Designing Learning Environments for Developing Understanding of Geometry and Space

By Richard Lehrer; Daniel Chazan | Go to book overview

13
Conjecturing and Argumentation in High-School Geometry Students

Kenneth R. Koedinger Carnegie Mellon University

There is a tendency to think of individuals who can discover new ideas or develop convincing arguments as having special "talent" or superior "intelligence." This view of conjecturing and argumentation abilities as fixed traits suggests that instruction directed toward such abilities is pointless for all but the most gifted of students. In direct contrast to that view, this chapter argues that successful conjecturing and argumentation performances are the consequence of particular skills and knowledge. In an appropriately structured learning environment, such skills can be acquired by anyone.

One reason for doubt regarding the instructability of conjecturing skills is our limited understanding of what these skills are. Developing a model of these skills is a key step toward creating effective learning environments for conjecturing. This model can then provide design guidance in creating elements of a learning environment: conjecturing tasks that appropriately challenge students and forms of assistance (including manipulatives, facilitative talk, and computer software) that support student learning. The learning approach being advocated here has important similarities with the Vygotskian notion of assisted performance ( Vygotsky, 1978) and more recent variations like cognitive apprenticeship ( Collins, Brown, & Newman, 1989).

This chapter presents a cognitive analysis of student conjecturing that includes a task analysis and an initial model of conjecturing, observations of student performance in a dynamic assessment, and modifications to the proposed model as guided by the results of this assessment. This cognitive analysis is then used to suggest forms of student assistance, including computer software tools, activities that draw out conjecturing skills, and facilitative "talking points" (hints or prompts), to help students through the most difficult terrain on their ways to conjecturing skill.

-319-

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.

    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.