Designing Learning Environments for Developing Understanding of Geometry and Space

By Richard Lehrer; Daniel Chazan | Go to book overview

facilitated introduction of better conjecturing and argumentation techniques, and the use of modern software tools that facilitate the conjecturing process and that include, where possible, the additional just-in-time support of a computer-based Tutor Agent.


ACKNOWLEDGMENTS

This research was supported by a minigrant from the National Center for Research in the Mathematical Sciences Education at the University of Wisconsin-Madison. Thanks to Jeremy Resnick for his major contributions to the Kite study and to Rich Lehrer for extensive comments on earlier drafts.


REFERENCES

Anderson, J. R., Corbett, A. T., Koedinger, K. R., & Pelletier, R. ( 1995). "Cognitive tutors: Lessons learned". The Journal of the Learning Sciences, 4( 2), 167-207.

Anderson, J. R., Greeno, J. G., Kline, P. J., & Neves, D. M. ( 1981). "Acquisition of problem-solving skill". In J. R. Anderson (Ed.), Cognitive skills and their acquisition. (pp. 191-230). Hillsdale, NJ: Lawrence Erlbaum Associates.

Cavalli-Sforza, V., Lesgold, A., & Wiener, A. ( 1992). "Strategies for contributing to collaborative arguments". In Proceedings of the fourteenth annual conference of the Cognitive Science Society (pp. 755-760). Hillsdale, NJ: Lawrence Erlbaum Associates.

Chazan, D. ( 1993). "High school geometry students' justifications for their views of empirical evidence and mathematical proof". Educational Studies in Mathematics, 24(4), 359-387.

Collins, A., Brown, J. S., & Newman, S. E. ( 1989). "Cognitive apprenticeship: Teaching the crafts of reading, writing, and mathematics". In L. B. Resnick (Ed.), Knowing, learning, and instruction: Essays in honor of Robert Glaser. Hillsdale, NJ: Lawrence Erlbaum Associates.

Ericsson, K. A., & Simon, H. A. ( 1984). Protocol analysis: Verbal reports as data. Cambridge, MA: MIT Press.

Gelernter, H. ( 1963). "Realization of a geometry theorem proving machine". In E. A. Feigenbaum & J. Feldman (Eds.), Computers and thought (pp. 134-152). New York: McGraw-Hill.

Healy, C. ( 1993). Creating miracles: A story of student discovery. Berkeley, CA: Key Curriculum Press.

Jackiw, N. ( 1991). The Geometer's Sketchpad [Computer software]. Berkeley, CA: Key Curriculum Press.

Klahr, D., & Carver, S. M. ( 1988). "Cognitive objectives in a LOGO debugging curriculum: Instruction, learning, and transfer". Cognitive Psychology, 20, 362-404.

Klahr, D., & Dunbar, K. ( 1988). "Dual space search during scientific reasoning". Cognitive Science, 12, 1-48.

Koedinger, K. R., & Anderson, J. R. ( 1990). "Abstract planning and perceptual chunks: Elements of expertise in geometry". Cognitive Science, 14, 511-550.

Koedinger, K. R., & Anderson, J. R. ( 1991). "Interaction of deductive and inductive reasoning strategies in geometry novices". In Proceedings of the thirteenth annual conference of the Cognitive Science Society. Hillsdale, NJ: Lawrence Erlbaum Associates.

Koedinger, K. R., & Anderson, J. R. ( 1993a). "Reifying implicit planning in geometry: Guidelines for model-based intelligent tutoring system design". In S. Derry & S. Lajoie (Eds.), Computers as cognitive tools (pp. 15-45). Hillsdale, NJ: Lawrence Erlbaum Associates.

-346-

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

Items saved from this book

This book has been saved
Highlights (0)
Some of your highlights are legacy items.

Highlights saved before July 30, 2012 will not be displayed on their respective source pages.

You can easily re-create the highlights by opening the book page or article, selecting the text, and clicking “Highlight.”

Citations (0)
Some of your citations are legacy items.

Any citation created before July 30, 2012 will labeled as a “Cited page.” New citations will be saved as cited passages, pages or articles.

We also added the ability to view new citations from your projects or the book or article where you created them.

Notes (0)
Bookmarks (0)

You have no saved items from this book

Project items include:
  • Saved book/article
  • Highlights
  • Quotes/citations
  • Notes
  • Bookmarks
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, APA and Chicago citation styles.

(Einhorn, 1992, p. 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.

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
/ 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, 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."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.

    Author Advanced search

    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.