Build, Draw, and Interpret:3-D Visualization Activities Using Somas and Cubes
NCTM Annual Meeting
Salt Lake City, April 10, 2008
Jacqueline Sack
Rice University School Mathematics Project
Houston, Texas
The Context
• Why?
• What?
• Where?
• Who?
• How?
• Support/Funding?
• Surprising extras
Framework for 3-Dimensional Visualization
3-DIMENSIONAL MODEL
CONVENTIONAL GRAPHIC REPRESENTATION OF THE
3-D MODEL
VERBAL DESCRIPTION OF THE 3-D MODEL
(oral or written)
REBUILD IT
TALK ABOUT IT
REPRESENT IT ABSTRACTLY
DRAW OR RECOGNIZE IT IN A
PICTURE
1
12
top front side
SEMIOTIC OR ABSTRACT REPRESENTATION OF THE
3-D MODEL
This slide is not to be reproduced in any form without the expressed permission of Jackie Sack.
Sequence of Activities
• Pre-interview• Single Soma figures:
Verbal task cards• Two-Soma assembly figures:
Shaded and unshaded task cards • Geocadabra interface:
Integrates top-view coding and face views• …
Reflection Questions: The Big Picture
• What instructional strategies observed or shared in this presentation can be applied to any strand in a mathematics classroom?
• How is literacy development addressed in the classroom shown in this presentation?
Verbal Description
• Put the first block down
• Place the second block in front of the first block
• Place the third block to the right of the first block
• Place the fourth block on top of the third block
Semiotic or Abstract Representation of the 2-D Picture
Verbal Description
Listen for and list the descriptive terms this student uses in his explanations.
Conventional Graphic Representation of the 3-D Model
Conventional Graphic Representation of the 3-D Model
Semiotic or Abstract Representation of the 3-D Model
Semiotic or Abstract Representation of the 3-D Model
Semiotic or Abstract Representation of the 3-D Model
Semiotic or Abstract Representation of the 3-D Model
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Semiotic or Abstract Representation of the 3-D Model
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Semiotic or Abstract Representation of the 3-D Model
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Semiotic or Abstract Representation of the 3-D or
2-D Model
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Change to “2”
Summary to Date
• Verbal representation:Continue to emphasize verbal descriptions BY the child to assess accurate use of descriptive language
• Semiotic representation:What is more difficult, code reading or code creation?
• 2-D conventional figures:Reproduction of corresponding 3-D models and codes using 2-Soma assemblies
Closing Questions: The Big Picture
• What instructional strategies observed or shared in this presentation can be applied to any strand in a mathematics classroom?
• How is literacy development addressed in the classroom shown in this presentation?
Contact Information
Dr. Jacqueline Sack [email protected]
Assistant Clinical Professor of Mathematics Wiess School of Natural Sciences, Rice University
Associate Director for Curriculum Development Rice University School Mathematics Project
http://rusmp.rice.edu
Geocadabra [Computer software]www.geocadabra.nl/setupeng.exe
