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Elk-Math: Fostering the acquisition of mathematical argumentation competence with heuristic worked examples and collaboration scripts

ELK 2

Type of project and funding:

Research project, funded by the Deutsche Forschungsgemeinschaft (DFG; FI 792/7-1)

Duration:

2010 - 2013

Involved staff members:

Description:

In this project, a learning environment for computer-supported collaborative learning (CSCL) was developed to investigate the question to what extent different kinds of instructional support can help learners in the acquisition of mathematical argumentation skills. Based on approaches from mathematic education on the one hand and educational psychology on the other, two kinds of instructional support were integrated into this learning environment to foster the acquisition of different components of mathematical argumentation skills. Heuristic worked examples should help learners with the domain-specific, individual cognitive component of argumentation skills by combining the traditional approach of worked examples with the idea of heuristic strategies. To support the acquisition of a more general, social-discursive component of mathematical argumentation skills, a CSCL script was provided. CSCL scripts structure collaborative learning in a way that learners are supported in the appliance of argumentation.
The outcomes of the first study showed that heuristic worked examples and CSCL scripts were effective for the acquisition of mathematical argumentation competence especially for learners with rather good learning pre-requisites. In two further studies we investigated if these effects could be optimized by allowing students to adapt the amount of instructional support according to their subjective needs. First results show that the opportunity to adapt the instructional support to one’s own needs is actively used by the learners. However, to benefit from the adaptability of the instructional support, learners need good self-regulation skills.

Goal:

In this project we investigated to what extent learning with heuristic worked examples and CSCL scripts can foster the acquisition of different components of mathematical argumentation skills. Furthermore we studied if an adaptable design of the instructional support with heuristic worked examples and CSCL scripts can enhance the effectiveness of both kinds of instructional support.

Results:

The results of the first study showed that heuristic worked examples and CSCL scripts were effective for the acquisition of mathematical argumentation competence especially for learners with rather good learning pre-requisites. First results of the study about learning with adaptable heuristic worked examples and adaptable CSCL scripts show that the opportunity to adapt the instructional support to one’s own needs is actively used by the learners. However, to benefit from the adaptability of the instructional support, learners need good self-regulation skills.

Possible qualification thesis:

Bachelor's and Master's level

Cooperation partners:

  • Prof. Dr. Kristina Reiss (Heinz-Nixdorf-Stiftungslehrstuhl für die Didaktik der Mathematik, Technische Universität München)
  • Prof. Dr. Stefan Ufer (Lehrstuhl für die Didaktik der Mathematik, Ludwig-Maximilians-Universität München)

Important publications:

  • Kollar, I., Ufer, S., Reichersdorfer, E., Vogel, F., Fischer, F., & Reiss, K. (2014). Effects of heuristic worked examples and collaboration scripts on the acquisition of mathematical argumentation skills of teacher students with different levels of prior knowledge. Learning and Instruction, 32, 22-36. [doi:10.1016/j.learninstruc.2014.01.003]
  • Vogel, F., Kollar, I., & Fischer, F. (2012). Effects of Computer-Supported Collaboration Scripts on domain-general learning outcomes: a meta-analysis. In J. van Aalst, K. Thompson, M. J. Jacobson & P. Reimann (Eds.), The future of learning: Proceedings of the 10th International Conference of the Learning Sciences (ICLS 2012). Vol. 2: Short Papers, Symposia, and Abstracts (pp. 446-450). Sydney: International Society of the Learning Sciences.
  • Vogel, F., Reichersdorfer, E., Kollar, I., Ufer, S., Reiss, K., & Fischer, F. (2013). Learning to argue in mathematics: Effects of heuristic worked examples and CSCL scripts on transactive argumentation. In N. Rummel, M. Kapur, M. Nathan & S. Puntambekar (Eds.), To see the world and a grain of sand: Learning across levels of space, time and scale - Proceedings of the International Conference on Computer-Supported Collaborative Learning (CSCL) (Vol 1. Full Papers and Symposia) (pp. 526-533). International Society of the Learning Sciences.