Assessment of Authentic Performance in School Mathematics

By Richard Lesh; Susan J. Lamon | Go to book overview
There are differences between definition, postulate, theorem, conjecture, and observation.
Choice is involved in making definitions and postulates. These choices determine what are theorems.
A proof proves the statement for all of the drawings that satisfy the given.
All Euclidean geometry has not been created/discovered/developed.

NOTE AND REFERENCES

Some people may find it strange to imagine that doing a proof can lead to conjectures, yet as one tries to explain a phenomenon, by deductive proof or otherwise, one sometimes comes to understand the key aspects of the phenomenon. In this way, one may understand that the phenomenon is more general than was thought, or one may find conditions that may be relaxed, resulting in new conjectures.

Bell, A. ( 1976). "A study of pupils' proof explanations in mathematical situations". Educational Studies in Mathematics, 7, 23-40.

Brown, S., and Walter, M. ( 1983). The art of problem posing. Philadelphia: The Franklin Institute Press.

Chazan, D., and Houde, R. ( 1989). How to use conjecturing and microcomputers to teach high school geometry. Reston, VA: National Council of Teachers of Mathematics.

Chi, M., and Bassok, M. ( 1989). "Learning from examples via self explanations". In L. Resnick (Ed.), Knowing, learning, and instruction. Hillsdale, NJ: Lawrence Erlbaum Associates.

Clement, J. ( 1983, April). Observed methods for generating analogies in scientific problem solving. Paper presented at the annual meeting of the American Educational Research Association. Montreal.

Gentner, D., and Gentner, D. R. ( 1983). "Flowing water and teeming crowds: mental models of electricity". In D. Gentner and Stevens (Eds.), Mental models. Hillsdale, NJ: Lawrence Erlbaum Associates.

Hawkins, J., and Sheingold, K. ( 1986). "Microcomputers and education". In Curbertson and Cunningham (Eds.), The 1986 Yearbook of the NSSE. Chicago: University of Chicago Press.

Holland, J., Holyoak, K., Nisbett, R., and Thagard, P. ( 1986). Induction: Processes of inference, learning, and discovery. Cambridge, MA: Massachusetts Institute of Technology.

Kidder, R. ( 1985, April 19). "How high-schooler discovered new math theorem". Christian Science Monitor.

-114-

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 ...
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
Assessment of Authentic Performance in School Mathematics
Table of contents

Table of contents

Settings

Settings

Typeface
Text size Smaller Larger
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
/ 446

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.