The Synergy of Heuristic Worked Examples and Collaboration Scripts in Fostering Mathematical Argumentation Skills

• In Event: 75.019 - Scaffolding Students' Learning in Formal and Informal Contexts

Abstract

Mathematical argumentation skills (e.g. while solving mathematical proof tasks) are relevant for engaging in meaningful mathematical work. Yet, students often struggle when requested to discuss during mathematical proof. To foster students’ acquisition of argumentation skills in mathematics a rather domain-specific approach would provide students with instructional support that structures the mathematical content while a collaboration support would rather structure the social-discursive aspects of the mathematical argumentation.

We conducted a project in which we applied both approaches in mathematics education, namely heuristic worked examples as domain-specific instructional support and a collaboration script as social-discursive support. By combining both types of instructional support we aimed to reach synergistic scaffolding (i.e. effects that go beyond an simple addition of the effects of eachinstructional support, Tabak, 2004). Earlier results of the project (Kollar, et al. 2014) have shown that both heursitic worked examples and collaboration scripts could enhance students’ argumentation skills. Yet, it is still an open question, to what extent both means of instructional support affect specific aspects of the collaborative learning activities and how these activities are related to the effects on the acquisition of argumentation skills. Therefore, this paper is concerned with the question to what extent transactive argumentation as collaborative learning activity (Teasley, 1997) can be induced by the heuristic worked examples and the collaboration script and to what extent the transactive argumentation mediates the effects of both types of instructional support.

We conducted a 2-factorial experiment with the factors collaboration script (with vs. without) and heuristic worked examples (with vs. without) with N = 101 first semester math teacher students. The students learned on three mathematical proof tasks in a computer-supported collaborative learning environment in three different dyads.
Results from the mediation analysis show that both means of instructional support induced the transactive argumentation in the collaborative learning process in a synergistic way. Further, it was the self-generated transactive argumentation that mediated the effectiveness of the heuristic worked examples and the collaboration script on the acquisition of argumentation skills. But the transactive argumentation generated by the learning partner did not mediate any of the effects on mathematical argumentation skills.

To learn general argumentation skills in a domain that is not prototypical for a discursive domain, the learning environment needs to offer well-designed domain-specific support to provide learners with structured content to use in their argumentation. Also, educators should design the domain-specific and the collaboration scaffolds with a specific focus on evoking transactive argumentation during the collaborative learning process.

Kollar, I., Ufer, S., Reichersdorfer, E., Vogel, F., Fischer, F., & Reiss, K., (2014). Combined effects of heuristic worked examples and collaboration scripts on the acquisition of mathematical argumentation skills. Learning & Instruction 32, 22-36. doi:10.1016/j.learninstruc.2014.01.003

Tabak, I. (2004). Synergy: A Complement to Emerging Patterns of Distributed Scaffolding. Journal of the Learning Sciences, 13(3), 305–335.

Teasley, S. D. (1997). Talking about reasoning: How important is the peer in peer collaborations? In C. O’Malley (Ed.), Disourse, Tools, and Reasoning: Situated Cognition and Technologically Supported Environments (pp. 361–384). Berlin: Springer.

Authors

• Freydis Vogel, University of Munich

• Elisabeth Reichersdorfer, Technical University of Munich

• Ingo Kollar, University of Munich

• Stefan Ufer, University of Munich

• Kristina Maria Reiss, Technische Universitaet Munich

• Frank Fischer, Ludwig Maximilian University of Munich