Psychology

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Psychology Education OptionNumeracy Lecture
9 December

• 1. Introduction.
• 2. Piagetian approaches.
• 3. Information processing approaches
• a) metacognition
• b) psycholinguistics.
• 4. Things to think about
• comments on the reading list.

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1. Introduction.

• a numeracy standards
• 1995 childrens lack of numeracy can be put
  down to
• the fact that calculators have taken over from
  the
• use of their brains (David Blunkett)
• 1998 National Numeracy Strategy Numeracy
  Hour
• 2004 greater benefits for higher...attaining
  pupils
• little progress in developing the use of
  numeracy across the curriculum
• ICT...little used in...mathematics
• OFSTED

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• b potential psychological contributions
• piagetian approaches
• lecture reading
• information processing approaches
• lecture reading
• social psychology
• reading

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• c what I hope youll gain from the lecture
• an understanding of some ways in which
  piagetian information processing approaches
  can inform educational debates about numeracy
• an understanding of some key research into
  mathematics, and its implications for enhancing
  numeracy skills
• an understanding of some methodological issues in
  numeracy research
• an enhanced ability to critically evaluate
  reports of research into mathematical skills
  including seminar articles

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2. Piagetian approaches.

• a potential applications
• i role of concrete operations in arithmetic
• class inclusion
• number conservation
• seriation
• ii readiness
• iii developmental sequence
• concrete operations 4 sweets 2 sweets
• formal operations 4 2
• iv active self discovery learning

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• b evidence
• i readiness concrete ops
• Mpiangu Gentile 1975
• Participants
• children aged 5 - 6 years
• conservers non-conservers
• Procedure
• pre-test
• ten arithmetic training sessions
• eg counting / recognising numbers
• post-test
• Results
• conservers did better both tests BUT
• both groups improved equally

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• Hughes 1981
• Participants
• preschool children 3 - 5 years
• Procedure
• box problem using bricks
• Results
• small numbers 83 correct

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• ii developmental sequence
• Hughes 1981
• Procedure
• School arithmetic problems
• eg What does 1 2 make?
• Results
• 10 correct

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• Carraher, Carraher Schlieman 1985
• Participants
• 4 working children 9-15 yrs
• Procedure
• informal test
• interviewer as customer
• formal test word problems
• Mary bought 8 bananas each banana cost
• 40 how much did she pay altogether?
• formal test maths operations
• 8 x 40 ?
• Results
• informal 92.8 correct
• formal WP 73.7 correct
• formal MO 36.8 correct
• eg participant S

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• iii active self-discovery
• LOGO Papert 1980
• Outline Turtle graphics
• ? ? ?
• evidence
• Hughes, Macleod Potts, 1985
• Participants
• 15 children 5 - 6 years
• Procedure
• 24 Turtle sessions per child over 5 months
• Results interviews with staff
• concentration understanding maturity

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3. Information processing approaches

• a metacognition
• metacognition algebra
• Mevarech Kramarski 2003
• Participants
• 142 adolescents 14 years
• Procedure
• 2 types of group work in normal algebra classes
  for 4 weeks
• Traditional Tasks
• Metacognitive Questions
• Results
• pre-test no differences
• post-test
• MQ better than TT effect size bigger for low
  ach.
• explanations as well as answers

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• b psycholinguistics
• classifying semantic structures in word
  problems
• Riley, Greeno Heller 1983
• Combine
• Pete has 3 apples Ann has 5 apples
• how many apples do they have altogether?
• Change
• Pete has some apples he gave 3 apples to Ann
• now Pete has 5 apples
• how many apples did Pete have in the beginning?
• Compare
• Pete has 3 apples Ann has 5 apples more than
  Pete
• how many apples does Ann have ?

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• relative difficulty of different structures
• De Corte Verschaffel 1989
• Participants
• 30 Grade 1 children
• Procedure
• asked to solve combine, change compare problems
• Results
• Combine 26 ? 4 x
• Change 12 ? 18 x
• Compare 5 ? 25 x

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Things to think About comments on the
reading list.

• Role of Imagery
• Will imagining teddies in a box transform a
  formal
• operations task into a concrete operations task?
• National Numeracy Strategy
• Recommends real life examples.
• Eg A beetle has 6 legs. How many legs have 9
  beetles? How many legs have 15 beetles? DFEE,
  1999
• Is this real life Maths?
• Relative Difficulty of Different Types of Word
  Problem
• What implications might the result have for a
  teacher?

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• Reading List
• Light et al
• Light, P., Sheldon, S Woodhead, M.
• (1991). Learning to Think.
• London Routledge.