Cognitive science: Problem solving and learning for physics education

1. Cognitive science: Problem solving and learning for physics education Brian H. Ross Department of Psychology and Beckman Institute University of Illinois PERC August 2007

2. 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

3. Rules of stylePolya (1945) • The first rule of style is to have something to say.

4. 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.

5. Plan for talk:Two 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)

6. Selected ideas of how the mind works • (1) Specialized systems • (2) Importance of content • (3) Use of prior experience • Analogies • Categories

7. (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)

8. Anterograde amnesia Declarative memories Cannot form new ones Procedural memories Can form new ones

9. H.M.’s performance on mirror drawing

10. 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”

11. 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

12. 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

13. (2)Importance of content(problem features) • Content-dependence of much of our knowledge • 5 + 2 • Abstractions, principles etc. are difficult

14. Importance of content • Novices • Domains • Experts

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

16. Importance of content: Domains • Content often correlated with structure, principles • Inclined plane problem: what is likely principle to use?

17. 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

18. 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?

19. 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

20. (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

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

22. 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

23. 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

24. Additional influences on cues, knowledge • Representations (e.g., Newell & Simon, 1972) • Explanations, conceptual analyses

25. 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

26. 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

28. 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

29. Representations matter:Number 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

30. 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…