This document discusses differentiated instruction in mathematics. It provides examples of how Singapore implemented differentiated instruction through their education system. The key aspects of differentiated instruction discussed are: 1) Differentiating content, process, and product based on student needs. For example, Singapore differentiated their mathematics curriculum between grades 1-4. 2) Using different models and levels of differentiation like acceleration and enrichment to meet students' varying ability levels. 3) Applying differentiated instruction allows teachers to ensure all students learn key concepts in ways that are appropriate for their level, such as using physical modeling or more abstract algebra methods to teach ratios.

1. Differentiated Instruction
incorporating ratio, whole numbers and fractions
Course Code: MAP114, MAP115 and MAP116
Yeap Ban Har
yeapbanhar@gmail.com
Marshall Cavendish Institute
Slides are available at www.banhar.blogspot.com

2. introduction |

3. | Hanusek, Jamison, Jamison & Woessmann 2008

4. | Hanusek, Jamison, Jamison & Woessmann 2008
Score 1960-1970s 1980s 1990s 2000s
500’s Japan Hong Kong
Japan
Korea
Hong Kong
Japan
Korea
Singapore
Hong Kong
Japan
Korea
Singapore
400’s Thailand Philippines
Singapore
Thailand
Malaysia
Thailand
Malaysia
Thailand
300’s Indonesia
Philippines
Indonesia
Philippines

5. opening examples |

6. In the 1970’s, Singapore needed a way to help students, most
of whom were not performing well in mathematics, learn
mathematics.
CPA Approach based on Bruner’s work and a host of other
learning theories were applied. Today, many people refer to
this approach as Singapore Math.

10. 29 + 52 =

11. 29 + 52 =
1 51

12. 29 + 52 = 81
1 51

13. 29 + 52 = 30 + 51 = 81

14. Nanakuli Elementary School, Hawaii

15. Nanakuli Elementary School, Hawaii

16. Nanakuli Elementary School, Hawaii

17. differentiation |

19. “The idea of differentiating instruction is an approach to
teaching that advocates active planning for and
attention to student differences in classrooms,
in the context of high quality curriculums.”
| www.caroltomlinson.com

20. Goh’s Report (1978) recommended a
differentiated education system for
Singapore.
Grade 1 to 4
Mathematics
Foundation
Mathematics

21. Grade 1
Regular Program
Learning Support
Goh’s Report (1978) recommended a
differentiated education system for
Singapore.

22. We want to make our education system even
more student-centric, and sharpen our focus
in holistic education – centred on values and
character development.
| Heng 2011

23. Differentiated instruction is reflected in the Professional
Learning Communities (PLC) four critical
questions
| DuFour 2004
Educational Leadership
May 2004 | Volume 61 | Number 8
Schools as Learning Communities

24. what is it that the teacher wants
students to learn

25. how does a teacher know when
students have learnt it

26. what if students do not learn it

27. what if they already learnt it

28. model of
differentiation |

29. What to Differentiate
• Content
• Process
• Product

30. the content of instruction

31. Grade 1 to 4
Mathematics
Foundation
Mathematics
Example
Singapore Grade 5 and 6 Curriculum is
an example of content differentiation.

32. the processes and techniques used to help make
sense of a given topic

33. the products produced by students that demonstrate
their learning

34. Levels of Differentiation
• Student Level
• Class Level

35. differentiation for the entire class

36. differentiation for groups
within a class

37. Differentiation for Advanced Learners
• Acceleration model
• Enrichment model

38. acceleration

39. enrichment

40. concept learning |

41. Struggling students get to understand the idea of line of symmetry through paper
folding. Ideas such as the two parts overlap when folded at the line of symmetry makes
more sense after having actually done it. At the same time, students who already know
about 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.

42. concept learning |

45. concept learning |

50. word problem|

54. There is a
method of
solving that is
more literal and
concrete – guess-
and-check.
The model method is visual. The use of algebra is more abstract.
Differentiated instruction provides students with methods of different
level of abstraction to respond.

55. practice|

62. teaching of ratio |

63. Ratio is about multiplicative comparison.

72. The number of boys to the number of
girls in a group was in the ratio 2 : 3.

73. The number of boys to the number of
girls in a group was in the ratio 2 : 3.
After ¼ of the boys and 69 girls left
the group, there were 51 more girls
than boys in the group.

75. reflections |