Cognitive science: Problem solving and learning for physics education

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Cognitive science Problem solving and
learning for physics education

• Brian H. Ross
• Department of Psychology and Beckman Institute
• University of Illinois
• PERC
• August 2007

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Why cognitive science might be useful for people
interested in how students learn physics

• Intuitions
• Need for general principles, methods
• Perspectives on how the mind works
• Relate to transfer difficulties

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Rules of stylePolya (1945)

• The first rule of style is to have something to
  say.

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Rules of stylePolya (1945)

• The first rule of style is to have something to
  say.
• The second rule of style is to control yourself
  when, by chance, you have two things to say say
  first one, then the other, not both at the same
  time.

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Plan for talkTwo things to say

• Selected ideas about how the mind works
• 3 selected with physics learning in mind
• Implications for physics learning
• (more in Proceedings, references)

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Selected ideas of how the mind works

• (1) Specialized systems
• (2) Importance of content
• (3) Use of prior experience
• Analogies
• Categories

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(1) Specialized systems Memory

• Declarative -- knowing what (relational)
• Quick to learn
• Can be accessed flexibly
• Can be used flexibly
• Procedural -- knowing how
• Slow to learn
• Specific circumstances for access
• Specific use (not flexible)

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Anterograde amnesia
Declarative memories Cannot form new
ones Procedural memories Can form new ones
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H.M.s performance on mirror drawing
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Specialized systems Reasoning

• Deliberative -- slow -- similar to rule
  application
• When not well-learned -- especially if difficult,
  unusual
• Much of student learning
• Heuristic -- quick recognition -- associative
• Expert
• Blink

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Specialized systems - implications

• Transfer-appropriate processing (Morris,
  Bransford, Franks, 1977)
• -- later performance depends
• Not just on what you learned and how you learned
  it
• Need to access knowledge at appropriate time
• Influenced by the similarity of current
  processing to how it was learned
• Transfer often depends on procedural and
  declarative overlap
• Experimental variety showing little transfer for
  related tasks
• Singley Anderson (1989) ACT-R model detailed
  transfer in text editors
• Pennington et al (1995) Only some transfer
  between evaluating and generating programming
  (LISP)
• Anecdotal
• Problem solving courses -- Understand solution
  versus generate solution

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Specialized systems - implications

• Problem solving
• Proceduralizing of routine knowledge--fast
• very specific learning, much practice
• little transfer
• Conceptual understanding
• analyze new problems and see relations
• Often requires explicit relational learning
  (declarative)
• Leads to next topics
• Difficult due to content
• Analogies and categories

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(2) Importance of content (problem
features)

• Content-dependence of much of our knowledge
• 5 2
• Abstractions, principles etc. are difficult

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Importance of content

• Novices
• Domains
• Experts

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Importance of content Novices

• Chi et al. (1981) novices rely on superficial,
  objects
• Influence of examples to illustrate principles
• Generalizations from comparing problems --
  conservative

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Importance of content Domains

• Content often correlated with structure,
  principles
• Inclined plane problem what is likely principle
  to use?

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Importance of content Experts

• Chi et al. (1981)
• experts often categorize problem type by
  structure
• True, but if content is correlated with
  structure, principles, then experts will take
  advantage of this correlation
• Content often more readily available so can speed
  access

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Importance of content Experts (Algebra --
Blessing Ross,1996)

• Usual age problem
• Michelle is 4 times older than her niece. In 5
  years, Michelle will be 3 times older than her
  niece. How many years older is Michelle than her
  niece?
• Inappropriate age problem (using mixture
  contents)
• A mason mixed 4 times as much cement in one
  container as another. He adds 5 liters of cement
  to each mixer. Now the first has 3 times the
  cement as the second. How much does each contain
  now?

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Importance of content Experts (Algebra --
Blessing Ross,1996)

• Algebra -- content highly correlated with
  structure (names)
• Vary problem content usual, neutral, or
  inappropriate
• Slower (and a bit less likely to solve)
• Categorizations initially misled
• Even schema includes the content

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(3) Use of prior experience

• Behavior influenced by past experience. But how?
• What knowledge is retrieved?
• How does it affect problem solving?
• Two important ways in which prior knowledge is
  used
• Analogy
• Categorization
• Closely related processes - think of both as the
  access and use of relevant information

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Memory Retrieval (in Problem Solving)
Retrieved
Cues
information
So, examine Cues, Knowledge, and Retrieved
Information
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Novices

• Cues
• Often mainly superficial (objects), specific
  variables
• Little structure (do not understand it well)
• Knowledge
• Some examples
• Formulae
• Some object-based categorizations
• Retrieved information
• Formula
• Example or early category - procedure tied to
  content
• Problem solving
• Formula-based (e.g., working backwards)
• Analogy

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Experts

• Cues
• Some superficial (objects)
• Some structure (more with greater experience)
• Knowledge
• Some examples
• Many categories characterized by structure
  (principle) as well as some superficial
• Retrieved information
• Category knowledge with associated procedures
• If unusual content or structure, perhaps example
• Problem solving
• Category-based (principle) -- schema, plan and
  procedures
• Analogy or deliberative use of principles if
  unusual, difficult

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Additional influences on cues, knowledge

• Representations (e.g., Newell Simon, 1972)
• Explanations, conceptual analyses

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Methods

• Qualitative and quantitative studies
• Often protocols, followed by larger experiment
• Many independent variables -- what matters?
• Superficial vs. structure types of superficial
• Variations in instructions, types of explanation
• Relation of training to testing
• Dependent variables
• Tests - problem solving, conceptual, problem
  categorization
• Finer analyses of what is learned
• Reading times
• Eye tracking
• fMRI

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Conclusions

• Cognitive science can offer some useful tools and
  perspectives on physics learning and research
• Plus, effects the other way
• Strong test of ideas in classroom setting
• New issues arise
• Formal but knowledge related to physical
  situations
• Rich hierarchical knowledge
• Variables have meaning

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Additional influences on cues, knowledge

• Representations (e.g., Newell Simon, 1972)
• Cues not simply problem, but interpretation
• Representations also influenced by knowledge
• Bassok -- tulips/roses vs tulips/vases
• Solving representations of problems
• Different representations have huge influence

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Representations matterNumber scrabble (e.g.,
Newell Simon, 1972)

• How to play
• Digits 1-9 on scraps of paper, face up
• Take turns choosing one digit
• First to get 15 with 3 digits wins
• Very difficult -- much bookkeeping, checking
• How to make it easier -- tic-tac toe

8 1 6 3 5 7 4 9 2
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Additional influences on cues, knowledge

• Representations (e.g., Newell Simon, 1972)
• Explanations, conceptual analyses
• Interrelate pieces of knowledge
• Provide understanding (helps connect, retain)
• Affects knowledge, cues, and retrieval
• Explaining, strategy-writing