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LEAP Educators’ Conference 2011 Promoting Higher-Order Thinking through Drill-and-Practice in Elementary School Mathematics Yeap Ban Har Marshall Cavendish Institute Singapore [email protected] Presentation is available on www.banhar.blogspot.com

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

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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.

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

PowerPoint Presentation

LEAP Educators Conference 2011Promoting Higher-Order Thinking through Drill-and-Practice in Elementary School Mathematics

Yeap Ban HarMarshall Cavendish InstituteSingapore

[email protected]

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 persons 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.

314522345125341Total = 10Total = 8Total = 9Example

Arrange consecutive numbers 2 to 6 in the given arrangement so that the vertical sum is equal to the horizontal sum.

524633645234562Total = 12Total = 11Total = 13

314522345125341Total = 10Total = 8Total = 9524633645234562Total = 12Total = 11Total = 131 83 95 102 114 126 13

1 83 95 102 114 126 131, 2, 3, 4, 52, 3, 4, 5, 63, 4, 5, 6, 73 5 7 14 15 16 20, 21, 22, 23, 2420 22 24 ? ? ? m, mm + 2m + 4 ?3(m + 2) ?

Princess Elizabeth Primary School, Singapore24635

Princess Elizabeth Primary School, SingaporeExample

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.xSourceTeacher Professional Development Course in Singapore1 2x 56 04 3x 28 62 9x 38 71 5x 46 01 2x 78 41 5x 23 01 8x 23 61 8x 35 41 8x 47 21 4x 79 81 2x 89 6responses

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 = 60 9 x 6 = ?18 x 6 = ?17 x 6 = ? Source: Primary Mathematics (Singapore)25Example

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.

481644812810 0164160

48164481640008001648128160 1604

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

SourceGrade 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.

Chart50.380.730.910.440.770.930.080.330.640.060.240.51

AdvancedHighIntermediateComparison between Grade 4 and Grade 8 Mathematics Performance

Sheet1Grade 4 MathsBenchmarksSingaporeInternational AverageAdvanced38%8%High73%33%Intermediate91%64%Grade 4 ScienceBenchmarksSingaporeInternational AverageAdvanced25%7%High61%32%Intermediate86%65%Grade 8 MathsBenchmarksSingaporeInternational AverageAdvanced44%6%High77%24%Intermediate93%51%Grade 8 ScienceBenchmarksSingaporeInternational AverageAdvanced33%6%High66%26%Intermediate85%56%Comparison between Grade 4 and Grade 8 Mathematics PerformanceSingaporeInternationalGrade 4Grade 8Grade 4Grade 8Advanced38%44%8%6%High73%77%33%24%Intermediate91%93%64%51%

Sheet1

SingaporeInternational AverageInternational Benchmark Grade 4 Mathematics Performance

Sheet2

SingaporeInternational AverageInternational Benchmark Grade 4 Science Performance

Sheet3

SingaporeInternational AverageInternational Benchmark Grade 8 Mathematics Performance

SingaporeInternational AverageInternational Benchmark Grade 8 Science Performance

AdvancedHighIntermediateComparison between Grade 4 and Grade 8 Mathematics Performance