Facilitating flexible problem solving: A cognitive load perspective

The development of flexible, transferable problem-solving skills is an important aim of contemporary educational systems. Since processing limitations of our mind represent a major factor influencing any meaningful learning, the acquisition of flexible problem-solving skills needs to be based on known characteristics of our cognitive architecture in order to be effective and efficient. This paper takes a closer look at the processes involved in the acquisition of flexible problem-solving skills within a cognitive load framework. It concludes that (1) cognitive load theory can benefit from putting more emphasis on generalized knowledge structures; (2

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

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

Worked Examples and Tutored Problem Solving:Redundant or Synergistic Forms of Support?

The current research investigates a combination of two instructional approaches, tutored problem solving and worked-examples. Tutored problem solving with automated tutors has proven to be an effective instructional method. Worked-out examples have been shown to be an effective complement to untutored problem solving, but it is largely unknown whether they are an effective complement to tutored problem solving. Further, while computer-based learning environments offer the possibility of adaptively transitioning from examples to problems while tailoring to an individual learner, the effectiveness of such machine-adapted example fading is largely unstudied. To address these research questions, one lab and one classroom experiment were conducted. Both studies compared a standard Cognitive Tutor with two example-enhanced Cognitive Tutors, in which the fading of worked-out examples occurred either fixed or adaptively. Results indicate that the adaptive fading of worked-out examples leads to higher transfer performance on delayed post-tests than the other two methods