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ZDM

, Volume 50, Issue 1–2, pp 91–102 | Cite as

Open word problems: taking the additive or the multiplicative road?

  • Tine Degrande
  • Jo Van Hoof
  • Lieven Verschaffel
  • Wim Van Dooren
Original Article
First Online:

Abstract

Previous studies have repeatedly shown that children often incorrectly use an additive model for multiplicative word problems, and a multiplicative model for additive word problems. The present study aimed to investigate which model upper primary school children tend to choose in word problems that are open to both ways of reasoning. In particular, a non-symbolic variant of the snake task of Lamon (Teaching fractions and ratios for understanding: Essential content knowledge and instructional strategies for teachers, Taylor & Francis Group, New York, NY, 2008) was administered to 279 children in fifth and sixth grade of primary education. Children were asked to indicate which of two snakes had grown the most, and to verbally explain the reasoning behind their answer. Results revealed that additive reasoning (i.e., absolute growth) was more frequently used than multiplicative reasoning (i.e., relative growth), although it appeared to be harder to verbalize. Second, both trends were more prominent for fifth than sixth graders. Third, contrary to previous studies with younger children, we did not find any differences between answers on discrete and continuous variants of the task. Nevertheless, children’s answers were more often explicitly verbalized in discrete than continuous items. Theoretical, methodological, and educational implications for solving word problems, and more generally for modelling in the domain of additive and multiplicative reasoning, are discussed.

Keywords

Modelling Word problem solving Additive reasoning Multiplicative reasoning Open word problems 
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Copyright information

© FIZ Karlsruhe 2017

Authors and Affiliations

  • Tine Degrande
    • 1
  • Jo Van Hoof
    • 1
  • Lieven Verschaffel
    • 1
  • Wim Van Dooren
    • 1
  1. 1.KU Leuven, Centre for Instructional Psychology and TechnologyLeuvenBelgium

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