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
2
2
1
5
2
3
5
1
5
4
1
4
4
3
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
3
3
2
6
3
6
5
2
4
6
2
4
4
5
Total = 12
Total = 11
Total = 13

3
2
2
1
5
2
3
5
1
5
4
1
4
4
3
1 8
Total = 10
Total = 8
Total = 9
3 9
5 10
2 11
4 12
5
3
3
6 13
2
6
3
6
5
2
4
6
2
4
4
5
Total = 12
Total = 11
Total = 13

1 8
1, 2, 3, 4, 5
3 9
5 10
2 11
4 12
2, 3, 4, 5, 6
6 13
3
14
5
3, 4, 5, 6, 7
15
7
16
20
?
22
20, 21, 22, 23, 24
?
24
?
m
m + 2
m + 4
?
3(m + 2)
?
m, …

2
4
3
5
6
Princess Elizabeth Primary School, Singapore

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 correct multiplication sentence.
x
Source
Teacher Professional Development Course in Singapore

1 2
x 5
6 0
4 3
x 2
8 6
2 9
x 3
87
15
x 4
60
1 2
x 7
8 4
1 5
x 2
3 0
18
x 2
3 6
1 8
x 3
5 4
1 8
x 4
7 2
1 2
x 8
9 6
responses
1 4
x 7
9 8

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: Maths Champion (Indonesia)

2 x 7 = 14
5 x 7 = 35
7 x 7 = ?
3 x 8 = 24
6 x 8 = ?
12 x 8 = ?
10 x 6 = 60
9 x 6 = ?
18 x 6 = ?
17 x 6 = ?
2 x 8 = 13
3 x 8 = ?
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.

1
2
0
4
4816
4
4
8
8
1
0
16
16
0

1
2
0
4
4816
4
4816
4
8
4000
16
8
800
16
16
0

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

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.

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

by Jimmy Keng on Feb 14, 2011

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LEAP Educators’ Conference 2011, Manila, The Philippines, 11 - 12 February 2011 — Presentation Transcript