LEAP Educators' Conference 2011, Manila, The Philippines, 11 - 12 February 2011

LEAP Educators’ Conference 2011

Promoting Higher-Order Thinking through Drill-and-Practice in Elementary School Mathematics

Yeap Ban Har

Marshall Cavendish Institute

Singapore

banhar@sg.marshallcavendish.com

Presentation is available on www.banhar.blogspot.com

This lecture is dedicated to the fifteen students in the Elementary Mathematics Content and Pedagogy Course held at NIE (Sep – Dec 2010)

Introduction

Mathematics is an excellent vehicle for the

development and improvement of a person’s

intellectual competence…

Ministry of Education 2006

Example

Arrange consecutive numbers 1 to 5 in the given

arrangement so that the vertical sum is equal to

the horizontal sum.

3

1

4

52

2

3

4

51

2

5

3

41

Total = 10 Total = 8 Total = 9

Example

Arrange consecutive numbers 2 to 6 in the given

arrangement so that the vertical sum is equal to

the horizontal sum.

5

2

4

63

3

6

4

52

3

4

5

62

Total = 12 Total = 11 Total = 13

3

1

4

52

2

3

4

51

2

5

3

41

Total = 10 Total = 8 Total = 9

5

2

4

63

3

6

4

52

3

4

5

62

Total = 12 Total = 11 Total = 13

1 83 9

5 10

2 11

4 12

6 13

1 83 9

5 10

2 11

4 12

6 13

1, 2, 3, 4, 5

2, 3, 4, 5, 6

3, 4, 5, 6, 7

3

5

7

14

15

16

20, 21, 22, 23, 24

20

22

24

?

?

?

m, …

mm + 2m + 4

?3(m + 2)

?

Princess Elizabeth Primary School, Singapore

2

4

6

3 5

Princess Elizabeth Primary School, Singapore

Example

Students get to practise addition of three

numbers while developing higher-order thinking

such as looking for patterns and relations, as

well as their number sense.

Use the digits 0 to 9 not more than

once to make a correctmultiplication sentence.

x

Source

Teacher Professional Development Course in Singapore

1 2x 56 0

4 3x 28 6

2 9x 38 7

1 5x 46 0

1 2x 78 4

1 5x 23 0

1 8x 23 6

1 8x 35 4

1 8x 47 2

1 4x 79 8

1 2x 89 6

responses

The Anchor Problem – to make a correct division sentence

using one set of digit tiles 0 to 9.

Source: Springhurst Elementary School, New York

Example

How about the learning of multiplication facts or

the multiplication table?

Can it involve the development of higher-order

thinking?

Source: Pensar sin Limites (Chile)

Source: Pensar sin Limites (Chile)

Source: Maths Champion (Indonesia)

2 x 7 = 145 x 7 = 357 x 7 = ?

2 x 8 = 133 x 8 = ?

3 x 8 = 246 x 8 = ?12 x 8 = ?

10 x 6 = 609 x 6 = ?

18 x 6 = ?17 x 6 = ?

Source: Primary Mathematics (Singapore)

Example

Students have a chance to develop the ability to

make connections and also to develop

visualization ability which is fundamental in the

learning of mathematics.

481644

8

12

8

1

0

0

16

4

16

0

481644816

4000800

16

4

8

12

8

16

0

16

0

4

Source

Grade 4 Lesson on Long Division in Keys Grade School, Manila

Source

Grade 4 Lesson on Long Division in Keys Grade School, Manila

Comparison between Grade 4 and Grade 8

Mathematics Performance

38%44%

8% 6%

73% 77%

33%24%

91% 93%

64%

51%

Grade 4 Grade 8 Grade 4 Grade 8

Singapore International

Advanced

High

Intermediate

Conclusion

Drill-and-practice is mot mutually exclusive from

higher-order thinking. This lecture gives

examples of how drills can be used to develop a

range of higher-order thinking.