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Effects of prompting multiple solutions for modelling problems on students’ performance

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Abstract

Prompting students to construct multiple solutions for modelling problems with vague conditions has been found to be an effective way to improve students’ performance on interest-oriented measures. In the current study, we investigated the influence of this teaching element on students’ performance. To assess the impact of prompting multiple solutions in mathematics instruction compared with the prompting of a single solution, we conducted an experimental study with 144 ninth graders from six German classes from middle track schools. We had two experimental groups: In one experimental group, students were required to provide two solutions for modelling problems related to the topic of Pythagoras’ theorem; in the other group, they were asked to find one solution for each problem. Students’ performance in solving tasks with and without a connection to the real world was assessed before and after a five-lesson teaching unit. In addition, the number of solutions developed and students’ experience of competence were assessed with a questionnaire during the teaching unit. The findings showed that, similar to previous studies, prompting students to find multiple solutions does not improve their performance directly. However, using path analysis, we found indirect effects of the treatment on students’ performance via the number of solutions they developed and their experience of competence.

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Notes

  1. In the multiple-solution condition, the number of students who reported developing more than two solutions varied between 9 and 16 % for each of four problems presented to the class.

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Author note

The research project MultiMa, directed by Stanislaw Schukajlow, has been funded by the German Research Foundation [Deutsche Forschungsgemeinschaft] since 2011.

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  1. Department of Mathematics, University of Münster, Fliednerstr. 21, 48149, Münster, Germany

    Stanislaw Schukajlow & André Krug

  2. Department of Educational Quality and Evaluation, German Institute for International Educational Research, Frankfurt, Germany

    Katrin Rakoczy

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  1. Stanislaw Schukajlow
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Schukajlow, S., Krug, A. & Rakoczy, K. Effects of prompting multiple solutions for modelling problems on students’ performance. Educ Stud Math 89, 393–417 (2015). https://doi.org/10.1007/s10649-015-9608-0

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