
Built around authentic video clips from grades 6-8 classrooms
Focus on similarity and its mathematical use in teaching
Modular in design--coherent, sequenced set of videocase professional development sessions
Well-specified facilitator support materials:
Explicitly communicates the underlying core principles
Clearly laid out rationale for principles
Detailed sample agendas and mathematical notes designed with an eye toward making the design and values explicit
Foundation module: ten, 3 hour sessions
A sequence of learning experiences
Help teachers develop a deep, flexible understanding of similarity
Promote a dynamic, transformational view of similarity, and geometry in general.
Provide insight into students developing conceptions of similarity
Equip teachers with specialized content knowledgein the area of similarity
“The mathematical knowledge and skill unique to teaching- not typically needed for purposes other than teaching.
This work involves an uncanny kind of unpacking of mathematics that is not needed--or even desirable--in settings other than teaching. Many of the everyday tasks of teaching are distinctive to this special work.”
Evaluating the plausibility of students’ claims (often quickly)
Giving or evaluating mathematical explanations
Choosing and developing useable definitions
Recognizing what is involved in using a particular representation
Linking representations to underlying ideas and to other representations
(Ball, Thames, & Phelps, 2008)
The 2007 8th grade NAEP item below was classified as “Use similarity of right triangles to solve the problem.”
Only 1% of students answered this item correctly.
Only 24% of high school students answered this item correctly.
I. Mathematical Definition Through Similarity
II. Communication & Language in Similarity
III. Using Representations and Tools in Similarity
IV. Justifying and Proving Geometric Similarity
the Foundation Module
Two figures are similar if one is the same as an enlargement or reduction of the other.
“the same” ~ “congruent” or “can be matched by rotating, translating, and/or reflecting.”
“an enlargement or reduction”~ “stretching or shrinking” or “dilating a figure where the distance from the center of dilation can be multiplied by a fixed scale factor.”