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

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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 jsack@rice.edu

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