leap educators' conference 2011, manila, the philippines, 11 - 12 february 2011
DESCRIPTION
This plenary lecture on elementary school mathematics was given at the conference which marks the end of the three-year Leaders and Educators in Asia Programme.TRANSCRIPT
LEAP Educators’ Conference 2011
Promoting Higher-Order Thinking through Drill-and-Practice in Elementary School Mathematics
Yeap Ban Har
Marshall Cavendish Institute
Singapore
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)
?
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.