Exploring Adaptive and Representational Expertise

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Exploring Adaptive and Representational Expertise

• Short Oral Discussant Remarks
• Jon R. Star
• Michigan State University

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Common questions

• What strategies or representations should
  students know how to use when solving proportion
  problems?
• How do we interpret students failure to use
  strategies or representations intelligently or
  adaptively?
• How do we assess students knowledge of and use
  of particular strategies and representations?

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1. What strategies or representations should
students know how to use when solving proportion
problems?
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1. Known strategies.

• Very detailed framework of strategies in Alatorre
  Figueras (A F)
• Framework for representations and concepts in
  Ledesman Alvarez (L A)
• Difficult for me to get a handle on from brief
  short oral papers
• (A bit more clear after hearing short oral
  presentations)
• I would push authors about the following

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1. Known strategies..

• (a) To what extent does categorization of
  strategies in A F help in exploring a
  particular issue?
• Landscape of A F strategy domain can be
  divided up into 2, 5, 10, 21 different
  strategies. How to map this landscape is not an
  exercise in itself but rather is a tool for
  exploring a particular issue.
• In the little that I read/heard from A F,
  connection between how the landscape of
  strategies is mapped and the problem that is
  being explored is not particularly clear.

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1. Known strategies...

• For example in A F simple (centrations or
  relations) vs. compound. Centrations can be on
  totals, on antecents, on consequents. Relations
  can be order, subtractive, or proportionality.
  Proportionality relations can be semi-formal or
  formal. Compound can take four forms.
• How is difference between centration and relation
  (or semi-formal and formal relations) critical to
  issue under exploration?

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1. Known strategies.....

• In L A, similar issue in classification scheme
  using registers and concepts
• Three registers (table, graph, numbers)
• verbal? hybrid representations?
• Concepts - classification scheme not
  well-articulated
• what is a proportion concept?
• concepts and meanings - what is the difference?
• Do these classification schemes help you to
  explore particular issues? Are there better
  classification schemes?

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1. Known strategies....

• (b) Reliability of framework
• To what extent is the framework for classifying
  strategies or representations one that someone
  other than you, if trained, could use reliably?
• Is this framework useful for the field, or
  primarily for you?

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Summary - known strategies

• What strategies or representations should
  students know how to use when solving proportion
  problems?
• (a) To what extent does categorization of
  strategies or representations help in exploring a
  particular issue?
• (b) Reliability of framework

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2. How do we interpret students failure to use
strategies or representations intelligently or
adaptively?
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2. Interpret failure to use.

• What do we think it means when someone doesnt
  use strategies or representations in the way that
  an expert does?
• Consider Vicente in A F
• PhD in Chemistry
• Behaved as a routine expert - used same
  strategy on almost all problems

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2. Interpret failure to use..

• Was Vicentes routine expertise a concern?
• Likely not, because
• It apparently didnt prevent Vicente from doing
  the kinds of math problems he does in his work
• It apparently didnt prevent Vicente from doing
  the A F problems correctly either
• No evidence that Vicentes purported routine
  expertise affected his ability to problem solve
  in this study

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2. Interpret failure to use...

• Is ability to vary strategies according to
  context and structure (a key feature of adaptive
  expertise, or procedural flexibility, in my work)
  a benefit in itself?
• Or is it beneficial because it enables one to
  solve problems that a less flexible or more
  routine expert is not able to?
• If the latter, where is the evidence that this is
  the case in Vicente?

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2. Interpret failure to use....

• Case of Nuria in L A
• She demonstrated an ability to make connections
  across the registers, which enabled her to
  construct knowledge of the concepts
• Ability to use multiple registers, rather than
  rely upon a single register - why is this useful?
  
• If using one representation only allowed Nuria to
  solve photograph problem, is this a concern?

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2. Summary - failure to use

• Perhaps not sufficient to merely say that
  adaptive expertise (using multiple strategies) is
  better than routine, or using multiple
  representations is better than reliance on a
  single one
• Need to demonstrate the limits of routine
  expertise and reliance on single representations
• What kinds of tasks cannot be done when one has
  only these less-desirable outcomes?

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3. How do we assess students knowledge of and
use of particular strategies and representations?
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3. Assessing knowledge.

• Need to demonstrate benefits to problem solving
  of use of multiple strategies and representations
• Give tasks where routine experts have trouble,
  but adaptive experts do not
• Give problems where reliance on a single
  representation leads to difficulty, but use of
  multiple representations leads to solutions
• Coming up with such tasks is difficult but
  critical

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3. Assessing knowledge..

• Examples of tasks that directly assess benefits
  of adaptive expertise
• Problem itself includes multiple representations,
  and participant must use information from
  different representations to complete problem
• We can be creative about the problems that we ask
  students to do

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3. Assessing knowledge...

• Another level of creativity involves creating
  tasks that indirectly assess benefits of
  knowledge of multiple strategies
• Solve a problem in more than one way
• Show a problem solved with an unfamiliar strategy
  and then ask participant to interpret, analyze,
  or use this new strategy
• Show two problem strategies and solutions and ask
  which one is better and why
• Show a very hard worked example and see which
  students learn from it

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3. Assessing knowledge....

• Keep the case of Vicente in mind
• Weakens claim that adaptive expertise is goal if
  you say that (a) PhD in chemistry has routine
  expertise, and (b) his problem-solving
  performance (accuracy) is not different than
  someone with adaptive expertise
• If other kinds of tasks used, either Vicente does
  more poorly because of routine expertise, or...

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3. Assessing knowledge.....

• Vicente might have adaptive expertise, but
  assessment did not push him to demonstrate it
• Did current assessment tap performance (what
  Vicente chose to do on these problems) or
  competence (what he was capable of doing)?
• Did he have knowledge of multiple strategies but
  choose not to use them, because it was not
  necessary to do so?

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3. Summary - assessment

• Create tasks that show limits of routine
  expertise
• Choose tasks that indirectly assess benefits of
  knowledge of multiple strategies and
  representations
• In addition to assessing performance, choose
  tasks that specifically address competence

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This presentation and other related papers can be
downloaded at

• www.msu.edu/jonstar

Jon R. Star Michigan State University
jonstar_at_msu.edu