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Learning to solve story problems—supporting transitions between reality and mathematics

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Abstract

Applying mathematics to real problems is increasingly emphasized in school education; however, it is often complained that many students are not able to solve mathematical problems embedded in contexts. In order to solve story problems, a transition from a textual description to a mathematical notation has to be found, intra-mathematical calculations have to be performed, and the results have to be interpreted with respect to the described situation. On the one hand, it is often suggested to consider problems which are embedded in a context from the very beginning; on the other hand, step-by-step procedures at the beginning of learning processes are widely proposed. In the present work, it was tested experimentally whether starting a learning process in a “pure” intra-mathematical way (thus, without a textual description of a context) is more beneficial than starting a learning process with problems providing a very short context or with problems providing a detailed context, both with respect to objective measures and with respect to subjective measures. The results indicate that starting with intra-mathematical problems and starting with detailed story problems can both be very effective; however, interaction effects with prior knowledge have to be taken into account. With respect to motivational aspects, the results indicate that intra-mathematical problems and focused story problems are substantially more appreciated by the learners than detailed story problems.

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Acknowledgments

This work was supported by the Central Research Development Fund (CRDF) of the University of Bremen and by the German Research Foundation (DFG) under contract number GR2706/4-1. The author would like to thank these institutions for their support.

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Authors and Affiliations

  1. Group of Computer Architecture, Institute of Computer Science, University of Bremen, 28359, Bremen, Germany

    Cornelia S. Große

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  1. Cornelia S. Große
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Correspondence to Cornelia S. Große.

Additional information

Dr. Cornelia S. Große. Group of Computer Architecture, Institute of Computer Science, University of Bremen, 28359 Bremen, Germany. Email: cornelia.grosse@uni-bremen.de

Current themes of research:

• Learning to solve story problems and modeling problems

• Learning with multiple solution methods

• Learning with correct and incorrect worked examples

Most relevant publications in the field of Psychology of Education:

Große, C. S., & Renkl, A. (2007). Finding and fixing errors in worked examples: Can this foster learning outcomes? Learning and Instruction, 17, 612–634.

Große, C. S., & Renkl, A. (2006). Effects of multiple solution methods in mathematics learning. Learning and Instruction, 16, 122–138.

Große, C. S., & Renkl, A. (2005). Example-based learning with multiple solution methods: effects on learning processes and learning outcomes. In B. G. Bara, L. Barsalou & M. Bucciarelli (Eds.), Proceedings of the 27th Annual Conference of the Cognitive Science Society (pp. 839–844). Mahwah, NJ: Erlbaum.

Große, C. S. (2005). Lernen mit multiplen Lösungswegen [Learning with multiple solution methods]. Münster: Waxmann.

Renkl, A., Atkinson, R. K., & Große, C. S. (2004). How fading worked solution steps works—a cognitive load perspective. Instructional Science, 32, 59–82.

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Große, C.S. Learning to solve story problems—supporting transitions between reality and mathematics. Eur J Psychol Educ 29, 619–634 (2014). https://doi.org/10.1007/s10212-014-0217-6

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  • DOI: https://doi.org/10.1007/s10212-014-0217-6

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