Theories of Difficulty

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Theories of Difficulty
David Perkins, May 20, 2005, Edinburgh
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Why the fish?
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• Towers, Holes, Other Troubles

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The tower problem
10 kg

100 m
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The hole problem

10 kg
100 m
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A fundamental corrective loop

• Teach harder

• We teach

• Blame the learners

• We discover recurrent trouble spots

• We figure out what we think the barrier is

• We figure out a way to address it

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• Tower hole problems

• Conflation
• Omission
• Overgeneralization
• Assimilation
• Encapsulation
• Surface account
• Ritualization
• Inert knowledge
• Resistance
• Adaptive (sort of) responses

• Presentism

• Progress toward freedom, democracy, and happy
  ethnic integration

• Its just behavioral objectives, good activities,
  activities where you think

• Concept of formal proof

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• Pretty good general teaching practice

• Fundamental corrective loop via theories of
  difficulty

Avexedenterprise
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• What more precisely is a theory of difficulty?
• What sorts of theories of difficulty are there?
• Can they powerfully inform instruction?
• How can they prove problematic?

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• What is a Theory of Difficulty?

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Theory of Difficulty

• Where problems linger after pretty good
  instruction.
• The symptoms of those problems
• Causes located in challenges of the knowledge to
  be learned
• Aimed at prevention and cure
• Informal or academic

• NOT weak pedagogy
• NOT unmotivated students
• NOT learning or study styles
• (except as exacerbates)

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• What Theories of Difficulty Are There?

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Structural TDs, research oriented

• Formal operations, concrete operations, Piaget

• Central conceptual structures in areas like
  narrative, number, etc., Case

• Ontological shift, Chi

• P-prims, di Sessa

• Distributed causality, systemic thinking, M.
  Resnick

• Complex causality (mechanism, interaction,
  probability, agency), Grotzer Perkins

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Structural TDs, more practitioner friendly

• Inner logic of the subject, Entwistle

• Ways of thinking and practicing (WTPs), Hounsell

• Ways of knowing, Schwab, Bruner, Perkins

• Troublesome knowledge, Perkins

Threshold concepts, Meyer Land
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Other TDs

• Complex knowledge, capacity bottleneck

• Gestalt processing needed, fluency bottleneck

• Entrenchment

• Alien, foreign knowledge

• Context-bound

• Knowledge overload

• Subtle differences

• Tacit knowledge

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• Can Theories of Difficulty Powerfully Inform
  Instruction?

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• central conceptual structures
• Mathematics understanding, the Rightstart
  initiative

• complex causality
• Understanding of elementary electrical circuits,
  weight and density, ecological concepts

• fluency bottleneck
• Some cases of early reading development

• entrenchment
• Israelis studying Northern Ireland

• subtle difference, foreign conception
• Anticipate conflations of Teaching for
  Understanding, active discrimination exercises

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• How are Theories of Difficulty Problematic?

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Testing TDs

• The Researchers Page

• Alternative theories often do not compete in a
  strong sense

• Deep theories not necessarily the most helpful

• Theory of difficulty does not entail intervention

• Failure, success of intervention ? strong test

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ShallowTDs

• The Practitioners Page

• If you dont simply blame the leaner
• Todays students

• Overgeneral
• Complex, confusing

• Topic Instead of Cause
• Teach harder

• Symptom Instead of Cause
• Teach to correct

• Formulaic Fix
• Handle it this way

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Work on your Theories of Difficulty Heuristic
Advice

• Dont blame the learner
• Dont settle for a formulaic fix
• Get beyond the topics to the symptoms
• Get beyond the symptoms to the causes
• For help with that, review typical theories of
  difficulty
• Epistemes paradigm shift, complex causality,
  entrenchment, fluency bottleneck, subtle
  differences, tacit knowledge, knowledge overload,
  context bound, etc.
• Base a pedagogical strategy on your explanation
• Treat it all as an informal hypothesis as you
  continue to teach

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Coda

• How Theories of Difficulty Apply to Themselves

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the case of Theories of Difficulty Themselves

• Blame the learner

• Complexity bottleneck, too much going on already
• Tacit knowledge, knowledge of the discipline
• Foreign character of the novice learner

• Heuristic fix

• Resistance
• Surface account
• Ritualization

• Topic instead of cause

• Symptom instead of cause

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• The built-in irony of theories of difficulty

• still leaves them tremendously powerful

• And maybe a good hook

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