Rational Numbers: An Integration of Research

By Thomas A. Romberg; Elizabeth Fennema et al. | Go to book overview

problems as an undeniable source of incorrect additive reasoning with ratios.

The relapse at the end of the project, after a period of considerable stability in most of the students' learning processes, can be explained by the search for explicit rules for calculating with fractions in the context of an especially designed theme called Land of Together. Here all numbers still reflected fair sharing. The number 2, for instance, appeared as 4/2 expressing that 4 goodies were shared by 2 people, or as 6/3, and so on. The main question that was tackled was: Which procedures will students in the Land of Together have to apply when calculating? (See Streefland, 1991.) These procedures, within the context of the Land of Together, had not crystallized yet into general methods. Another cause for relapse was the search for a solution in cases where the numerical obstacles were too complex and contact with the acquired insights was broken. As can be seen in the final graph, there was great differentiation in the group with respect to N- distractors.


CONCLUSIONS

First and foremost, we feel that little importance should be attributed to computations involving fractions as such. Fractions themselves are not the point. The intention of the intertwining of fractions and ratios was primarily to emphasize the mathematization of connections and relations. In other words, the point of this investigation was to determine how students learn to assimilate mathematically situations in which quantities are brought together functionally in one way or another.

In the mathematization of such relations, the students learn to standardize in such a way that equating in one component is achieved, whereby comparing and ordering then can be simply rounded off by determining the relative difference or by performing the demanded division. If mathematics education will deal with fractions in the suggested manner in the future, the following statement of Goethe will lose its meaning for the generations of students to come:

Remember once and for all
The most important aphorism is:
Whole numbers won't bear a secret for you,
But fractions a big one, sure they do!
(translated from German by Leen Streefland)


REFERENCES

Behr, M. J., Post, T. R., & Silver, E. A. ( 1983). "Rational number concepts". In R. Lesh & M. Landau (Eds.), Acquisition of mathematics concepts and processes (pp. 92-144). New York: Academic.

-323-

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
Rational Numbers: An Integration of Research
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
/ 378

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.