Designing Learning Environments for Developing Understanding of Geometry and Space

By Richard Lehrer; Daniel Chazan | Go to book overview

are too intriguing to ignore (see, e.g., Cuoco & Goldenberg, in press). So is the evidence in students' eyes and on their faces. We must come to understand the new terrain well, so that its roughness becomes a part of, and not a detraction from, its beauty.


ACKNOWLEDGMENTS

The perspective, rationale, planning, and writing of this chapter were supported in part by development funds from Education Development Center, Inc. (EDC), with additional support from the National Center for Research in Mathematical Sciences Education (NCRMSE) and EDC's Connected Geometry project, funded by the National Science Foundation (grant MDR-9252952). Major funding for the interviews with Jean-Marie and Colette Laborde and others at Institut d'Informatique et Mathématiques Appliquées (IMAG) was provided by NCRMSE, with additional support from Connected Geometry. Interviews with Nick Jackiw, Eugene Klotz, Judah Schwartz, and Michal Yerushalmy (whose significant intellectual contributions are, as yet, only partially reflected in this writing) and the final preparation of this chapter were supported in part by National Science Foundation grant RED-9453864. We are particularly grateful to Jean-Marie and Colette for the time they spent not only during our initial discussions, but also in reviewing the manuscript. We also acknowledge the contributions of Nicolas Balacheff, Bernard Capponi, and James King. Opinions (and errors) are ours, and do not necessarily reflect the views of any of the funders or contributors.


REFERENCES

Abelson, H., & diSessa, A. ( 1980). Turtle geometry, Cambridge, MA: MIT Press.

Baulac, Y., Bellemain, E, & Laborde, J. M. (Designers). ( 1992). Cabri: The interactive geometry notebook (Cabri Géomètre). Pacific Grove, CA: Brooks-Cole.

Baulac, Y., Bellemain, E, & Laborde, J. M. (Designers). ( 1994). Cabri II. Dallas, TX: Texas Instruments.

Brock, C. F., Cappo, M., Dromi, D., Rosin, M., & Shenkerman, E. (Designers). ( 1994). Tangible math: Geometry Inventor. Cambridge, MA: Logal Educational Software and Systems.

Cuoco, A. ( 1993). "Action to process: Constructing functions from algebra word problems". Intelligent Tutoring Media, 4(3-4), 117-127.

Cuoco, A. ( 1995). "Computational media to support the learning and use of functions". In A. diSessa , C. Hoyles, & R. Noss, with L. Edwards (Eds.), Proceedings of the Advanced NATO Workshop: Computational media to support exploratory learning (pp. 79-107). New York: Springer-Verlag.

Cuoco, A., & Goldenberg, E. P. ( 1996). "Dynamic geometry as a bridge from Euclidean geometry to analysis". In D. Schattschneider & J. King (Eds.), Geometry turned on: Dynamic software in learning, teaching and research (MAA Notes, Vol. 41). Washington, DC: Mathematical Association of America.

de M. Villiers ( 1994). "The role and function of a hierarchical classification of quadrilaterals". For the Learning of Mathematics, 14(1), 11-18.

Feurzeig, W. ( 1993). "Explaining function machines". Intelligent Tutoring Media, 4(3-4), 97-108.

-366-

Notes for this page

Add a new note
If you are trying to select text to create highlights or citations, remember that you must now click or tap on the first word, and then click or tap on the last word.
One moment ...
Default project is now your active project.
Project items
Notes
Cite this page

Cited page

Style
Citations are available only to our active members.
Buy instant access to cite pages or passages in MLA 8, MLA 7, APA and Chicago citation styles.

(Einhorn, 1992, p. 25)

(Einhorn 25)

(Einhorn 25)

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

Note: primary sources have slightly different requirements for citation. Please see these guidelines for more information.

Cited page

Bookmark this page
Designing Learning Environments for Developing Understanding of Geometry and Space
Table of contents

Table of contents

Settings

Settings

Typeface
Text size Smaller Larger Reset View mode
Search within

Search within this book

Look up

Look up a word

  • Dictionary
  • Thesaurus
Please submit a word or phrase above.
Print this page

Print this page

Why can't I print more than one page at a time?

Help
Full screen
Items saved from this book
  • Bookmarks
  • Highlights & Notes
  • Citations
/ 506

matching results for page

    Questia reader help

    How to highlight and cite specific passages

    1. Click or tap the first word you want to select.
    2. Click or tap the last word you want to select, and you’ll see everything in between get selected.
    3. You’ll then get a menu of options like creating a highlight or a citation from that passage of text.

    OK, got it!

    Cited passage

    Style
    Citations are available only to our active members.
    Buy instant access to cite pages or passages in MLA 8, MLA 7, APA and Chicago citation styles.

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn, 1992, p. 25).

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences."1

    1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

    Cited passage

    Thanks for trying Questia!

    Please continue trying out our research tools, but please note, full functionality is available only to our active members.

    Your work will be lost once you leave this Web page.

    Buy instant access to save your work.

    Already a member? Log in now.

    Search by... Author
    Show... All Results Primary Sources Peer-reviewed

    Oops!

    An unknown error has occurred. Please click the button below to reload the page. If the problem persists, please try again in a little while.