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# MAP114 Hawaii 28 May 2013

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This is an updated file including the discussion we had in class.I will teach this course to three different groups. Today, it was with teachers from Grade 4 to Grade 6.

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### MAP114 Hawaii 28 May 2013

1. 1. Differentiated Instructionincorporating ratio, whole numbers and fractionsCourse Code: MAP114, MAP115 and MAP116Yeap Ban Haryeapbanhar@gmail.comMarshall Cavendish InstituteSlides are available at www.banhar.blogspot.com
2. 2. introduction |
3. 3. | Hanusek, Jamison, Jamison & Woessmann 2008
4. 4. | Hanusek, Jamison, Jamison & Woessmann 2008Score 1960-1970s 1980s 1990s 2000s500’s Japan Hong KongJapanKoreaHong KongJapanKoreaSingaporeHong KongJapanKoreaSingapore400’s Thailand PhilippinesSingaporeThailandMalaysiaThailandMalaysiaThailand300’s IndonesiaPhilippinesIndonesiaPhilippines
5. 5. opening examples |
6. 6. In the 1970’s, Singapore needed a way to help students, mostof whom were not performing well in mathematics, learnmathematics.CPA Approach based on Bruner’s work and a host of otherlearning theories were applied. Today, many people refer tothis approach as Singapore Math.
7. 7. 29 + 52 =
8. 8. 29 + 52 =1 51
9. 9. 29 + 52 = 811 51
10. 10. 29 + 52 = 30 + 51 = 81
11. 11. Nanakuli Elementary School, Hawaii
12. 12. Nanakuli Elementary School, Hawaii
13. 13. Nanakuli Elementary School, Hawaii
14. 14. differentiation |
15. 15. “The idea of differentiating instruction is an approach toteaching that advocates active planning for andattention to student differences in classrooms,in the context of high quality curriculums.”| www.caroltomlinson.com
16. 16. Goh’s Report (1978) recommended adifferentiated education system forSingapore.Grade 1 to 4MathematicsFoundationMathematics
17. 17. Grade 1Regular ProgramLearning SupportGoh’s Report (1978) recommended adifferentiated education system forSingapore.
18. 18. We want to make our education system evenmore student-centric, and sharpen our focusin holistic education – centred on values andcharacter development.| Heng 2011
19. 19. Differentiated instruction is reflected in the ProfessionalLearning Communities (PLC) four criticalquestions| DuFour 2004Educational LeadershipMay 2004 | Volume 61 | Number 8Schools as Learning Communities
20. 20. what is it that the teacher wantsstudents to learn
21. 21. how does a teacher know whenstudents have learnt it
22. 22. what if students do not learn it
23. 23. what if they already learnt it
24. 24. model ofdifferentiation |
25. 25. What to Differentiate• Content• Process• Product
26. 26. the content of instruction
27. 27. Grade 1 to 4MathematicsFoundationMathematicsExampleSingapore Grade 5 and 6 Curriculum isan example of content differentiation.
28. 28. the processes and techniques used to help makesense of a given topic
29. 29. the products produced by students that demonstratetheir learning
30. 30. Levels of Differentiation• Student Level• Class Level
31. 31. differentiation for the entire class
32. 32. differentiation for groupswithin a class
33. 33. Differentiation for Advanced Learners• Acceleration model• Enrichment model
34. 34. acceleration
35. 35. enrichment
36. 36. concept learning |
37. 37. Struggling students get to understand the idea of line of symmetry through paperfolding. Ideas such as the two parts overlap when folded at the line of symmetry makesmore sense after having actually done it. At the same time, students who already knowabout lines of symmetry get to (1) look for a pattern (2) explain the pattern.Differentiated instruction provides every student to learn what they need to learn.
38. 38. concept learning |
39. 39. concept learning |
40. 40. word problem|
41. 41. There is amethod ofsolving that ismore literal andconcrete – guess-and-check.The model method is visual. The use of algebra is more abstract.Differentiated instruction provides students with methods of differentlevel of abstraction to respond.
42. 42. practice|
43. 43. teaching of ratio |
44. 44. Ratio is about multiplicative comparison.
45. 45. The number of boys to the number ofgirls in a group was in the ratio 2 : 3.
46. 46. The number of boys to the number ofgirls in a group was in the ratio 2 : 3.After ¼ of the boys and 69 girls leftthe group, there were 51 more girlsthan boys in the group.
47. 47. reflections |