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Different Learners – General Learning Processes in Learning Math?

Different Learners – General Learning Processes in Learning Math?. Applied in general math teaching . Applied in teaching the “different” learner. Consequences for practice. Theoretical basis. Gunvor Sønnesyn, Pedverket Kompetanse gunvors@online.no.

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Different Learners – General Learning Processes in Learning Math?

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  1. Different Learners – GeneralLearning Processes in Learning Math? Applied in general math teaching Applied in teaching the “different” learner Consequences for practice Theoretical basis Gunvor Sønnesyn, Pedverket Kompetanse gunvors@online.no

  2. Luria (1973): Three Functional Units of the Brain 1. The unit for regulating tone and waking and mental states. 2. The unit for receiving, analyzing and storing information. 3. The unit for programming, regulation and verification of activity

  3. Knowledge, Conceptual Systems Skills Illustration of different structures concerning knowledge and skills with reference to Nyborg, Das, and McNamara

  4. NUMBERS Knowledge, Conceptual Systems Changes in numbers Relations between numbers Increase in number Decrease in number Similarity in number Large/ small number related to Skills

  5. Two concepts from Vygotsky: • Zone of proximal development (ZPD), the discrepancy between a child’s actual mental age and the level he reaches in solving problems with assistance. Vygotsky 1962, p. 103

  6. Word function from nominative to significative: • We distinguish a word’s nominative from its significative function. • In the beginning only the nominative function exists; and semantically, only the objective reference; signification independent of naming, and meaning independent of reference appear later. Vygotsky 1962, p. 130

  7. Raising the questions: How to create zones of proximal development in ways that facilitate processes towards zones of actual development? How to create a context for language learning in terms of words becoming signifiers rather than just “names”?

  8. Concept learning M E D IATION Skill learning • Cognition Phase;Learning about the skill 1. Learning Association; Categories connected to verbal expression 2. Imitation; “Trial and error” 2. Learning Difference; Differences within and between categories 3. Exercise, training towards automation 3. Verbalizing Partial Similarities; they are similar in... ANALYTIC CODING/MULTIPLE CLASSIFICATION/ABSTRACTION

  9. Example: The task is to find similarities and differences between the two boxes in each row. This enforces processes of analytic coding, and verbal consciousness about these similarities and differences. 5 8

  10. 0,5 5 10 five tenths 310 three tenths 0,3 seven tenths 7 10 0,7 seven tenths 7 10 0,7 7 10 0,3 7 10 0,7

  11. CASE. Tanja has general learning problems; Difficulties in -processes of analysis-detecting partial similarities She requires a different progression, but the same learning processes as other children.

  12. It is a ten, because there are ten tassels

  13. I put ten beads on the pipe cleaner, and make a ten.

  14. It is a ten, because there are ten flags

  15. ten treklossar

  16. They are similar in that they are tens How are they similar ?

  17. Multiplication in terms of repeated addition When each set contains an identical number, we can multiply.

  18. Multiplication 2 Point to the row where we can find the number by multiplication

  19. Multiplication 3 Find the number of round shapes Find the number of four sided shapes. How are these two tasks similar?

  20. Count in nines multiplication 4| Kjetil puts 9 marbles in each bag. How many marbles are there in bags marbles bags marbles bags marbles bags marbles bags marbles bags marbles

  21. Mattis og Mattea 1 Mattis og Mattea 1, Resource book Mattis og Mattea 2A Mattis og Mattea 2B Mattis og Mattea 2, Resource book

  22. Directing attention j Number Figures Digits

  23. Look at the two groups in each row.In what respect are they similar?In what respect are they different? • To verbalize

  24. To learn concepts of ...symbols The red colour of the milk carton is a symbol, because it has a meaning

  25. .......... are symbols, because they mean something

  26. Which pink colour is a symbol?

  27. Which red colour is a symbol?

  28. 3 Which is a symbol, the figure or the number of three round shapes?

  29. Look at the pink colour of the milk pack and the red colour at the traffic light. In what respect are they similar?

  30. 2 The Ringo-logo and the figure 2, in what respect are they similar?

  31. To practise

  32. Math learning, general and different Knowledge of the general processes provides tools to with which to meet each different learner. • Math learning, different or general? General learning processes Different learners

  33. Who has the figure with a triangular shape and the colour green? Who has the figure with the straight line shape, the number two, vertical position and the colour blue?

  34. Concepts of numbersThe number three Count, and find the number of dinosaurs. Make a group with the number of three pigs.

  35. Point to the groups which have the number three.

  36. How are these groups similar?

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