9: Education, Literacy Numeracy

1. 1 Education: theories of education what influences education why don’t 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 aren’t children learning these skills? 9: Education, Literacy & Numeracy

2. 2 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

3. 3 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

4. 4 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 Vygotsky’s ideas

5. 5 Why don’t 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

6. 6 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.

7. 7 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

8. 8 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

9. 9 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)

10. 10 Attitude: Parental and child attitude important (Wells, 1981; Goodman, 1990) Phonological awareness: conscious awareness of the sound structure of language lack of phonological awareness -> 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 Influences on literacy

11. 11 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). Influences on literacy

12. 12 Numeracy Maths isn’t 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

13. 13 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)

14. 14 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)

15. 15 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. The wider problem

16. 16 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

17. 17 Cardinal knowledge: cardinal and ordinal number Derived number understanding Multiplication and division Fractions, wholes and parts Written numbers - base, place and space! Skills we need to be numerate

18. 18 Piaget Understanding of number based on discovery of number invariance 6/7 years – concrete operations But can’t solve proportion problems Understanding proportion 11/12 years – formal operations BUT, effects of: Content Mathematical representation (Nunes, 1993) Social situation (Lave, 1988)

19. 19 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)

20. 20 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 Complex arithmetic

21. 21 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) Why aren’t children learning these skills?

22. 22 Perhaps we’re 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 Why aren’t children learning these skills?

23. 23 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

24. 24 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?