Edgemont 2013
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  • 1. Professional Development in Singapore Math Focus on Conceptual Understanding Edgemont Union Free School District Yeap Ban Har Marshall Cavendish Institute Singapore yeapbanhar@gmail.com Slides are available at www.banhar.blogspot.com
  • 2. Seely Place Elementary School, New York
  • 3. Seely Place Elementary School, New York
  • 4. Learning with concrete materials www.banhar.blogspot.com
  • 5. Anchor Task | Show 2 equal parts.
  • 6. SEED Institute, Singapore Let’s Learn Fractions Show 2 equal parts Edgemont School District, New York
  • 7. Theoretical Underpinnings Skemp • relational, instrumental Bruner • concrete, pictorial, abstract Vygotsky • social interaction Piaget • assimilation, accommodation
  • 8. Greenville Elementary School, New York 2,476 x 3 Bruner CPA Approach
  • 9. Greenville Elementary School, New York The concrete materials show 2,476 = 2,000 + 400 + 70 + 6 The concrete materials make students do partial multiplication The concrete materials allow regrouping (18 = 10 + 8)
  • 10. Using Concrete Materials They are used in tandem with pictorial and symbolic representations, not one after another. Avoid jargon and employ more ‘revoicing’ i.e. students’ language in early stages of learning Concrete material embodies the essential ideas
  • 11. Assessment www.banhar.blogspot.com
  • 12. Bruner CPA Approach
  • 13. Formative Assessment Level • Class • Individual Criteria • Collect data to decide if a student is approaching or has met or has exceeded expectations Strategies • Observation • Interview • Written work
  • 14. Basic skill items
  • 15. Conceptual items
  • 16. Direct application
  • 17. Unusual items
  • 18. adv high int low Singapore 606 43 78 94 99 South Korea grade four mathematics ave 605 39 80 97 100 Hong Kong 602 37 80 96 99 Taiwan 591 34 74 93 99 Japan 585 30 70 93 99 Northern Ireland 562 24 59 86 96 Belgium 549 10 50 89 99 Finland 545 12 49 85 98 England 542 18 49 78 93 Russia 542 13 47 82 97 United States 541 13 47 81 96 International 500 4 28 69 90
  • 19. advanced high intermediate low South Korea grade eight mathematics average 613 47 77 93 99 Singapore 611 48 78 92 99 Taiwan 609 49 73 88 96 Hong Kong 586 34 71 89 97 Japan 570 27 61 87 97 Russia 539 14 47 78 95 Israel 516 12 40 68 87 Finland 514 4 30 73 96 United States 509 7 30 68 92 England 507 8 32 65 88 International 500 3 17 46 75
  • 20. Professional Development in Singapore Math Focus on Differentiated Instruction Edgemont Union Free School District Yeap Ban Har Marshall Cavendish Institute Singapore yeapbanhar@gmail.com Slides are available at www.banhar.blogspot.com
  • 21. Advanced Learners • Make a story • Give another way. Give an original way. • Explain to a friend. Write an explanation. Draw a diagram to show. • My friend has an idea. What do you think of it? Singapore Math adopts enrichment model and not acceleration model.