Multiple Solutions for Real-World Problems, Experience of Competence and Students’ Procedural and Conceptual Knowledge

  • Kay AchmetliEmail author
  • Stanislaw Schukajlow
  • Katrin Rakoczy


An effective way to improve students’ mathematical knowledge is to have them construct multiple solutions for real-world problems. Prior knowledge is a relevant prerequisite for learning outcomes, and the experience of competence is a basic need that has to be fulfilled to improve achievement. In the current experimental study (N = 307), we investigated how the construction of multiple solutions for real-world problems by applying multiple (two) mathematical procedures affected students’ procedural and conceptual knowledge and their experience of competence. Path analyses showed that constructing multiple solutions for real-world problems increased students’ feelings of competence and affected their procedural and conceptual knowledge indirectly through the experience of competence. Moreover, students’ prior knowledge affected their knowledge at posttest directly as well as indirectly via their experience of competence.


Experience of competence Multiple solutions Procedural and conceptual knowledge Real-world problems Teaching methods 

Supplementary material

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Copyright information

© Ministry of Science and Technology, Taiwan 2018

Authors and Affiliations

  • Kay Achmetli
    • 1
    Email author
  • Stanislaw Schukajlow
    • 1
  • Katrin Rakoczy
    • 2
  1. 1.Department of MathematicsUniversity of MünsterMünsterGermany
  2. 2.Center for Research on Educational Quality and EvaluationGerman Institute for International Educational ResearchFrankfurtGermany

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