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Educational Studies in Mathematics

, Volume 100, Issue 1, pp 43–60 | Cite as

Does constructing multiple solutions for real-world problems affect self-efficacy?

  • Stanislaw SchukajlowEmail author
  • Kay Achmetli
  • Katrin Rakoczy
Article

Abstract

The development of multiple solutions for a given problem is important for learning mathematics. In the present intervention study, we analyzed whether prompting students to construct multiple solutions (more precisely: prompting them to apply multiple mathematical procedures to real-world problems) and prior self-efficacy influenced students’ self-efficacy directly as well as indirectly via perceived competence. Students’ self-efficacy (N = 304) was measured before and after a 4-lesson teaching unit, and students’ perceived competence was measured during the unit. Results of the path model showed that although prompting multiple solutions did not positively affect self-efficacy, indirect effects of teaching method on self-efficacy were found. Students who were asked to develop multiple solutions perceived higher competence and reported higher self-efficacy than students who were required to provide one solution. These indirect effects were significant for students with low prior self-efficacy and nonsignificant for students with high prior self-efficacy, indicating the moderating effect of prior self-efficacy. This finding indicates that students with unfavorable learning prerequisites such as low self-efficacy might benefit from teaching methods that require them to construct multiple solutions. Further, students with low prior self-efficacy reported lower competence during the lessons regardless of whether they were asked to develop one or multiple solutions; they also reported lower self-efficacy at posttest prior self-efficacy was controlled for. Our findings therefore indicate that disadvantages for students with low prior self-efficacy for the further development of self-efficacy during learning might be balanced by teaching students to construct multiple solutions.

Keywords

Multiple solutions Self-efficacy Mathematical modeling Real-world problems Word problems Teaching methods 

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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MünsterMünsterGermany
  2. 2.Center for Research on Educational Quality and Evaluation, German Institute for International Educational ResearchFrankfurt am MainGermany

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