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How to combine collaboration scripts and heuristic worked examples to foster mathematical argumentation – when working memory matters

  • Matthias Schwaighofer
  • Freydis Vogel
  • Ingo Kollar
  • Stefan Ufer
  • Anselm Strohmaier
  • Ilka Terwedow
  • Sarah Ottinger
  • Kristina Reiss
  • Frank Fischer
Article
First Online:

Abstract

Mathematical argumentation skills (MAS) are considered an important outcome of mathematics learning, particularly in secondary and tertiary education. As MAS are complex, an effective way of supporting their acquisition may require combining different scaffolds. However, how to combine different scaffolds is a delicate issue, as providing learners with more than one scaffold may be overwhelming, especially when these scaffolds are presented at the same time in the learning process and when learners’ individual learning prerequisites are suboptimal. The present study therefore investigated the effects of the presentation sequence of introducing two scaffolds (collaboration script first vs. heuristic worked examples first) and the fading of the primarily presented scaffold (fading vs. no fading) on the acquisition of dialogic and dialectic MAS of participants of a preparatory mathematics course at university. In addition, we explored how prior knowledge and working memory capacity moderated the effects. Overall, 108 university freshmen worked in dyads on mathematical proof tasks in four treatment sessions. Results showed no effects of the presentation sequence of the collaboration script and heuristic worked examples on dialogic and dialectic MAS. Yet, fading of the initially introduced scaffold had a positive main effect on dialogic MAS. Concerning dialectic MAS, fading the collaboration script when it was presented first was most effective for learners with low working memory capacity. The collaboration script might be appropriate to initially support dialectic MAS, but might be overwhelming for learners with lower working memory capacity when combined with heuristic worked examples later on.

Keywords

Mathematical argumentation skills Collaboration scripts Heuristic worked examples Working memory capacity 
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Notes

Acknowledgements

This research was funded by the Deutsche Forschungsgemeinschaft (DFG) under grants FI 792/7-2, KO 3462/2-2, RE 1247/9-2, and UF 59/3-2.

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© International Society of the Learning Sciences, Inc. 2017

Authors and Affiliations

  1. 1.LMU MunichMunichGermany
  2. 2.TUM School of EducationTechnical University of MunichMunichGermany
  3. 3.University of AugsburgAugsburgGermany
  4. 4.LMU MunichMunichGermany

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