Assessment of Authentic Performance in School Mathematics

By Richard Lesh; Susan J. Lamon | Go to book overview

continuous growth is needed, even when high levels of excellence have been achieved. There is no fixed and final state of expertise, nor of excellence. In teaching, as in other fields, experts must always continue to develop. In sports, when Michael Jordan develops new capabilities, his environment soon adapts to him, so he must engage in another round of development The situation is similar in mathematics teaching. The ways that teachers think about mathematics, teaching, learning, and real-life problem solving strongly influence what goes on in their classrooms; but what goes on in their classrooms also requires teachers to develop more powerful and sophisticated understandings about mathematics, teaching, and learning. The cycle is never-ending, and teachers who fail to get better risk being not very good at all.

These principles should be taken into account in assessment programs for teachers. Just as in the assessment for K-12 students, the assessment of teaching should focus on activities that are meaningful and important in their own right. These activities should enable teachers to both develop and document their development without interrupting their instructional activities. And, as in assessments of students or of programs, assessment activities for teachers are more than indicators of progress. They are interventions that can induce either positive or negative changes in the systems and individuals they describe. Therefore, care must be taken to ensure that these influences are positive. This "progress-focused assessment" is aimed at documenting progress in directions that are increasingly "better" without necessarily beginning with a fixed and final definition of "best" and without labeling individuals as good or poor relative to one another.

In the Teachers project, teachers collaboratively write performance assessment problems for their students and analyze students' responses to such items. Then, in weekly meetings over a ten-week period, these teachers produce a library of useful problems and response analysis procedures while refining their collective conceptions about the nature of good problems and good responses. During the process, many participants have developed new insights about the nature of their discipline, of its applications, and of students' understandings and capabilities. And the problems that were written and responses that were analyzed produced a trace of the teachers' own progress that was very impressive to school administrators.


SUMMY

Enormous progress has been made in clarifying future-oriented instructional objectives in mathematics. Now efforts are being made to create new types of tests and test items consistent with these instructional objectives. Yet, precisely because significant progress has been made at the

-421-

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
Assessment of Authentic Performance in School Mathematics
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
/ 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

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.