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The Average Student on Top The High School Renewal Committee 27 October 2010 Yeap Ban Har Marshall Cavendish Institute Singapore [email protected] Slides are available at www.banhar.com
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This presenttaion was made to a group of parnets, business leaders, administrators, teachers, school board members and university representatives in Cache School District in Logan, Utah. This group, The High School Renewal Committee, is keen to develop a world-class high school mathematics programmed. In this presentation, some recommendations were made on how to make the average high school student perform well in mathematics.
Transcript of Cache county thsrc
The Average Student on TopThe High School Renewal Committee
27 October 2010
Yeap Ban HarMarshall Cavendish Institute
Singapore
Slides are available at www.banhar.com
vision and focus
Singapore mathematics curriculum has its focus mathematical problem solving and it is set within an education system that emphasizes thinking.
mathematical problem solving
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
thinking
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
strong fundamentals
Princess Elizabeth Primary School, Singapore
24
6
3 5
Princess Elizabeth Primary School, Singapore
pedagogy
Pedagogy that focuses on visuals, patterning and number sense.
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.
Fuchun Primary School, Singapore
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. Princess Elizabeth Primary School, Singapore
For example, students learn to do division of discrete quantities without the need to write division sentence in Grade 1.
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
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
assessment
SourcePSLE Mathematics Singapore Examination and Assessment Board
SourcePrimary Three Examination Item from Henry Park Primary School, Singapore
Angela, Bala, and Cheng Hao have 872 marbles altogether. Angela has 4 times as many marbles as Bala. Cheng Hao has 50 more marbles than Bala. How many marbles does Bala have?
SourcePrimary Three Examination Item from Henry Park Primary School, Singapore
Angela, Bala, and Cheng Hao have 872 marbles altogether. Angela has 4 times as many marbles as Bala. Cheng Hao has 50 more marbles than Bala. How many marbles does Bala have?
Angela
Bala
Cheng Hao
50
872
SourcePrimary Three Examination Item from Henry Park Primary School, Singapore
Angela, Bala, and Cheng Hao have 872 marbles altogether. Angela has 4 times as many marbles as Bala. Cheng Hao has 50 more marbles than Bala. How many marbles does Bala have?
Angela
Bala
Cheng Hao
822
1 unit = 822 ÷ 61 unit = 137Bala has 137 marbles.
600180
42
SourcePrimary Three Examination Item from Henry Park Primary School, Singapore
Angela, Bala, and Cheng Hao have 872 marbles altogether. Angela has 4 times as many marbles as Bala. Cheng Hao has 50 more marbles than Bala. How many marbles does Bala have?
Angela
Bala
Cheng Hao
50
872y
y y y y
y
4y + y + (y + 50) = 872
6y + 50 = 872
6y = 872 – 50
y = 822 ÷ 6
y = 137
outcomes
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
Ind
onesi
a
Th
aila
nd
2 30
15 124
46 4414
75 6648
Grade 8
Method Used in Singapore Textbooks
TIMSS 2007Trends in International Mathematics and Science Studies
Mala
ysi
a
Sin
gapor
e
402
7018
8850
9782
Inte
rnati
onal
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
TIMSS 2007Trends in International Mathematics and Science Studies
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.
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
Making the Average Student on Top • Thinking-oriented Curriculum• Theoretically-sound Pedagogy• Assessment that is coherent with the curriculum• Teacher professional development• Changing mindset about what mathematics is• Constructing knowledge• Enhancing capacity to learn
