chile moe seminar english
DESCRIPTION
This is the English version of the presentation at Avancemos en las Matematicas: La Mirada de SingapurTRANSCRIPT
This seminar is about mathematics teaching and learning that focuses on helping average and struggling learners do well in mathematics while maintaining a suitable challenge for advanced learners.
Dr Yeap Ban HarMarshall Cavendish Institute
Singapore
Presentation is available at www.banhar.com
Seminar on Singapore Math in
ChileSANTIAGO CONCEPTION
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
The emphasis on thinking continues in the late 1990s with the introduction of Thinking School, Learning Nation philosophy to the entire education system in 1997.
thinking schoolslearning nation
The assessment reflects the focus of the curriculum. For example, the Grade 6 national examination (Primary School Leaving Examination or PSLE) includes a significant section that requires problem solving.
Mrs Hoon made some cookies to sell. 3/4 of them were chocolate cookies and the rest were almond cookies. After selling 210 almond cookies and 5/6 of the chocolate cookies, she had 1/5 of the cookies left.
How many cookies did Mrs Hoon sell?
210
5
1
8
3
Mrs Hoon made some cookies to sell. 3/4 of them were chocolate cookies and the rest were almond cookies. After selling 210 almond cookies and 5/6 of the chocolate cookies, she had 1/5 of the cookies left.
How many cookies did Mrs Hoon sell?
210
5
1
8
3210
40
7
5
1
8
3
3040
1
96040
32
5
4
Mrs Hoon sold 960 cookies.
Mrs Hoon made some cookies to sell. 3/4 of them were chocolate cookies and the rest were almond cookies. After selling 210 almond cookies and 5/6 of the chocolate cookies, she had 1/5 of the cookies left.
How many cookies did Mrs Hoon sell?
Schools make problem solving a priority in their mathematics programme because of the demands of the PSLE. Grade 3 Examination Item (Raffles Girls’ Primary School 2009)
Devi had some $2 notes and $5 notes.She had a total of $76.She had 4 more $5 notes than $2 notes.How many $2 notes did she have?
Schools make problem solving a priority in their mathematics programme because of the demands of the PSLE. Grade 3 Examination Item (Raffles Girls’ Primary School 2009)
Devi had some $2 notes and $5 notes.She had a total of $76.She had 4 more $5 notes than $2 notes.How many $2 notes did she have?Number of $5 notes
Number of $2 notes
4 $20
$78
$58
$58 ÷ 7 = 8
8
8She had eight $2 notes.
Textbooks place an emphasis on problem solving and thinking.
Mr Khan
Mr Chen
2740 + 3560= 6300
5 units = 6300
1 unit = 1260
4 units = 4 x 12604 units = 5040
In the end, Mr Chen had 5040 sacks and Mr Khan had 1260 sacks.
Textbooks place an emphasis on problem solving and thinking.
first day
first day
first day
A strong foundation is necessary for the students to do well in mathematics. In the Singapore textbooks, such a strong foundation is achieved through the application of a few learning principles. Singapore Math in Chile
bruner’s theoryconcrete
Singapore Math in Malaysia
concreteexperiences
Singapore Math in Malaysia
The CPA Approach – the progression from concrete to pictures to abstract symbols is recommended for concept development. This is based on the work of Jerome Bruner.
For example, students learn the idea of division by sharing 12 cookies among 4 persons as well as by putting 12 eggs in groups of 4 before progressing to using drawings to solve division problems. Later they learn to use division sentence 12 ÷ 4 = 3.
The Spiral Approach – students get to revisit core ideas as they deepen their understanding of those ideas. This is also one of Jerome Bruner’s ideas.
Singapore Math in the Netherlands
For example, students learn to do division of discrete quantities without the need to write division sentence in Grade 1. In Grade 2, the revisit this idea and use division sentences to represent the situations. In Grade 3, the idea is extended to include the idea of a remainder. They also learn to regroup before dividing for 2-digit and 3-digit numbers.
Singapore Math in USA
In Grade 4, 4-digit numbers are used. In Grade 5, division of continuous quantities are dealt with where 13 ÷ 4 = 3.25 rather than 3 remainder 1.
Singapore Math in The Philippines
Systematic Variation – students are presented with a variety of tasks in a systematic way. This is based on the idea of Zoltan Dienes.
Students in Singapore have demonstrated high achievement and positive attitude towards mathematics.
In Trends in Mathematics and Science Study, more than 40% of Singapore’s 4th and 8th graders are in the Advanced International Benchmark (the international average is 5% and 2% respectively).
Advanced
Intermediate
Low
High
199
5
200
3
200
7
38 4138
70 7473
89 9291
96 9897
Gra
de 4
Inte
rnati
on
al
5
26
67
90
Advanced
Intermediate
Low
High
Aver
age
Hon
g Ko
ng
Sing
apor
e
2 4031
15 7064
46 8885
75 9794
S. K
orea
Taiw
an
4540
7171
8690
9598
Gra
de 8
Singapore Math in Indonesia
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
In the PSLE, the national average for students who are capable of completing the most challenging items in the examination is between 40% and 45%. We saw one such challenging items earlier.
Mrs Hoon made some cookies to sell. 3/4 of them were chocolate cookies and the rest were almond cookies. After selling 210 almond cookies and 5/6 of the chocolate cookies, she had 1/5 of the cookies left.
How many cookies did Mrs Hoon sell?
The attitude index for Singapore students in TIMSS is also relatively high compared to other high-performing countries.
Also, the majority of students in Singapore opt to study mathematics in Grades 11 and 12 when they are no longer required to.
Singapore
Taiwan
Japan
Hong Kong
Att
itude
Ach
ievem
en
t
71 41
67 40
50 24
62 23
Gra
de 4
Kazakhstan
Russia
International
England
89 19
62 16
80 16
72 5
Taiwan
Singapore
Hong Kong
S Korea
Att
itude
Ach
ievem
en
t
37 45
33 40
60 40
47 31
Gra
de 8
Japan
England
International
Hungary
30 26
30 10
40 8
54 2
Other than the curriculum, assessment and textbooks, another important factor is the teachers.
Teachers received about 100 hours of courses in mathematics teaching and learning during pre-service training.
Teachers are expected to engage in professional development throughout their career.
Some study for certification while others just for improvement. It is also an expectation.
Textbooks are designed for teachers to learn the mathematics that they teach.
Dr Yeap Ban HarMarshall Cavendish Institute
Singapore
Presentation is available at www.banhar.com
Seminar on Singapore Math in
ChileSANTIAGO CONCEPTION
Singapore Math in Chile