Designing Learning Environments for Developing Understanding of Geometry and Space

By Richard Lehrer; Daniel Chazan | Go to book overview

7
Developing Understanding of Geometry and Space in the Primary Grades

Richard Lehrer, Cathy Jacobson, Greg Thoyre, Vera Kemeny, Dolores Strom, Jeffrey Horvath, Stephen Gance, and Matthew Koehler University of Wisconsin-Madison

Our approach to geometry with young children begins with students' in- formal knowledge about situations, followed by progressive mathemati- cal reinterpretation of these experiences, an approach consistent with the Dutch approach to "realistic mathematics education" (see Gravemeijer, chap. 2, this volume). Young children's everyday activities--looking, walking, drawing, building, and manipulating objects--are a rich source of intuitions about spatial structure ( Freudenthal, 1983; Piaget & Inhelder, 1948/ 1956; Streefland, 1991; van Hiele, 1986). By looking at pattern and form in the world, children develop informal knowledge about geometric constructs like perspective, symmetry, and similarity. For example, preschoolers pretend that miniatures are small-scale versions of familiar things, and even infants distinguish contour and symmetry ( Fantz, 1958; Gravemeijer, chap. 2, this volume; Haith, 1980). By walking in their neigh- borhoods, children learn to reason about landmarks, routes, and other el- ements of large-scale space ( Piaget, Inhelder, & Szeminska, 1960; Siegel & White, 1975). By drawing what they see, children represent form ( Good- now , 1977). By building structures with blocks, toothpicks, or Tinkertoys, children experience first-hand how shape and form play roles in function (e.g., objects that roll vs. those that do not) and structure (e.g., sturdiness; see Middleton & Corbett, chap. 10, this volume).

Everyday experiences like these, and the informal knowledge chil- dren develop over time by participating in them, constitute a springboard into geometry. For example, the ideas that children develop about position and direction while walking in their neighborhood can be elaborated mathematically in a variety of ways--as coordinate systems, as compass

-169-

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.
Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

(Einhorn, 1992, p. 25)

(Einhorn 25)

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 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?

Full screen
/ 506

matching results for page

Cited passage

Style
Citations are available only to our active members.
Sign up now 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

Welcome to the new Questia Reader

The Questia Reader has been updated to provide you with an even better online reading experience.  It is now 100% Responsive, which means you can read our books and articles on any sized device you wish.  All of your favorite tools like notes, highlights, and citations are still here, but the way you select text has been updated to be easier to use, especially on touchscreen devices.  Here's how:

1. Click or tap the first word you want to select.
2. Click or tap the last word you want to select.

OK, got it!

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.

For full access in an ad-free environment, sign up now for a FREE, 1-day trial.

Already a member? Log in now.