1. 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

2. The Context Why? What? Where? Who? How? Support/Funding? Surprising extras

3. 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 topfrontside 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.

4. 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 …

5. 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?

6. 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

7. Semiotic or Abstract Representation of the 2-D Picture

8. Verbal Description Listen for and list the descriptive terms this student uses in his explanations.

9. Conventional Graphic Representation of the 3-D Model

12. Semiotic or Abstract Representation of the 3-D Model

15. 1 1 2 1 1 2

16. 1 1 1 1 1 1 1 1 1 1

17. 1 1 1 1 1 1 1 1 1 1

18. Semiotic or Abstract Representation of the 3-D or 2-D Model

21. Change to “2”

22. 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

23. 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?

24. 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