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Do students value modelling problems, and are they confident they can solve such problems? Value and self-efficacy for modelling, word, and intra-mathematical problems

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Abstract

Posing modelling problems in class is supposed to increase students’ motivation. As motivation is assumed to emerge from task value and self-efficacy expectations, the present study considered both constructs with the aims to examine (1) whether students have different values and self-efficacy expectations concerning modelling problems versus dressed up word problems and intra-mathematical problems and (2) whether mathematical content influences task value and self-efficacy concerning different types of problems. We asked 90 high- and middle-track students (ninth- and tenth-graders) how much they valued modelling problems, dressed up word problems, and intra-mathematical problems and if they were confident they could solve these types of problems. All of the problems that we used could be solved by applying mathematical procedures from two different mathematical content areas (Pythagorean theorem or linear functions). The results indicated that there were significant differences in students’ task values and self-efficacy depending on the type of problem. Students reported the lowest task values and self-efficacy expectations for modelling problems compared with the other types of problems. Moreover, the differences between students’ task values (but not between students’ self-efficacy expectations) within the three types of problems seemed to depend on the mathematical content area. Intra-mathematical problems that could be solved by applying the Pythagorean theorem were valued higher than problems involving linear functions, whereas for modelling and dressed up word problems, it was the other way around. Implications for future research and classroom practice are discussed.

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Authors and Affiliations

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

    Janina Krawitz & Stanislaw Schukajlow

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  1. Janina Krawitz
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  2. Stanislaw Schukajlow
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Correspondence to Janina Krawitz.

Appendix

Appendix

Sample tasks involving the Pythagorean theorem as a representative of one mathematical content area (see Figs. 6, 7, 8).

Fig. 6
figure 6

Modelling problem for the mathematical content area represented by the Pythagorean theorem (Schukajlow and Leiss 2011)

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Fig. 7
figure 7

Dressed up word problem for the mathematical content area represented by the Pythagorean theorem (Krug and Schukajlow 2013)

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Fig. 8
figure 8

Intra-mathematical problem for the mathematical content area represented by the Pythagorean theorem (Krug and Schukajlow 2013)

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Krawitz, J., Schukajlow, S. Do students value modelling problems, and are they confident they can solve such problems? Value and self-efficacy for modelling, word, and intra-mathematical problems. ZDM Mathematics Education 50, 143–157 (2018). https://doi.org/10.1007/s11858-017-0893-1

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