IDEAS home Printed from
   My bibliography  Save this paper

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


  • 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)


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.

Suggested Citation

  • De Bock, Dirk & Van Dooren, Wim & Verschaffel, Lieven, 2009. "From addition to multiplication and back. The development of students' additive and multiplicative reasoning skills," Working Papers 2009/37, Hogeschool-Universiteit Brussel, Faculteit Economie en Management.
  • Handle: RePEc:hub:wpecon:200937

    Download full text from publisher

    File URL:
    Download Restriction: no

    More about this item


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. 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). General contact details of provider: .

    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.

    We have no references for this item. You can help adding them by using 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 RePEc Author Service 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.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.