Education:

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9 Education, Literacy Numeracy

• Education
• theories of education
• what influences education
• why dont we have improved standards?
• Literacy
• the problems
• skills we need to be literate
• influences on literacy
• Numeracy
• simple arithmetic
• the problems
• skills we need to be numerate
• influences on numeracy
• complex arithmetic
• why arent children learning these skills?

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Theories of education

• Piagetian view
• stresses the internal/endogenous control of
  cognitive development
• attribute development to nature
• role of schooling
• Socio-culturally oriented approaches (e.g.
  Vygotsky)
• stresses the external/exogenous influences
• attribute development to process of social
  construction
• role of schooling

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Theories of education

• Case
• basic processes change over time
• culture and society have an impact
• modular structure of mind must be taken into
  account
• Bruner
• 1960s theory ignored influence of culture
• 1990s theory surrounding affect ability to learn

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How can we influence the success of education?

• Peer learning
• (Slavin, 1990 Littleton Hakkinen, 1999 Phelps
  Damon, 1989 Piaget and Vygotsky)
• School class size
• small is best?
• The role of the teacher
• the role of expectations and the Pygmalion effect
  (Rosenthal Jacobson, 1968 vs. Pilling
  Pringle, 1978)
• classroom management strategies (Brophy, 1986
  Rutter et al, 1979 Rutter, 1983).
• Supports Bruner and Vygotskys ideas

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Why dont we have improved standards?

• Politics and economics
• Some effects are beyond our control
• parental influence (Grolnick, Ryan Deci, 1991)
• peers (Kindermann, 1993)
• self esteem (Byrne, 1984, Wattenberg Clifforn,
  1964 Hoge, Smith Hanson, 1990)
• cultural differences
• Disagreements about the best educational methods
• Traditional
• open classroom (Horwitz, 1979)
• magnet schools (Steel Levine, 1994)
• academic tracking

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Literacy The problem

• Only 11 of all 13 year olds in the USA are adept
  readers - meaning they can understand relatively
  complex written information (Mullis Jenkins,
  1990)
• By age 17, less than half of American students
  are able to read and understand complex info (US
  Dept of Education, 1996)
• USA about 18 million adults have reading ages of
  below 9 years.
• Britain Bullock Report (1975) 2 million people
  in England and Wales do not reach this level.
• These people not made shift to functional
  literacy - unable to read tabloid newspapers,
  recipes etc.

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Literacy the benefits

• Once functional levels of literacy are achieved
  reader is able to read text at much faster rate
  than normally hears speech. Why?
• grammatical structures are more compressed and
  more varied than those of speech
• Level of redundancy is low
• NO pauses, hesitations, false starts
• Reader may review, anticipate, skip paragraphs
  etc - go at own pace
• greater efficiency and autonomy in reading than
  in hearing speech

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Skills we need to be literate

• Letter recognition
• a A A A A A are same letter
• Grapheme-phoneme correspondence rules
• relationship between letter and sound
• how to segment words into constituent phonemes
• Word Recognition
• Semantic knowledge
• Comprehension and interpretation

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Influences on literacy

• Homelife
• influence of preschool reading (Durkin, 1966 vs
  Phillips McNaughton, 1990)
• financial consideration (Orr, 1995)
• importance of privacy and space (Wilson Dupuis,
  1992)
• Parental interest (Snow et al, 1991)
• Cultural and language influences
• cultural compatibility hypothesis (Tharp, 1989)
• Kamehameha Early Education Program in Hawaii
  (Tharp et al, 1984)

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Influences on literacy

• Attitude
• Parental and child attitude important (Wells,
  1981 Goodman, 1990)
• Phonological awareness
• conscious awareness of the sound structure of
  language
• lack of phonological awareness -gt poor reading
  (Bryant et al, 1990)
• ability to monitor and correct speech
• ability to play with sounds (nursery rhymes, I
  spy)
• ability to compare words for rhyme and
  alliteration
• ability to split words into phonemes and
  manipulate phonemes

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Influences on literacy

• What is the best way to teach?
• phonics
• Matching letters to phonemes
• Not necessarily the best way on its own Gollasch,
  1977 Harste et al, 1984)
• look say
• memorisation of whole word shapes
• whole language approach
• introduce children to the PURPOSE of reading
• combination? (Bradley Bryant, 1983 Goswami
  Bryant, 1990).

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Numeracy

• Maths isnt just about facts and procedures, but
  also about understanding
• Need to think about facts and procedures to
  reveal the underlying principles
• So we need to analyse their productions

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Single digit arithmetic

• More complex than may appear
• Strategies (Fuson Kwon, 1992)
• Retrieve
• Count all
• Count up
• Infer (decompose)
• MRI studies show that several areas of the brain
  are active during arithmetic problem solving
  (Rueckert et al., 1996)
• Strategy use changes with experience
• Speed and accuracy improve with age
• ASCM (Siegler Shipley, 1995)

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Mathematical disabilities

• 6 of US children labeled as having mathematical
  disabilities (Gross-Tsur et al., 1996)
• Difficulty executing backup strategies and
  retrieving correct answers (Geary et al., 2000)
• Immature counting procedures at age 5
• Leads to problems with more complex arithmetic
  and algebra, which build on basic skills.
• Why?
• Limited exposure to numbers before entering
  school
• WM capacity
• Limited conceptual understanding of counting,
  arithmetic operations and place value (Geary et
  al, 2000)

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The wider problem

• Concepts in secondary mathematics and science
  (CSMS) study (Hart, 1981)
• examined 10000 11 year old children's ability in
  10 mathematical subjects.
• Concluded that 'the overwhelming impression
  obtained is that mathematics is a very difficult
  subject for most children.
• In particular, argued that the introduction of
  'modern mathematics' - which attempted to
  engender greater conceptual understanding in
  children about the 'foundations' of maths - had
  not succeeded.

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Skills we need to be numerate

• Counting and 1 to 1 correspondence
• Strategies
• fingers
• counting on
• counting silently
• mixture of addition and subtraction
• tens and units
• retrieval from memory

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Skills we need to be numerate

• Cardinal knowledge
• cardinal and ordinal number
• Derived number understanding
• Multiplication and division
• Fractions, wholes and parts
• Written numbers - base, place and space!

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Piaget

• Understanding of number based on discovery of
  number invariance
• 6/7 years concrete operations
• But cant solve proportion problems
• Understanding proportion
• 11/12 years formal operations
• BUT, effects of
• Content
• Mathematical representation (Nunes, 1993)
• Social situation (Lave, 1988)

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Concepts and context

• Concepts
• Inversion
• Mathematical equality
• Context
• Application of procedures (Carraher, Carraher
  Schliemann, 1985)
• Strategy choice (Bjorklund Rosenblum, 2002)
• Conceptual knowledge (McNeil Alibali, in press)
  

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Complex arithmetic

• Subtraction errors (Brown Burton, 1978)
• Common in American children, but not in Korean
  children (Fuson Kwon, 1992)
• Fractions
• 1/3 1/2 2/5
• Carpenter et al, 1981
• Less common problem in Korean children

• 606
• 568
• 168

• 307
• 182
• 285

• 308
• 287
• 181

• 835
• 217
• 618

• 856
• 699
• 157

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Why arent children learning these skills?

• Perhaps school maths is just too hard
• requires understanding of written numerical
  values and mathematical concepts
• Problems of understanding language
• Problems of understanding the written and verbal
  number system (Fuson, 1992)
• requires understanding of logical concepts
• children are not capable of these (c.f. Piaget)
• probably not true (Nunes Bryant, 1996 Bruner,
  1996)

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Why arent children learning these skills?

• Perhaps were not teaching properly
• Restricted range of maths problems
• Lack of use of materials (Fuson, 1992)
• Not enough mapping between school and real world
  (Greer, 1992)
• darts maths
• Brazilian street vendors street maths (Nunes,
  Schlieman Carraher, 1993)
• use real world examples that require maths in the
  real world

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Learning Outcomes Reading

• Be able to describe the skills that are necessary
  for literacy and numeracy
• Be aware of and be able to evaluate psychological
  theories and research on education, literacy and
  numeracy.
• Explain why children do not do as well as we
  could expect in schools.
• Essential Reading (on Digital Resources)
• Education Literacy
• Bruning, R.H. et al. (2004). Cognitive psychology
  and instruction. Upper Saddle River, NJ Pearson.
  Chapter 11.
• Siegler, R. S. Alibali, M. W. (2005).
  Children's thinking. Upper Saddle River, NJ
  Prentice Hall. Chapter 11.
• Numeracy
• Karmiloff-Smith, A. (1992). Beyond modularity.
  Cambridge, MA MIT Press. Chapter 4.
• Nunes, T. Bryant, P. (1996). Children doing
  mathematics. Oxford Blackwell. Chapter 5.
• Siegler, R. S. Alibali, M. W. (2005).
  Children's thinking. Upper Saddle River, NJ
  Prentice Hall. Chapter 11.
• Wood, D. (1998) How children think and learn.
  Oxford Blackwell. Ch 8. pp.225-275
• Further Reading
• See pdf handout

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Questions to ask

• What cognitive factors influence numeracy and
  literacy?
• What do psychological theories and research tell
  us about how we learn the necessary skills and
  concepts?
• Can this knowledge be used to address the
  problems that many children have?