Videocases for Learning and Teaching Geometry: Promoting an Understanding of Similarity Nanette Seag

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Videocases for Learning and Teaching Geometry
Promoting an Understanding of Similarity
Nanette Seago, WestEdMark Driscoll, EDC
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Project Overview

• Beginning 2nd year of a 5-year project
• Developing videocase-based, PD materials
• 1 foundation module
• 4 extension modules
• Staff
• Advisory Board

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LTG vs LTLF

• Learning and Teaching Geometry grew out of the
  work of Learning and Teaching Linear Functions
  (Seago, Mumme Branca, 2004)
• Similarities
• Videocase based
• Modular Foundation module extension modules
• Differences
• Mathematical focus
• Tasks vetted by mathematicians prior to
  videotaping
• Videos of a variety of teachers using the same
  tasks

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Project 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 strategies to foster their
  students thinking

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Definition of Similarity

• 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.

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Static vs Dynamic Conceptions Connecting
Similarity to Linearity
1/3
1/3
2
1
3
6
x 2
y 1/3 x
y/x 1/3
1xK
1
y
3
3xK
x
x K
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Potential Foundation Module Mathematical Storyline
Exploring Congruence Laying Similarity
Groundwork Goal Unpack sameness
Introducing Similarity through Transformations Goa
l Unpack what is the same and different in
similar figures
Implications of Similarity Goals (1) Explore
ratios/proportions within and across figures (2)
Explore preservation of angles
Further Implications of Similarity Goals (1)
Explore the relationship of the area of similar
figures, leading into 3-D (2) Explore
linearity and slope
Closure Goal Pull together the big ideas of
static and dynamic understanding of similarity
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Sorting Rectangles

• Examine the pink rectangles in the bag
• Which rectangles are similar? Which are reduced
  or enlarged?
• Decide which of the rectangles doesnt belong and
  explain why it doesnt belong

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Saras Lesson

• 6th Grade
• April, 2008
• Urban
• The Lesson we will see
• From a lesson entitled Sorting Rectangles (70
  minutes)
• Two video clips Greg and Kenny

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Video Viewing - Greg

• What is Gregs method for finding the rectangle
  that doesnt belong?
• Describe Gregs method and/or explanation for
  identifying the rectangle that doesnt belong in
  the family.
• What events and discussions in the video can you
  identify that support your description of Gregs
  mathematical thinking?

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Video Viewing - Kenny

• What is Kennys method for finding the rectangle
  that doesnt belong?
• Describe Kennys method and/or explanation for
  identifying the rectangle that doesnt belong in
  the family.
• What events and discussions in the video can you
  identify that support your description of Kennys
  mathematical thinking?

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