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

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.

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Fig. 5: The path model for testing direct and indirect effects of treatment on self-efficacy.

Notes

  1. 1.

    In addition, we applied a bootstrapping procedure (5000 bootstrapped samples) to analyze the significance of indirect and interaction paths, as the distribution of product terms might be only asymptotically normal (MacKinnon, Lockwood, & Williams, 2004). The p values for the effects under investigation were identical or even lower than when using the type = MLR analysis.

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Schukajlow, S., Achmetli, K. & Rakoczy, K. Does constructing multiple solutions for real-world problems affect self-efficacy?. Educ Stud Math 100, 43–60 (2019). https://doi.org/10.1007/s10649-018-9847-y

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Keywords

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