PSLE - New Format for Maths
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Mandy-Alex:
Hi Mandy-AlexDear all,
One of the problems here in Singapore for PR 6 pupils - algebra is not enough taught. They teach a ratio, but do not teach them that A/B=C/D is the same as AxD=BxC and the same as A/C=B/D. Every time when I was trying to teach my gal how to solve the problems using algebra, she was telling me \"No, the teacher did not solve that way-by algebra\". Not teaching algebra they / I mean MOE / did not give them a chance to choose the method. Models, models and again models. Algebra is an abstraction for the pupils here. Yes, I know, for PSLE, its important to get the correct answer-the method is not important. But how to use algebra like a method if you are not confident enough with it? The other problem-geometry, again insufficiently taught.
One more thing. Why the Maths Paper is not published yet ? Anybody to answer ? In my country, even under the blackout- 25 years ago, it was possible to see all of the MATHS Problems from the Paper and their solving in the newspapers on the next day, published by Ministry of Education. So I am waiting to see 48 Maths problems and there solving in The Newspaper.
Best to all of our Pr 6 children today for the Science paper!
The school teachers here not only did they not teaching their pupils using algebra, they even discourage and \"prohibit\" them to use algebra. Whenever my girl encounters more complex maths questions found in her homework, she would use algebra to solve them. When the homework are marked and returned, you can even see the teacher remarks written on the paper \"USE MODEL\". When the teacher goes through the difficult questions, if she happens to ask my girl for the answer and method used, she would comment \" Algebra again! any pupils with other better method?\" Nobody raises their hands.
My gal likes to use both model and algebra solving methods. She will use algebra whenever she hits problems on models such as the \"cutting up parts\" looks big, messy, odd fraction, etc, then she will immediately cancelled her model drawing or ratio method and use algebra instead. For this PSLE maths paper, I even told her beforehand to use half of a page for her usual workings and make sure that she has at least half page left, in case, she needs it for algebra working.
In fact, some of the so-called model drawing method is similar to algebra, just that instead of using “x” or “y”, they use big units/small units. Somehow I feel that the teachings of maths in school do not equip them the skills to answer those complex questions. Model drawing is only good for the lower primary level and non-complex questions.
And to your question on \"Why the Maths Paper is not published in the Newspaper yet?\" For so many years, I never see the PSLE maths paper published in the papers, so no need to wait . Even in the 5 years PSLE Maths Booklet, not all questions are published, leaving out the so-called challenging ones. -
Augmum:
My kid now is P5. So can i ask whether algebra method be use in PSLE maths paper? Will student be marked as wrong if they use algebra instead of model?
Hi Mandy-AlexMandy-Alex:
Dear all,
One of the problems here in Singapore for PR 6 pupils - algebra is not enough taught. They teach a ratio, but do not teach them that A/B=C/D is the same as AxD=BxC and the same as A/C=B/D. Every time when I was trying to teach my gal how to solve the problems using algebra, she was telling me \"No, the teacher did not solve that way-by algebra\". Not teaching algebra they / I mean MOE / did not give them a chance to choose the method. Models, models and again models. Algebra is an abstraction for the pupils here. Yes, I know, for PSLE, its important to get the correct answer-the method is not important. But how to use algebra like a method if you are not confident enough with it? The other problem-geometry, again insufficiently taught.
One more thing. Why the Maths Paper is not published yet ? Anybody to answer ? In my country, even under the blackout- 25 years ago, it was possible to see all of the MATHS Problems from the Paper and their solving in the newspapers on the next day, published by Ministry of Education. So I am waiting to see 48 Maths problems and there solving in The Newspaper.
Best to all of our Pr 6 children today for the Science paper!
The school teachers here not only did they not teaching their pupils using algebra, they even discourage and \"prohibit\" them to use algebra. Whenever my girl encounters more complex maths questions found in her homework, she would use algebra to solve them. When the homework are marked and returned, you can even see the teacher remarks written on the paper \"USE MODEL\". When the teacher goes through the difficult questions, if she happens to ask my girl for the answer and method used, she would comment \" Algebra again! any pupils with other better method?\" Nobody raises their hands.
My gal likes to use both model and algebra solving methods. She will use algebra whenever she hits problems on models such as the \"cutting up parts\" looks big, messy, odd fraction, etc, then she will immediately cancelled her model drawing or ratio method and use algebra instead. For this PSLE maths paper, I even told her beforehand to use half of a page for her usual workings and make sure that she has at least half page left, in case, she needs it for algebra working.
In fact, some of the so-called model drawing method is similar to algebra, just that instead of using “x” or “y”, they use big units/small units. Somehow I feel that the teachings of maths in school do not equip them the skills to answer those complex questions. Model drawing is only good for the lower primary level and non-complex questions.
And to your question on \"Why the Maths Paper is not published in the Newspaper yet?\" For so many years, I never see the PSLE maths paper published in the papers, so no need to wait . Even in the 5 years PSLE Maths Booklet, not all questions are published, leaving out the so-called challenging ones. -
Can use algebra and my personal view is should always use it for complex question. Model is very good for tricky question
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Augmum:
Yup. MOE should be very clear on this issue of using algebra. I bet some of the PSLE students who found the paper easy used algebra to solve. While teachers discourage students from using algebra to solve complex qns. , they are allowed to use it during exams if I am not mistaken. This would certainly create a disadvantage for those who are not taught how to use it.Hi Mandy-Alex
The school teachers here not only did they not teaching their pupils using algebra, they even discourage and \"prohibit\" them to use algebra. Whenever my girl encounters more complex maths questions found in her homework, she would use algebra to solve them. When the homework are marked and returned, you can even see the teacher remarks written on the paper \"USE MODEL\". When the teacher goes through the difficult questions, if she happens to ask my girl for the answer and method used, she would comment \" Algebra again! any pupils with other better method?\" Nobody raises their hands.
My gal likes to use both model and algebra solving methods. She will use algebra whenever she hits problems on models such as the \"cutting up parts\" looks big, messy, odd fraction, etc, then she will immediately cancelled her model drawing or ratio method and use algebra instead. For this PSLE maths paper, I even told her beforehand to use half of a page for her usual workings and make sure that she has at least half page left, in case, she needs it for algebra working.
In fact, some of the so-called model drawing method is similar to algebra, just that instead of using “x” or “y”, they use big units/small units. Somehow I feel that the teachings of maths in school do not equip them the skills to answer those complex questions. Model drawing is only good for the lower primary level and non-complex questions.
And to your question on \"Why the Maths Paper is not published in the Newspaper yet?\" For so many years, I never see the PSLE maths paper published in the papers, so no need to wait . Even in the 5 years PSLE Maths Booklet, not all questions are published, leaving out the so-called challenging ones.
On the other hand if algebra were strongly allowed in the future, I foresee more difficult and complex qns. to follow suit. :stupid: -
atutor2001:
All the more they need to be working hard practising the use of models. I see models as the visual expression of the question in pictorial form. I know some students can visual the qn mentally but most kids need to see it clearly in written form.endingteen:
actually i hae no idea why they introduced the use of calculators into the PSLE. i mean i do not see the point in making tough questions to cater for the use of the calculator. i remember my psle being a test for us to use your mental calculations and the 'model' method to solve questions. calculators are actually only needed in the upper secondary years.
Some people children cannot count mentally, so must help them lah :oops:
As for calculator, as I have shared earlier, it makes the students lazy to think and analysize complex questions. They would rathe tikam n tikam until they feel that a certain answer looks reasonable correct. :?: :?: :?: -
Vanilla Cake:
Hi Vanilla Cake,Hi kohjl,
Q18 of paper 2 (last question) is something like this and I think that your son has got the right answer ( 68 ).Here it goes (not in exact words):
Q18
Jim bought some chocolates and gave half of it to Ken. Ken bought some sweets and gave half of it to Jim.Jim ate 12 sweets and Ken ate 18 chocolates.The ratio of Jim's sweets to chocolates became 1 : 7 and the ratio of Ken's sweets to chocolates Ken became 1:4.How many sweets did Ken buy?
Suggested solutions
Draw a model to show \"after eating\" scenario, \t\t
\t\t\t
Ratio of Jim's sweets to chocolate (1:7)
Sweets []
Chocos [][][][][][][]
Ratio of Ken's sweets to chocolate (1:4)
Sweets [] +12 (+12 refers to the sweets eaten by Jim)\t\t\t
Chocos [][][][] (+12x4) - x 4 times
\t
Both amount of Chocolates are the same,so
(7-4) units = (12x4) + 18 (18 chocolates were eaten by Ken)
3 units = 66
1 unit = 22\t\t
\t\t\t
Amount of sweets bought by Ken->(unit +12)x2=(22+12) x 2 =68
Or use algebra which is easier.
Assume that sweets that Ken bought was S and chocolates that bought by Jim was C.
Before both of them ate, they had:
Ken -> 0.5C + 0.5S
Jim -> 0.5C + 0.5S
as each of them gave 1/2 to each other.
Jim ate 12 sweets and the ratio of Jim's sweets to chocolates became 1:7.
(0.5S-12)/0.5C = 1/7
3.5S-84=0.5C
Ken ate 18 chocolates and the ratio of Ken's sweets to chocolates became 1:4.
0.5S/(0.5C-18 ) = 1/4
(0.5C-18 ) / 0.5S = 4
0.5C-18 = 2S
3.5S-84-18=2S
3.5S-2S = 84+18
1.5S = 102
S = 102/1.5 = 68
Amount of sweets bought by Ken-> 68
There is a much easier way of solving it with ratios (and algebra).
Jim
S : C
1 : 7
(+12)
x : y
Ken
S : C
1 : 4
(+18 )
x : y
If you cross-multiply this, you get:
y = 7x-84 y + 18 = 4x
7x-84 = 4x-18
3x = 102
x = 34 (half total number of sweets)
34 X 2 =68
Hope I helped!
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Muffins:
That is the problem. Alegbra is easier to solve this kind of problem than model method. Some teachers encourage and train their students but others don't. :stupid: :stupid: :stupid:
Hi Vanilla Cake,Vanilla Cake:
Hi kohjl,
Q18 of paper 2 (last question) is something like this and I think that your son has got the right answer ( 68 ).Here it goes (not in exact words):
Q18
Jim bought some chocolates and gave half of it to Ken. Ken bought some sweets and gave half of it to Jim.Jim ate 12 sweets and Ken ate 18 chocolates.The ratio of Jim's sweets to chocolates became 1 : 7 and the ratio of Ken's sweets to chocolates Ken became 1:4.How many sweets did Ken buy?
Suggested solutions
Draw a model to show \"after eating\" scenario, \t\t
\t\t\t
Ratio of Jim's sweets to chocolate (1:7)
Sweets []
Chocos [][][][][][][]
Ratio of Ken's sweets to chocolate (1:4)
Sweets [] +12 (+12 refers to the sweets eaten by Jim)\t\t\t
Chocos [][][][] (+12x4) - x 4 times
\t
Both amount of Chocolates are the same,so
(7-4) units = (12x4) + 18 (18 chocolates were eaten by Ken)
3 units = 66
1 unit = 22\t\t
\t\t\t
Amount of sweets bought by Ken->(unit +12)x2=(22+12) x 2 =68
Or use algebra which is easier.
Assume that sweets that Ken bought was S and chocolates that bought by Jim was C.
Before both of them ate, they had:
Ken -> 0.5C + 0.5S
Jim -> 0.5C + 0.5S
as each of them gave 1/2 to each other.
Jim ate 12 sweets and the ratio of Jim's sweets to chocolates became 1:7.
(0.5S-12)/0.5C = 1/7
3.5S-84=0.5C
Ken ate 18 chocolates and the ratio of Ken's sweets to chocolates became 1:4.
0.5S/(0.5C-18 ) = 1/4
(0.5C-18 ) / 0.5S = 4
0.5C-18 = 2S
3.5S-84-18=2S
3.5S-2S = 84+18
1.5S = 102
S = 102/1.5 = 68
Amount of sweets bought by Ken-> 68
There is a much easier way of solving it with ratios (and algebra).
Jim
S : C
1 : 7
(+12)
x : y
Ken
S : C
1 : 4
(+18 )
x : y
If you cross-multiply this, you get:
y = 7x-84 y + 18 = 4x
7x-84 = 4x-18
3x = 102
x = 34 (half total number of sweets)
34 X 2 =68
Hope I helped!
Unfair lor to those 'unalegbraic' students liao. MOE must make it clear to encourage or disallow in future. -
Yes I agree. My girl’s teacher also did not teach her much on algebra. I am the one trying to teach her to solve using algebra but am afraid will confuse her so dare not teach too much. For kids whose parents are secondary school maths teachers, i am sure it is a breeze for them to learn to solve using algebra. certainly some unfairness here but really, no one is stopping anyone from teaching the kids any method so long it will lead to problem solving…
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[quote]MOE must make it clear to encourage or disallow in future[/quote]
MOE cannot disallow the use of algebra because algebra is one of the topics (in fact the first topics) to be taught in P6 maths. Just that the pupils only learn how to form algebraic expressions.
regarding the question whether algebra can be used in PSLE maths, MOE had given an official reply responding to one of the ST forum letter in 2007.
17 Feb 2007
Different Approaches Taught for Mathematics Techniques
1.\tMr Lim Boon Tong had sought clarification on whether mathematics techniques like algebra, other than the model drawing method, could be used in the Primary School Leaving Examination (PSLE) Mathematics. (“Can algebra be used to solve PSLE maths problems”, The Straits Times, 12/2).
2.\tThe model drawing method is a powerful approach for problem solving and learning mathematical concepts. By drawing models, pupils can represent the mathematical relationships in a problem pictorially. This helps them understand the problem and plan the steps for the solution.
3.\tThe pictorial form also helps pupils visualise what could otherwise be abstract concepts. In this way, model drawing supports the learning of fractions, ratio and percentages. Pupils will find model drawing useful when they solve problems involving these concepts in Primary Five and Six.
4.\tThe model drawing method is thus a developmentally sound approach for young children. It is recognised internationally as an effective way for young children to learn problem solving and to have early exposure to algebraic concepts. At Primary Six and Secondary One, pupils can draw upon their earlier experience of using models to help them understand algebraic relationships in problems.
5.\tOther than the model drawing approach, pupils are also taught different problem solving methods. They are encouraged to try different approaches and have the flexibility to choose the method that works best for them in solving the problems. They are also encouraged to present their solutions clearly so that these can be understood.
6.\tWhile pupils are not required to use algebra to solve word problems in the PSLE Mathematics, they are also not restricted to the use of any one particular method. In the marking of PSLE Mathematics, all mathematically correct solutions are acceptable and there is no loss of marks if a correct algebraic method is used.
7.\tWe thank Mr Lim for his feedback.
Ho Peng (Ms)
Director, Curriculum Planning and Development
Ministry of Education
Tan Yap Kwang
Chief Executive
Singapore Examinations and Assessment Board -
To p5 parents, train your kids algebra if he or she a high-ability learner !
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