Post on 10-May-2015
Singapore Math at Highline Public Schools March 2013 Session 5 Yeap Ban Har www.banhar.blogspot.com
The Merlion by Yeap Ken Min
John had 1.5 m of copper wire. He cut some of the wire to bend into the shape shown in the figure below. In the figure, there are 6 equilateral triangles and the length of XY is 19 cm. How much of the copper wire was left?
19 cm x 5 = 95 cm 150 cm – 95 cm = 55 cm 55 cm was left.
Lesson 6 12th March 2013
Lesson 6 12th March 2013
Lesson 6 12th March 2013
“… over-emphasising procedural skills without understanding the underlying
mathematical principles should be avoided.”
Ministry of Education 2006
Student Achievement Average Learners Performing
Well
Pathlight School, Singapore
Singapore Math allows
average learners perform at
a high level. The following
are some data from some
international research on
math achievement and
attitude.
East Coast Primary School, Singapore
Score 1960-1970s 1980s 1990s 2000s
500 Japan Hong Kong Japan Korea
Hong Kong Japan Korea
Singapore
Hong Kong Japan Korea
Singapore
400 Thailand The Philippines Singapore Thailand
Malaysia Thailand
Malaysia Thailand
300 Indonesia The Philippines
Indonesia The Philippines
Reference: E. Hanusek, D. Jamison, E. Jamison & L. Woessmann (2008)
All major international tests (literacy, science and mathematics) between 1964 and
2003 were placed on a common scale. Selected countries shown in the table.
mathematics
gra
de f
our
ma
them
atics
Singapore
South Korea
Hong Kong
Taiwan
Japan
Northern Ireland
Belgium
Finland
England
Russia
International
43
39
37
34
30
24
10
12
18
13
4
78
80
80
74
70
59
50
49
49
47
28
94
97
96
93
93
86
89
85
78
82
69
99
100
99
99
99
96
99
98
93
97
90
606
605
602
591
585
562
549
545
542
542
500
adva
nced
hig
h
inte
rmedia
te
low
average
gra
de e
ight
ma
them
atics
South Korea
Singapore
Taiwan
Hong Kong
Japan
Russia
Israel
Finland
United States
England
International
47
48
49
34
27
14
12
4
7
8
3
77
78
73
71
61
47
40
30
30
32
17
93
92
88
89
87
78
68
73
68
65
46
99
99
96
97
97
95
87
96
92
88
75
613
611
609
586
570
539
516
514
509
507
500
adva
nced
hig
h
inte
rmedia
te
low
average
gra
de e
ight
ma
them
atics
Singapore
Malaysia
Thailand
Indonesia
International
48
2
2
0
3
78
12
8
2
17
92
36
26
15
46
99
65
55
43
75
611
440
427
386
500
adva
nced
high
inte
rmedia
te
low
ave
rage
Singapore Math The CPA Approach, The Spiral
Approach and Emphasis on Relational
Understanding Globe Academy, London
J Bruner Enactive, Iconic, Symbolic
Representations
Edgewood Elementary School, New York
Greenville Elementary School, New York
Escuela de Guetamala, Chile
6
6
6
6
J Bruner Spiral Curriculum
Greenville Elementary School, New York
Bina Bangsa School, Indonesia
Z Dienes Play Structured Learning
Practice
Jenaplanschool Cleoplas, The Netherlands
x x x
x
x
L Vygotsky Interaction
Pathlight School, Singapore
Bina Bangsa School, Indonesia
Globe Academy, London
R Skemp Relational and Instrumental
Understanding
Using bar model to introduce solving
algebraic equations
Solve 7 – 3y = 1 .
7
3y 1
Using bar model to introduce solving
algebraic equations
Solve 7 – 3y = 1 .
7
3y 1
J Piager Assimilation, Accommodation
Keys Grade School, Manila
H Gardner Multiple Intelligences
Keys Grade School, Manila
Seely Place Elementary School, New York
Observing patterns and
making generalizations
involves reflection.
Find the value of 12.2 ÷ 4 .
Example 1
Answer : 3.05 [B1]
Singapore National Examination
12.20 4 3
12 0.20
.05
0.20 0
12.20
12 20 hundredths
Number Bond Method
Long Division Method
A show started at 10.55 a.m. and ended at 1.30 p.m. How long was the show in hours and minutes?
11 a.m. 1.30 p.m.
2 h 30 min
Answer : 2 h 35 min [B1]
Example 2
Find <y in the figure below.
360o – 210o = 150o
70 o 70 o
70 o
y
Example 3
Cup cakes are sold at 40 cents each. What is the greatest number of cup
cakes that can be bought with $95?
$95 ÷ 40 cents = 237.5
Answer: 237 cupcakes
Example 4
Mr Tan rented a car for 3 days. He was charged $155 per day and 60 cents for every km that he travelled. He paid $767.40. What was the total distance that he travelled for the 3 days?
$767.40 – 3 x $155 = $302.40
$302.40 ÷ 60 cents per km = 504 km
Example 5
“Mathematical problem solving is central to
mathematics learning.”
Ministry of Education 2006
“… including non-routine, open-ended and real-world
problems.”
Ministry of Education 2006
Parents Up In Arms
Over PSLE
Mathematics Paper TODAY’S 10 OCT 2009
SINGAPORE: The first thing her son did when he came out from
the Primary School Leaving Examination (PSLE) maths paper on
Thursday this week was to gesture as if he was "slitting his
throat".
"One look at his face and I thought 'oh no'. I could see that he felt
he was condemned," said Mrs Karen Sng. "When he was telling
me about how he couldn't answer some of the questions, he got
very emotional and started crying. He said his hopes of getting
(an) A* are dashed."
Not for the first time, parents are up in arms over the PSLE
Mathematics paper, which some have described as "unbelievably
tough" this year. As recently as two years ago, the PSLE
Mathematics paper had also caused a similar uproar.
The reason for Thursday's tough paper, opined the seven parents
whom MediaCorp spoke to, was because Primary 6 students were
allowed to use calculators while solving Paper 2 for the first time.
…
Said Mrs Vivian Weng: "I think the setters
feel it'll be faster for them to compute with a
calculator. So the problems they set are much
more complex; there are more values, more
steps. But it's unfair because this is the first
time they can do so and they do not know
what to expect!"
…
"The introduction of the use of calculators
does not have any bearing on the difficulty of
paper. The use of calculators has been
introduced into the primary maths curriculum
so as to enhance the teaching and learning of
maths by expanding the repertoire of learning
activities, to achieve a better balance between
the time and effort spent developing problem
solving skills and computation skills.
Calculators can also help to reduce
computational errors."
…
Another common gripe: There was not
enough time for them to complete the paper.
A private tutor, who declined to be named,
told MediaCorp she concurred with parents'
opinions. "This year's paper demanded more
from students. It required them to read and
understand more complex questions, and go
through more steps, so time constraints would
have been a concern," the 28-year-old said.
Trends in International Mathematics and Science
Study TIMSS
Students in the highest international benchmark are able to apply their knowledge in a variety of situations
and able to explain themselves.
“Skill proficiencies include the ability to use technology
confidently, where appropriate, for exploration and problem
solving.”
Ministry of Education 2006
1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16
17 18 19 20 21 22 23 24
25 26 27 28 29 30 31 32
33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48
49 50 51 52 53 54 55 56
Example 6
Table 1 consists of numbers from 1 to 56. Kay and Lin are given a plastic frame that covers exactly 9 squares of Table 1 with the centre square darkened.
Table 1 consists of numbers from 1 to 56. Kay and Lin are given a plastic frame that covers exactly 9 squares of Table 1 with the centre square darkened.
(a) Kay puts the frame on 9 squares as shown in the figure below.
3 4 5
11 13
19 20 21
What is the average of the 8 numbers that can be seen in the frame?
Table 1 consists of numbers from 1 to 56. Kay and Lin are given a plastic frame that covers exactly 9 squares of Table 1 with the centre square darkened.
(a) Kay puts the frame on 9 squares as shown in the figure below.
3 4 5
11 13
19 20 21
What is the average of the 8 numbers that can be seen in the frame?
Alternate Method 4 x 24 = 96 96 ÷ 8 = 12
3+4+5+11+13+19+20 = 96 96 ÷ 8 = 12
(b) Lin puts the frame on some other 9 squares. The sum of the 8 numbers that can be seen in the frame is 272. What is the largest number that can be seen in the frame?
1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16
17 18 19 20 21 22 23 24
25 26 27 28 29 30 31 32
33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48
49 50 51 52 53 54 55 56
Weiyang started a savings plan by putting 2 coins in a money box every day. Each coin was either a 20-cent or 50-cent coin. His mother also puts in a $1 coin in the box every 7 days. The total value of the coins after 182 days was $133.90. (a) How many coins were there altogether? (b) How many of the coins were 50-cent coins?
Example 7
three keys to successful implementation
assessment
Reference: Department of Education State of New York
teacher preparation
Teacher as a learner (professor as a
model)
Teacher as an observer of learning
(lesson study)
Teacher as reflective practitioner
(professional learning community)
Singapore teachers learn what they need to learn through an
approach that balances content and pedagogy.
teacher preparation
National Institute of Education
Singapore
The practice component is given emphasis – micro teaching,
practicum and lesson study.
teacher preparation
National Institute of Education
Singapore
There is an
emphasis on
teachers
solving the
problems
themselves
during the
course.
teacher preparation
Teachers learn from the
textbooks and teachers
guide.
teacher development
We learn from the Japanese method to help teachers
develop better skills in observing students. This is lesson
study.
teacher development
Princess Elizabeth Primary School
Singapore
TEDS-M Elementary Teachers
Content Knowledge TEDS-M Elementary Teachers
Pedagogical Content Knowledge
TEDS-M Findings
National Institute of Education, Singapore
Fuchun Primary School, Singapore
Edgewood Elementary School, New York
Bina Bangsa School, Indonesia
Keys Grade School, The Philippines
Kranji Secondary School, Singapore
leadership Mayor of Newark gave an inspirational message to
teachers attending professional development on
Singapore Math.
• What can I do as a teacher?
• What can my school do?
• What can the education schools do?
• What government support should be in place?
Slides are available at
www.banhar.blogspot.com
Singapore Math at Highline Public Schools March 2013 Yeap Ban Har yeapbanhar@gmail.com
The Merlion by Yeap Ken Min