3: The development of logical reasoning

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3 The development of logical reasoning

• Outline
• Piagets theory
• Conditional reasoning
• Limitations of the Piagetian view
• Research into conditional reasoning
• Analogical reasoning

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Piagets theory of logical development

• The sensory-motor period (0-2)
• action-based knowledge
• Period of concrete operations (7-11)
• symbolic knowledge
• (e.g., about transitivity)
• Period of formal operations (11-12)
• second-order reasoning
• hypothetico-deductive reasoning
• (e.g., pendulum task)
• ability to search for counter-examples
• scientific thinking

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Ifthen reasoning.

• Modus Ponens
• If there is a p then there is a q,
• There is a p,
• Therefore, there is a q.
• Modus Tollens
• If there is a p then there is a q,
• There is not a q,
• Therefore, there is not a p.
• Inhelder Piaget (1955)
• reasoning is nothing more than the propositional
  calculus itself

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Challenges to the Piagetian view.

• Over the last 20 years the Piagetian view has
  been challenged by two lines of questioning
• 1. Do adults really show formal operational
  competence at ifthen reasoning?
• 2. Are young children really as bad at ifthen
  reasoning as predicted by Piaget?
• The same factors that seem to help adults with
  ifthen reasoning also seem to help children.

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Ifthen reasoning with the Wason selection task

• If there is an A on one side of the card then
  there is a 3 on the other side of the card
• Indicate those cards that need to be turned over
  to determine whether the rule is true or false.

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Wason selection task

• To solve the task subjects must appreciate
• 1. That the rule would be false if an A was
  paired with a number other than 3.
• 2. That it is logically necessary to choose cards
  which could reveal the falsifying combination.

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Interpretation of this logical failure in adults

• 1. Reasoning with this task reflects a
  sophisticated stage of formal operational thought
  that adults havent yet achieved?
• 2. Adults havent yet reached the stage of formal
  operations advanced under Piagets theory?
• Complications
• Evidence that under suitable circumstances adults
  are able to solve the selection task.

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Other reasoning tasks

• Postal rule problem
• (Johnson-Laird, Legrenzi Legrenzi, 1972)
• If a letter is sealed then it has a 5d. stamp on
  it

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Other reasoning tasks

• Drinking Age Problem
• (Griggs Cox, 1982)
• If a person is drinking beer then that person
  must be over 19 years of age

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Other reasoning tasks

• Sears store-manager problem
• (D'Andrade, 1983)
• If a purchase exceeds 30 dollars then the
  receipt must be approved by the departmental
  manager

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Explaining content effects

• Content effects
• What is it about thematic versions of the rule
  that facilitate reasoning?
• Cheng Holyoak (1985) permission schemas.
• Rule 1 If the Action is to be taken, then the
  Precondition must be satisfied.
• Rule 2 If the Action is not to be taken, then
  the Precondition need not be satisfied.
• Rule 3 If the Precondition is satisfied, then
  the Action may be taken.
• Rule 4 If the Precondition is not satisfied,
  then the Action must not be taken.

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The story so far...

• Adult evidence suggests that people reason using
  clusters of domain-specific rules.
• These rules produce responses that only coincide
  with logical choices.
• BUT...
• Does childrens performance on the selection task
  mirror that of adults?

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Childrens performance on the RAST

• Girotto, Light Colbourn (1988)
• If a bee buzzes then it must stay outside
• The correct solution requires
• 1. Realisation of the need to test the not-q.
• 2. The systematic testing of all the not-q bees.
• 3. A final judgement that the rule was being
  obeyed.
• If a bee is sick then it must stay outside
• If a bee buzzes then it is outside
• Conclusion
• High success rates on these concrete ifthen
  forms is a problem for a Piagetian account of
  reasoning development.

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Reduced Array Selection Task (from Girotto
Light, 1992)
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Childrens performance on full selection task

• Girotto, Gilly, Blaye Light (1989)
• If you drive a car over 100 km/hr then you must
  have a fluorescent car
• If you sit in the front of a car then you must
  wear a seat belt
• Results
• Control condition (8).
• Unfamiliar rule but no rationale (55).
• Unfamiliar rule rationale (80).
• No age-related differences.

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Childrens performance on full selection task

• Conclusions
• Results confirm and extend those from the RAST.
• Direct experience with a specific permission rule
  is not necessary for success.
• Even 10 year-olds able to test an unfamiliar rule
  if a rationale is given.

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Analogical reasoning

• Involves finding correspondences between new and
  old problems (which involves relational
  reasoning).
• Can children identify correspondences?
• Can children use relational reasoning to solve
  problems in the absence of surface similarities?
• At what age do these abilities develop?

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The use of relational reasoning in children

• AB CD
• bird nest dog ?
• applecut apple playdoh ?
• chocolate melted chocolate snowman ?
• Goswami (1991, 1992 Goswami Brown, 1990)
• Analogical reasoning is evident by age 4 in
  ABCD item analogies.
• 3 year olds can do item analogies with causal
  relations.
• With children lt 3 you need activity-based
  analogies (e.g., the reaching-for-a-toy
  analogy, Chen et al., 1997).

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(Goswami Brown, 1990)
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(Chen, Sanchez Campbell, 1997 )
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Learning outcomes

• Understand what reasoning is and why we study it.
• Understand and be able to evaluate theories of
  reasoning
• Know and be able to evaluate current research on
  reasoning and the implications this research has
  for theories of reasoning

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Reading

• Essential Reading (on Digital Resources)
• Goswami, U. (1998). Cognition in children. Hove
  Psychology Press. Ch 7. pp.221-258
• Girotto, V., Light, P (1992) The pragmatic
  bases of children's reasoning. In P. Light G.
  Butterworth (Eds). Context and cognition Ways of
  learning and knowing. Harvester Wheatsheaf.
  pp.135-156
• Girotto, V., Gilly, M., Blaye, A. Light, P.H
  (1989) Children's performance in the selection
  task Plausibility and familiarity. British
  Journal of Psychology, 80, pp.79-95
• Further Reading
• See pdf handout

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Questions to ask.

• What was Piagets view of the development of
  logical reasoning?
• What does more recent research tell us about
  childrens reasoning abilities?
• What are the modern theories of reasoning
  development?