IDEAS home Printed from
MyIDEAS: Log in (now much improved!) to save this paper

From addition to multiplication and back. The development of students' additive and multiplicative reasoning skills

Listed author(s):
  • De Bock, Dirk


    (Hogeschool-Universiteit Brussel (HUB), Belgium; Centre for Instructional Psychology and Technology, KU Leuven, Belgium)

  • Van Dooren, Wim


    (Centre for Instructional Psychology and Technology, KU Leuven, Belgium)

  • Verschaffel, Lieven

    (Centre for Instructional Psychology and Technology, KU Leuven, Belgium)

Registered author(s):

    This study builds on two lines of research that so far developed largely separately: the use of additive methods to solve proportional word problems and the use of proportional methods to solve additive word problems. We investigated the development with age of both kinds of erroneous solution methods. They key question is whether and how an overall additive approach to word problems develops into an overall multiplicative approach, and how the transition from the first kind of errors to the second occurs. We gave a test containing missing-value problems to 325 third, fourth, fifth, and sixth graders. Half of the problems had an additive structure and half had a proportional structure. Moreover, in half of the problems the internal and external ratios between the given numbers were integer while in the other cases numbers were chosen so that these ratios were noninteger. The results indicate a development from applying additive methods anywhere in the early years of primary school to applying proportional methods anywhere in the later years. Between these two stages many students went through an intermediate stage where they simultaneously used additive methods to proportional problems and proportional methods to additive problems, switching between them based on the numbers given in the problem.

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

    File URL:
    Download Restriction: no

    Paper provided by Hogeschool-Universiteit Brussel, Faculteit Economie en Management in its series Working Papers with number 2009/37.

    in new window

    Length: 49 page
    Date of creation: Nov 2009
    Handle: RePEc:hub:wpecon:200937
    Contact details of provider: Web page:

    More information through EDIRC

    No references listed on IDEAS
    You can help add them by filling out this form.

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    When requesting a correction, please mention this item's handle: RePEc:hub:wpecon:200937. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sabine Janssens)

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.