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

在第一个项目阶段，我们调查了在计算机支持的协作学习环境中，启发式样例和协作脚本的组合在多大程度上促进了数学论证能力的个体认知和社会论述能力的促进作用。结果几乎没有提供这种协同支架效应的证据。因此，第二个项目阶段计划处理这样一个问题，即当启发式工作实例和协作脚本相结合时，需要满足哪些条件才能实现协同脚手架。计划进行三项研究。在研究II.1中，我们的目标是开发和验证一种工具，该工具能够基于数学论证能力的个人认知和社会论述方面来测量数学论证能力的整体指标。研究II.2采用2x2析因设计，考察协同支架是否依赖于两个干预措施的顺序呈现，以及第一个呈现的干预措施是否需要在第二个干预措施呈现之后继续呈现。最后，研究II.3采用1x3析因设计来考察提示被直接整合到启发式样例中的协作脚本是否比一般协作脚本或无脚本协作在学习过程和数学论证的结果方面导致更好的结果。研究二.2和二.3将提供关于两个不同支架的可持续和协同结合的信息，以及关于在大学数学课程开始时培养数学论证技能的可能性的经验性知识。

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.