Synergistic scaffolding to foster mathematical argumentation competence: Sequencing and integrating heuristic worked examples and collaboration scripts

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During the first project phase, we investigated to what extent a combination of heuristic worked examples and collaboration scripts causes synergistic scaffolding effects with respect to a facilitation of individual-cognitive and social-discursive components of mathematical argumentation competence in a computer-supported collaborative learning environment. Results provided little evidence for such synergistic scaffolding effects. Therefore, the second project phase is planned to deal with the question what conditions need to be fulfilled for synergistic scaffolding to take place when heuristic worked examples and collaboration scripts are combined. Three studies are planned. In study II.1, we aim at developing and validating an instrument that is capable of measuring a holistic indicator of mathematical argumentation competence, based on individual-cognitive and social-discursive facets of mathematical argumentation competence. Study II.2, following a 2x2-factorial design, investigates the question whether synergistic scaffolding depends on a sequential presentation of the two interventions, and whether the intervention that was presented first needs to be continuously displayed after the second intervention is presented. Study II.3, finally, uses a 1x3-factorial design to investigate whether a collaboration script whose prompts are directly integrated into a heuristic worked example leads to better results concerning learning processes and outcomes of mathematical argumentation than a generic collaboration script or unscripted collaboration. Studies II.2 and II.3 will provide information on the sustainable and synergistic combination of two different scaffolds as well as empirically based knowledge on possibilities to foster mathematical argumentation skills at the start of university mathematics programmes.