AME PSLE Seminar
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Transcript of AME PSLE Seminar
PSLE Mathematics Seminar
Association of Mathematics Educators
http://math.nie.edu.sg/ame
Yeap Ban HarNational Institute of Education
Nanyang Technological University
Part 1This section explains the PSLE format.
PSLE Mathematics
PSLE Mathematics
Paper 1 (50 min)
Type Mark Value
Number
MCQ 1 mark 10 (10%)
MCQ 2 marks 5 (10%)
SAQ 1 mark 10 (10%)
SAQ 2 marks 5 (10%)
Paper 2 (1 hr 40 min)
Type Mark Value
Number
SAQ 2 marks 5 (10%)
LAQ3 marks4 marks5 marks
13 (50%)
PSLE Foundation Mathematics
Paper 1 (1 hr)
Type Mark Value
Number
MCQ 1 mark 10 (10%)
MCQ 2 marks 10 (20%)
SAQ 2 marks 10 (20%)
Paper 2 (1 hr 15 min)
Type Mark Value
Number
SAQ 2 marks 10 (20%)
LAQ3 marks4 marks5 marks
8 (30%)
Part 2This section explains the curriculum that
the PSLE is based on.
PSLE Mathematics is Based on a Problem-Solving Curriculum
rationale of the curriculum
The rationale of teaching mathematics is that it is “a good vehicle for the development and
improvement of a person’s intellectual competence”.
Part 3This section explains that problem solving
is a basic ability in the PSLE.
“Mathematical problem solving is central to
mathematics learning.”
Ministry of Education 2006
Ali paid for a 85-cent pen with a $5 note.How much change should he get?
Example 1
Answer: $__________
A show started at 10.55 a.m. and ended at 1.30 p.m. How long was the show in hours and minutes?
Example 2
Prawns are sold at $1.35 per 100 g at a market. What is the price of 1.5 kg of prawns?
Example 3
$13.50 + $6.75 = $20.25
During a sale, mugs are sold in sets of 3 for $1.45. How much must Bala pay for buying 15 mugs during the sale?
Example 4
$1.45 x 5 = $14.50 ÷ 2 = $7.25
Sam had 295 eggs. He packed all the eggs into boxes of 9 with some left over. How many eggs are left over?
Example 5
295 ÷ 9 = (30 + 2) remainder 7
7 eggs are left over
295
270 25
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?
Example 5
$767.40 – 3 x $155 = $302.40
$302.40 ÷ 60 cents per km = 504 km
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?
Example 5
767.40 – 3 x 155 = 302.40
302.40 ÷ 0.60 = 504
He travelled 504 km.
Find <y in the figure below.
360o – 210o = 150o
70 o
70 o
70 o
y
Example 6
“Mathematical problem solving is central to
mathematics learning.”
Ministry of Education 2006
Part 4This section explains that there are other
competencies in mathematics learning e.g. practical skills.
Basic Skillscomputation and procedures is not
everything
The height of the classroom door is about __.
(1) 1 m(2) 2 m(3) 10 m(4) 20 m
Example 7
Practical Skillswritten examinations may include bits of
practical tasks
Possibilities
ExampleFind the area of the cover page of the examination paper.
Part 5This section explains the key competencies
in solving challenging problems.
““… including non-routine, open-ended and real-world
problems.”
Ministry of Education 2006
Example 8
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?
Example 10
chocolate cookies
almond cookies
210
1/5
5/83/8
3/8 – 1/5 = 7/40 210
1/40 30
32/40 960
She sold 960 cookies.
Example 11
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.
chocolates
Jim
Ken
sweets
12
12
3 parts 12 + 12 + 12 + 12 + 18 = 661 part 22
Half of the sweets Ken bought = 22 + 12 = 34So Ken bought 68 sweets.
18
12
12
12
12
18
Visualization – an intellectual competence - is one of the most
important ability in solving problems
Learning Basic Skillsemphasis on visualization in the learning
process
My Pals Are Here! Mathematics 4A
Shaping Maths 2A
Shaping Maths 4B
Catholic High School (Primary)
visualization
Wellington Primary School
Move 3 sticks to make 2 squares.
Task
Move 3 sticks to make 2 squares.
Task
Move 3 sticks to make 2 squares.
Photo: Princess Elizabeth Primary School
Division
My Pals Are Here! Mathematics 1B
visualization
Scarsdale Middle School New York
Primary Mathematics Standards Edition Grade 6
Primary Mathematics Standards Edition Grade 6
How to make sure the butterfly cannot fly
How do you get a butterfly?
First there is the egg which hatches into a caterpillar. The caterpillar eats and grows. At the right time, it makes a cocoon out of its own body. While in the cocoon, the caterpillar changes into a butterfly.
When the butterfly is ready, it starts to break through the cocoon. First a hole appears. Then the butterfly struggles to come out through the hole. This can take a few hours.
If you try to "help" the butterfly by cutting the cocoon, the butterfly will come out easily but it will never fly. Your "help" has destroyed the butterfly.
The butterfly can fly because it has to struggle to come out. The pushing forces lots of enzymes from the body to the wing tips. This strengthens the muscles, and reduces the body weight. In this way, the butterfly will be able to fly the moment it comes out of the cocoon. Otherwise it will simply fall to the ground, crawl around with a swollen body and shrunken wings, and soon die.
If the butterfly is not left to struggle to come out of the cocoon, it will never fly.
We can learn an important lesson from the butterfly.
Lim Siong Guan Head, Civil Service
How to make sure the butterfly cannot fly
How do you get a butterfly?
First there is the egg which hatches into a caterpillar. The caterpillar eats and grows. At the right time, it makes a cocoon out of its own body. While in the cocoon, the caterpillar changes into a butterfly.
When the butterfly is ready, it starts to break through the cocoon. First a hole appears. Then the butterfly struggles to come out through the hole. This can take a few hours.
If you try to "help" the butterfly by cutting the cocoon, the butterfly will come out
easily but it will never fly. Your "help" has destroyed the butterfly.
The butterfly can fly because it has to struggle to come out. The pushing forces lots of enzymes from the body to the wing tips. This strengthens the muscles, and reduces the body weight. In this way, the butterfly will be able to fly the moment it comes out of the cocoon. Otherwise it will simply fall to the ground, crawl around with a swollen body and shrunken wings, and soon die.
If the butterfly is not left to struggle to come out of the cocoon, it will never fly.
We can learn an important lesson from the butterfly.
Lim Siong Guan Head, Civil Service
Part 6The ability to monitor thinking as students read – metacognition as well as the ability to show working – communication are the
other important competencies.
Challenging MCQsfor problems that are difficult for students to
communicate solution methods
Ann, Beng and Siti each had some money at first. Ann gave Beng $0.50. Beng then gave Siti $0.75. Siti spent $0.25 on a ruler. At the end, they had $3 each. What is the difference between the amount of money that Ann and Siti had at first?
(1) $1.00
(2) $0.50
(3) $0.75
(4) $1.25
Ann $3
Beng $3
Siti $3 $3.25 $2.50
$3.75 $3.25
$3.50
Part 7This section explains the importance of
number sense and the role of mental computations in developing number sense.
“Although students should become competent in the various mathematical skills,
over-emphasising procedural skills without understanding the underlying mathematical
principles should be avoided.”
Ministry of Education 2006
Find the value of 12.2 ÷ 4 .
Example 5
Find the value of 6005 – 1947 .
Example 5
Find the value of(a) 99 + 97(b) 56 ÷ 8
Find the value of(a) 200 – 53 (b) 9 x 9
Find the value of(a) 73 – 15 (b) 42 ÷ 7
Find the value of(a) 169 + 34(b) 8 x 7
Basic Skillsmental computation is an important part of
the curriculum
Basic Skillsmental strategies strengthen visualization
ability
Part 8This section explains the role of the
calculator – it is just a computing device. Thinking is still what students need to do.
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
Basic Skill Item
Basic Application Item
Part 9This section summarizes the five key
competencies in mathematics.
Five Key Competencies Visualization Number Sense Metacognition Communication Patterns – this is shown on the next slide
Part 10Must one knows a formula to calculate the
area of a trapezium.
3 cm 5 cm
3 cm
7 cm
With visualization, one does not need to know a formula to calculate the area of a trapezium.
9 cm2
6 cm2