ARK Schools, London
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Transcript of ARK Schools, London
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Dr Yeap Ban Har [email protected]
Marshall Cavendish Institute Singapore
Presentation slides are available at www.banhar.blogspot.com
Singapore MathsTHE ESSENTIALSLondon June 2011
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Kembangan PCF Kindergarten
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Curriculum for all learners• Struggling students learn
enough• Average students perform
advanced skills• Advanced students are
challenged
Kembangan PCF Kindergarten
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Advanced
Intermediate
Low
High
Gra
de 4
19
95
38
70
89
96
TIMSSTrends in International Mathematics and Science Studies
Gra
de 8
19
9942
77
94
99
Gra
de 4
20
03
Gra
de 8
20
07
38
73
91
97
40
70
88
97
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Singapore Mathematics: Focus on Thinking
excellentvehicleanforthe
development&improvement of
a person’s intellectual
competenciesMinistry of Education Singapore 2006
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an identical
Allan puts some brown sugar on a dish.The total weight of the brown sugar and the dish is 110 g.Bella puts thrice the amount of brown sugar that Allan puts on an identical dish, and the total weight of the brown sugar and the dish is 290 g.
Find the weight of the brown sugar that Bella puts on the dish.
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110 g
290 g
110 g180 g
2 units = 180 g
1 unit = 90 g
3 units = 270 g
Bella puts 270 g brown sugar on the dish.
an identical
Allan puts some brown sugar on a dish.The total weight of the brown sugar and the dish is 110 g.Bella puts thrice the amount of brown sugar that Allan puts on an identical dish, and the total weight of the brown sugar and the dish is 290 g.
Find the weight of the brown sugar that Bella puts on the dish.
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110 g
290 g
110 g180 g
3 units = 180 g
1 unit = 60 g
3 units = 180 g
Bella puts 180 g brown sugar on the dish.
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Singapore MathVisualization
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1 2 3 4 5 6
11 10 9 8 7
12 13 14 15 16
21 20 19 18 17
22 23 24 25 26
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1 2 3 4 5
9 8 7 6
10 11 12 13
17 16 15 14
18 19 20 21
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Professional Development in Santiago de Chile
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Singapore MathPatterns
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Archipelschool De Tweemaster – Kameleon
The Netherlands
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In Singapore, a curriculum that focuses on mathematical problem solving was introduced in 1992.
Mathematical Problem
Solving
Attitudes
Metacognition
Proc
esse
s
Concepts
Skills
NumericalAlgebraic
GeometricalStatistical
ProbabilisticAnalytical
Reasoning, communication & connectionsThinking skills & heuristicsApplication & modelling
Numerical calculationAlgebraic
manipulationSpatial visualization
Data analysisMeasurement
Use of mathematical tools
Estimation
Monitoring of one’s own thinkingSelf-regulation of learning
BeliefsInterest
AppreciationConfidence
Perseverance
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Professional Development in ARK Schools, London
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Professional Development in Santiago de Chile
Problem Solving in Learning Basic Concepts and Skills
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Reference: Primary Mathematics (Standards Edition)
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Reference: Primary Mathematics (Standards Edition)
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Singapore MathLearn New Concept Through
Problem Solving
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Singapore MathDrill-and-Practice Through
Problem Solving
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Singapore MathApplying Knowledge in
Problem Solving
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The CPA ApproachFocus on Thinking
makes abstract concepts accessible to learners who are not yet ready for abstraction
builds fundamental intellectual competencies required for learners to handle abstraction
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Textbook
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Reference: My Pals Are Here! Maths
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1. Setting Up the Task
Each person should get 12 animals. I have given you some. How many more do you need?
Pupils had opportunities to work independently as the teacher attended to other pupils.
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2. Development (1)
Put four animals into one cup. Note only one cup is given.This mirrors drawing rings around four objects.
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Put four animals into a second cup.
Students should have positive experiences during the lesson.
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How many animals are there altogether? How many animals are there in one cup? How many cups do we use?
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3. Development (2)
This is like the workbook tasks except that the magnets can be moved. Built-in remedial strategy.
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Variations on the arrangements of magnets to increase the level of visualization required.
Pupils needs to monitor the number of magnets as well as to manage their visualization process.
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4. Extension
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5. Development (3) The use of colour to show the group. Built-in remedial strategy.
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CPA Approach
Links between concrete and pictorial representation must be carefully constructed.
Remedial steps are built into instruction
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Reference: Primary Mathematics (Standards Edition)
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51 – 17
51 x 351 + 26
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3 units = 18
1 unit = 6
8 units = 8 x 6 = 48
There were 48 coins at first.
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SingaporeMathsThe Essentials
Da Qiao Primary School, Singapore