Problem Solving

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Chapter 7

• Problem Solving
• and Content Area Learning

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Outline

• Skill Acquisition And Use
• Problem Solving
• Language Comprehension
• Reading
• Writing
• Mathematic
• Science

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1. General and Specific Skills(1/2)

• General skills apply to a wide of disciplines.
• Specific skills are useful only in certain
  domains.
• Skills may be differentiated according to degree
  of specific.
• Domain specificity.

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General and Specific Skills(2/2)

• Competence in a domain seems to require a rich
  knowledge base that includes the facts, concepts,
  principles of the domain coupled with strategies
  for learning that can be applied to different
  domains and that may have to be tailored to each
  specific domain.

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Novice-to-Expert Research Methodology

• Research interest in the process whereby learners
  develop competence.
• identify the skill to be learned
• find an expert and novice
• determine how the novice can be moved to the
  expert level as efficiently as possible
• This model is largely descriptive rather than
  explanatory this model does not automatically
  suggest teaching.

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2. Problem Solving Defined

• Initial state
• Goal
• Sub-goals
• Operations
• Not all activities include problem solving.

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Historical Influences(1/3)

• Trial and Error
• Trial and error is not reliable and often not
  effective
• Insight
• Preparation, Incubation, Illumination,
  Verification.
• Rote memorization vs. organization.

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Historical Influences(2/3)

• Heuristics
• Ployas
• Understand the problem
• Devise a plan
• Carry out the plan
• Look back

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Historical Influences(3/3)

• Bransford and Stein (1984), IDEAL
• I Identify the problem
• D Define and represent the problem
• E Explore possible strategies
• A Act on the strategies
• L Look back and evaluate the effects
• of your activities

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Problem-solving Strategies(1/6)

• General Strategies
• applies to problems in several domains,
  regardless of content specific strategies are
  useful only in a particular domain.
• Generate-and-Test Strategy
• It is useful when a limited number of problem
  solutions can be tested to see if they attain the
  goal.

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3. Problem Solving and Learning

• Production systems
• Much learning in school is highly regulated
• Problem solving involves the acquisition,
  retention, and use of production systems.

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Experts and Novices

• One difference involves the demands made on WM
• Differ in background domain-specific knowledge
• Qualitative differences are evident in how
  knowledge is structured in memory.
• Novices typically respond to problems in terms of
  how they are presented, experts reinterpret
  problems to reveal an underlying structure, one
  that most likely matches their own LTM network.
• Experts spend more time planning and analyzing.

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Problem-solving Strategies(2/6)

• Means-Ends Analysis
• One compare the present situation with the goal
  and identifies the differences between them.
• Sub-goals are set to reduce the differences.
• One performs operation to accomplish the
  sub-goal, at which point the process is repeated
  until the goal is attained.

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Problem-solving Strategies(3/6)

• Working forward start with initial state
• working backward start with goal requires a fair
  amount of knowledge in the problem domain
• Working forward (or called hill climbing) may be
  danger based on superficial problem analysis

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Problem-solving Strategies(4/6)

• Analogical Reasoning
• Involves drawing an analogy between the problem
  situation and a situation with which one is
  familiar.
• The sub-goals in this approach are relating the
  steps in the original (familiar) domain to those
  in the transfer (problem) area.

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Problem-solving Strategies(5/6)

• To be effective, it requires good knowledge of
  the familiar and problem domains.
• Developmental evidence indicates children can
  employ analogical reasoning.
• Useful in teaching.

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Problem-solving Strategies(6/6)

• Brainstorming
• Define the problem
• Generate as many solutions as possible without
  evaluating them
• Decide on criteria for judging potential
  solutions
• Use these criteria to select the best solution

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Implication for Instruction(1/2)

• Provide student with metaphorical
  representations.
• Have students verbalize during problem solving.
• Use questions.
• Provide examples.
• Coordinate ideas.

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Implication for Instruction(2/2)

• Use discovery learning.
• Give a verbal description.
• Teach learners learning strategies
• Use small groups.
• Maintain a positive psychological climate.

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4. Components of Comprehension(1/6)

• Three component
• Perception, parsing, and utilization
• perception (ch5) attending to and recognizing an
  input
• parsing mentally dividing the sound patterns
  into units of meaning
• utilization the disposition of the parsed mental
  representation

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Components of Comprehension(2/6)

• Parsing
• Linguistic research shows that people understand
  the grammatical rules of their language, even
  though hey usually cannot verbalize them.
• Deep structures containing prototypical
  representations of language structure.
• Parsing includes more than just fitting language
  into production systems.

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Components of Comprehension(3/6)

• Effective language parsing requires knowledge and
  inferences.
• The spoken language is incomplete can be shown by
  decomposing communications into propositions and
  identifying into propositions and identifying how
  propositions are linked.
• Features of communication influence comprehension.

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Components of Comprehension(4/6)

• Comprehension depends on WM capacity and
  individuals differ in this capacity.
• The gist representations include propositions
  most germane to comprehension.
• Stories exemplify how schemata are employed.

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Components of Comprehension(5/6)

• Utilization
• what people do with the language communications
  they receive.
• Speech act refers to the speakers purpose in
  uttering the communication, or what the speaker
  is trying to accomplish with the utterance.

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Components of Comprehension(6/6)

• Propositional content is information can be
  judged true or false.
• Thematic content refers to the context in which
  the utterance is made.
• One special importance for school learning is how
  students encode assertions.

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5. Reading

• Reading involves perception, parsing, and
  utilization.
• The perceptual part of reading (recognizing
  words) is referred to as lexical access or
  decoding.
• Comprehension, or the attachment of meaning to
  printed information, involves parsing and
  utilization.

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ReadingDecoding(1/2)

• Decoding means deciphering printed symbols or
  making letter-sound correspondences.
• Two ways whole-word approach ( matching pattern
  recognition in LTM) or phonetic approach
  (sound-out recoding) .
• All need word recognition first.
• bottom-up processing(data driven)

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ReadingDecoding(2/2)

• Top-down processing (conceptually driven)
• In skilled reading, much information is processed
  automatically.( e.g. automatically of word
  recognition)
• eye-tracking model
• Good readers spend significantly less time on
  both unfamiliar and familiar words
• Good readers tend to parse passages at the end of
  phrases and sentences

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Reading Comprehension(1/3)

• Basic Processes
• Comprehension involves attaching meaning to
  printed information and using the information for
  particular purpose .
• Successful comprehension requires conceptual
  understanding, automaed basic skills

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Reading Comprehension(2/3)

• Top-Down model
• Optical (receiving the visual input)
• Perceptual (identifying letters and words)
• Syntactic (identifying structure of the text)
• Meaning (constructing meaning for the input)
• Literal comprehension vs. inferential
  comprehension
• Inferential comprehension integration between
  and within sentences, summarization , elaboration
  .

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Reading Comprehension(3/3)

• Metacognition
• Metacognition comes into play during the process
  of goals, evaluating goal progress, and making
  necessary corrections.
• Strategy instruction.
• Informed Strategies for Learning (ISL).

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6. WritingComposition Processes

• Writing is goal-directed behavior.
• Rhetorical problem.
• Planning.
• Goal setting.
• Goal are substantive and procedural.
• Writers block.

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WritingReviewing Processes

• Reviewing consists evaluating and revising
• 70 of writing time pausing.
• Good writer top-down writing overall goal that
  they think of how to revise.
• Evaluation skills develop earlier than revision.

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7. Mathematic

• Computation use of rules, procedures and
  algorithms.
• Concepts problem solving and use of strategies.
  
• Mathematical proficiency requires learning
  computation and problem solving together.

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MathematicComputation skills

• Earliest computation skill counting, Sum model,
  min model.
• Buggy algorithms.
• Another source of computational difficulties
  poor declarative knowledge.
• Many difficulties in computation result from
  using overly complex but technically correct
  productions to solve problems.

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MathematicProblem-Solving Skills(1/2)

• The most basic type of knowledge involves
  resources, heuristics and metacognitive.
• Mathematical problem solving first represent
  problem and the goal and then select and apply
  problem-solving production.
• ?????????change problems, combine problems,
  comparative problems.

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MathematicProblem-Solving Skills(2/2)

• Successful problem solver problem model
  approach.
• Less-successful solvers direct translation
  approach
• Experts develop sophisticated procedural
  knowledge for classifying mathematical problem
  according to type.
• Classification procedures are developed through
  exposure to instruction and by solving different
  types of problems.

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MathematicConstructivism

• Constructed by individuals as consequence of
  their interactions.
• Biologically primary and biologically secondary
• Mathematical competence also depends on
  socio-cultural influence

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8. ScienceExpert-Novice Differences

• Experts in scientific domains differ from novices
  in quantity and organization of knowledge.
• Experts had more knowledge (in terms of
  principles) organized such that descriptors were
  subordinate to principles. Novice based on
  superficial features
• Another difference between novices and experts
  concerns the use of problem-solving strategies.

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ScienceReasoning

• Reasoning refers to the mental processes involved
  in generating and evaluating logical arguments.
• Clarification
• Basis
• Inference
• Evaluation
• Metacognition processes enter into all aspects of
  scientific reasoning.

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ScienceConstructivism and Scientific Beliefs

• One tradition is concerned with personal theories
  and the conceptions of phenomena that students
  develop during environmental interactions.
• Second constructivist tradition focuses on the
  role of mentors and apprenticeships in the
  development of scientific knowledge.
• Other students belief and from process of
  students being acculturated into scientific
  discourse and practice.

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ScienceConstructivism and Scientific Beliefs

• Finally, process of scientific literacy.
• Three-state model for changing student beliefs
• reveal and understand student preconceptions.
• create conceptual conflict with those
  conceptions.
• facilitate the development of new or revised
  schemata about the phenomena under consideration.