Articulating Your Thinking

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Articulating Your Thinking

• Dr. Mok, Y.F.

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Novice Expert Thinking Patterns

• Novice

• Expert

Read Analyze Explore Plan Implement Verify
Schoenfeld, 1987
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Thinking

• is
• usually
• invisible silent.

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Automaticity

• Certain thinking practised so extensively
• automaticity

executed with little or no conscious awareness
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Knowledge Categories

• Tacit set of categories of knowledge is for

thinking about the world
But there is little awareness of categorization
And tacit knowledge is difficult to teach.
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Difficulties in Teaching
Steps fused together
Cannot capture tacit categories
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Teachers Thinking

• In sum, teachers thinking
• is usually invisible silent
• is executed with little or no conscious awareness
• (this is called automaticity which is due to
  extensive practice over the years certain
  thinking has become automatic)
• is characterized by his own tacit categories of
  knowledge which are formulated for his own
  thinking hence difficult to capture or be
  taught
• steps are fused together

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Learning from Teachers Thinking

• Teachers ways of thinking are valuable to
  students.
• Particularly for solving problems in the subject
  domain.
• One way of articulating your thinking is to
  verbalize it.

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Thoughts

• the stream of consciousness
• put into words as they occur

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Verbalization

• Having to say it
• forces you
• to figure out
• exactly what your thinking process is.

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Direct Instruction ?

• There are disadvantages in using direct
  instruction to teach problem-solving methods
• Students will simply follow your methods like
  following a recipe.
• Students will have difficulty to understand the
  reasons behind a specific course of action.
• They will not know under what conditions in which
  the solution applies.
• Or conditions for the procedure.

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Articulate Your Thinking

• It is better to verbalize your thinking (not the
  solution method) while you problem-solve. Show
  and tell students how you
• find out traps blockages means for resolving
  them
• make assumptions about unknown information
• integrate large amounts of information
• consider reject alternatives that are wrong but
  tempting

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Articulate Your Thinking

• how you formulate specific solution paths
• how you use your own heuristicsrules that guide
  search but do not guarantee a result

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Articulating Experts Power

• Also, you may take reference of experts problem
  solving strategies incorporate some of them
  while you show and tell your students your
  thinking
• The ability to see typicality
• The ability to see distinctions
• The ability to see antecedents consequences
• The ability to plan monitor their
  problem-solving attempts

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e.g.

• Experienced doctors
• distinguish between relevant non-relevant data
• screen unnecessary data that can be confusing,
  unhelpful or sometimes dangerous

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• http//www.lessonplanspage.com/MathNumReasoningPro
  bSolvingThinkAlouds69.htm