Productive Failure

Keynote by Manu Kapur

• Cognitive strain and disfluency (fonts harder to read, higher cognitive load, paying more attention, less likely to be tricked up by problems etc)
• Theory of constructive failure (Clifford, 1978, 1984)
• Desirable difficulties (Schmidt & Bjork, 1992)
• Impasse-driven learning (VanLehn et al, 2003) (explanation shouldn't come before a learner is stuck)
• Assistance dilemma (Koedinger et al, 2008) (cognitive tutors)
• Preparation for future learning; Inventing to prepare for learning (Schwartz & Bransford, 1999; Schwartz & Martin, 2004) (classroom-based research)

Understand what students know about a novel concept that they have not been taught.

Opportunities to activate and differentiate prior and intuitive knowledge

• generate
• explore
• critique
• refine

representations and solution methods (RSMs) for solving complex problems.

This leads to failure, but may be locus of deep learning, provided soe form of structure follow subsequently.

Kapur & Bielaczyc, 2012

• generation & exploration
  • complex problems
  • collaboration
  • affective support for persistence
• consolidation & knowledge assembly
  • consolidation
    • well-structured problem solving
    • instruction
    • feedback
    • explanation
    • etc

Delay of structure (not if you should provide structure, but when)

• activation and differentiation of prior knowledge
• attention to critical conceptual features
• ownership - want to see the canonical solution
• becoming flexible and adaptive
• “feel like mathematicians”

• Marginal gains of providing cognitive support for productive failure groups during generation phase was not significant
• Teachers consistently underestimate students' ability to generate RSMs
• Students strikingly dissimilar on general and math abilities strikingly similar in terms of generative capacity
• How much they produce significantly correlated with learning gains
• Teachers - stressed and stretched to work with students' ideas - but they themselves understood the math better

• We can learn from our own failures, can we learn from other people's failure? Vicarious failure
• Empirically, you get effect from direct teaching, but even more from having students generate their own failures

• controlled experiments almost uniformly indicate that when dealing with novel information, learners should be explicitly shown what to do and how to do it (Kirschner et al 2006)
• Cognitive Load: un-guided or minimally-guided instruction increases working memory load that interferes with schema formation
• Compared some version of worked example or strong instructional guidance condition with a pure problem-solving or discovery conditions. Conclusion: little efficacy in letting learners solve novel problems

Better to compare this with letting students first solve novel problems on their own, then some form of structure.

“Any instructional theory that ignores the limits of working memory when dealing with novel information or ignores the disappearance of those limits when dealing with familiar information is unlikely to be effective” (Krischner et al, 2006, p 77).

The key is what is novel information.

• canonical: students don't have the canonical formulation in long-term memory (LTM), therefore concept is novel
• non-canconical: students may not have the canonical formulation, but may have some prior or intuitive ways of thinking about the concept in LTM

If so, could we not design tasks and activity structures to activate this knowledge in the LTM?

By activating and working with these priors in the long-term memory, leverage the “expandable” aspects of working memory capacity?

Productive success and productive failure are all good - but we don't want unproductive success. And certainly not unproductive failure!