Warm Up Problem
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)
2.
Using VideoCases to Develop Teachers’
Conceptual Understanding of Mathematics
Nanette Seago, WestEd
Patrick Callahan, Affiliation?
Mark Driscoll, EDC
Johannah Nikula, EDC
Jennifer Jacobs, University of Colorado
Session Agenda
• Overview of Project
• Geometric Transformation Workouts
• View and Discuss potential video clips
for Definition Module
• Using videocases in PD
• Q&A
Learning and Teaching
Geometry Project Overview
• 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
LTG Materials
• 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
LTG Foundation Module Map
LTG Foundation Module Goals
• 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 knowledge in the area of
similarity
Specialized Content Knowledge (SCK)
“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.”
For example:
• 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)
Introduction to GTWs
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.
The 1992 12th grade NAEP item below was classified as
“Find the side length given similar triangles.”
Only 24% of high school students answered this item correctly.
Common Core Standards
• Need to list the ones that fit
GTW Discussion
2.
Task 3
13
Intro to Use of VideoCases in LTG
• Not intended as models
• Used to analyze the dynamic nature of
classroom interactions
• Used to generate discussion, conjectures and
evidence
• Intended to respect teachers, students and
teaching
• Use of lesson graphs to situate the video clips
within the context of a whole lesson
Extension Modules
I.
II.
III.
IV.
Mathematical Definition Through Similarity
Communication & Language in Similarity
Using Representations and Tools in Similarity
Justifying and Proving Geometric Similarity
Definition Module
• Draft Ideas
– Goals
• Determine the components and implications of mathematical
definitions through the example of similarity
• Examine how mathematical definitions are introduced,
developed, and included in classroom lessons through the
example of similarity.
– A few mathematical punch lines:
• There is not one correct definition of similarity, but there are
incorrect definitions
• Definitions differ in their application and context
• A part of practice is being able to analyze, compare, and work
with the different definitions floating around in the classroom
• Geometry is dense with vocabulary, so the idea of definition is
highlighted
Definition of Similarity Used in
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.”
Potential Video Clips
• Series of three video clips from an 8th
grade classroom in Arkansas that the
staff thinks have potential to fit within
the Definition Module.
• Examine these clips with an eye
towards their use in furthering teachers
understanding of the specialized
knowledge in defining similarity
Terri Video Clips
Video Clips Discussion
• What opportunities to learn do the use
of these three clips offer teachers
around mathematical knowledge
specific to teaching?
• Do you see other learning opportunities
within these three clips?
Q&A
Stepping Back
• A central goal of the Foundation Module is to
support teachers to help their students
progress from using informal definitions of
similarity to using increasingly precise
definitions. Currently, we are planning to
show the Melanie clips early on in the
Module. Given the goal of the module, do you
think this is a wise decision? Why or why not?
• Pilot/Field-test sites needed!