Learning by Problem-Posing for Reverse-Thinking Problems

  • Tsukasa Hirashima
  • Megumi Kurayama
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6738)


Learning by problem-posing is a promising way to learn arithmetic or mathematics. We have already developed several interactive learning environments for learning by problem-posing. In this research, we have paid a special attention to “reverse-thinking problems” in arithmetic word problems that can be solved either by addition or subtraction. In the reverse-thinking problems, since “story operation structure” and “calculation operation structure” are different, they require learners to comprehend the relations between problems and solutions more than “forward thinking problems” where “story operation structure” and “calculation operation structure” are the same ones. Based on a learning environment for posing the forward thinking problems developed previously, we have expanded it for reverse thinking problems. This learning environment has been used in a class of fourth grade at an elementary school for eight lesson times. We have also reported the results of this practical use.


Problem-posing Reverse thinking problem Story operation structure Calculation operation structure 


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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Tsukasa Hirashima
    • 1
  • Megumi Kurayama
    • 1
  1. 1.Learning Engineering Group, Information Engineering, Graduate School of EngineeringHiroshima UniversityHigashi-HiroshimaJapan

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