Designing Learning Environments for Developing Understanding of Geometry and Space

By Richard Lehrer; Daniel Chazan | Go to book overview

with the aid of a computer-assisted design tool--a KidCAD. Here the technology facilitates a transition between experience and geometric representation. Further highlighting the diverse uses of technology, Zech and her colleagues at the Cognition and Technology Group at Vanderbilt University discuss and illustrate their work in developing visual (computer- based) toolkits to help middle-school students carry out real-world activities such as wayfinding and the designing of playgrounds. In the last chapter, Renninger, Weimar, and Klotz indicate that if we recast the form, substance, and tools of a geometry education, then it also becomes imperative to reconsider teachers' professional development. They discuss the development of a national electronic forum for geometry teachers and their students that encourages learning, discussion, and problem solving, as well as providing a resource for the field.

As Hershkowitz suggests in the epilogue, the contributors to this volume advance several related agendas for mathematics education. First, the authors help us better understand the wide range and influence of spatial reasoning and geometry in mathematics. The research presented here suggests that instead of the current arrangement of years of arithmetic with occasional small helpings of geometry, geometry and spatial reasoning can and should be incorporated as a central feature of a general mathematics education: geometry for all. Second, the contributors emphasize the diversity and range of student thinking encompassed by spatial reasoning and geometry. Not only are existing theories called into question, but several fruitful avenues for new theoretical development in mathematics education are suggested. Third, contributors explore how the development of spatial thinking is tied to tools, ranging from modest (but powerful) ones like PolydronsTM to mechanical curve-drawing devices and the new notational forms made possible by computer-based technologies. Taken together, the research suggests renewed curricular focus on geometry and space: Geometry is not only central to reform in mathematics curricula and the instructional focus on learning with understanding, but with its inherent (and in these studies, enhanced) emphasis on conjecture, argumentation, deductive proof, and reflection, is also central to a solid general education and, as many in this volume note, to good habits of mind.


ACKNOWLEDGEMENTS

Preparation of this volume was supported by the National Center for Research in Mathematical Sciences Education (NCRMSE), which in turn was supported by a grant from the Office of Educational Research and Improvement, U.S. Department of Education (grant No. R117G1002) and by the Wisconsin Center for Education Research, School of Education, University of Wisconsin-Madison. Any opinions, findings, or conclusions are those of the authors and do not necessarily reflect the views of the supporting agencies.

-xii-

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.