Forum Letter
ST 12/2/2007

Some parents of primary school pupils seem to be confused about their children’s mathematics as taught by some teachers. From comments I gathered when tutoring Primary 6 pupils, it appears that model drawing methods have to be used in order to score more marks in the Primary School Leaving Examination (PSLE).

The use of algebra methods may lead to loss of marks as it is not encouraged nor recommended. However, algebra is part of the Primary 6 Maths syllabus. Some parents are not even aware that algebra questions have been set in past PSLE Maths papers.

Can the Ministry of Education clarify the following doubts:

Can students use different maths techniques like algebra if they prefer it to model-drawing?

An example of a question in which both methods can be used:

At a funfair, two-fifths of the visitors were women. There were three times as many men as children. If there were 90 more women than children, how many visitors were there at the funfair?

Will there be loss of marks if algebra is used instead of model-drawing methods?

Are model-drawing methods so important that they continue to be highly used in secondary schools?

Should we not teach students to be more creative by using different approaches in maths if these can help them understand the subject better and more easily?

Lim Boon Tong

*****

Forum Letter Reply
ST 17/2/2007

Mr 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).

The 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.

The 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.

The 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.

Other 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.

While 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.

We 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

Source : http://www.moe.gov.sg/media/forum/2007/20070217.htm

Its been a long time since I want to spruce up the outlook of my web. Super procrastinator! Finally squeezed out some time to do up the design. Will work on the layout …

String of 2 big balloons is 90cm
String of 5 small balloons is 1.2m
If both strings are of the same length, there would be 105 more small balloons than the big balloons. How many balloons are there altogether? Ans: 345

Mei and Lin were in a bicycle race. Mei was travelling at a constant speed of 20km/hr and they both did not change their speed. When Lin completed half the race, Mei was 3.5km ahead. Mei completed the race at 10.45am. What time did Lin complete the race? Ans: 11.06am

6 friends decided to rent computers from 2pm to 4.30pm. While 4 of them were playing, the other two would watch. If the cycle continues, and each of them played for equal number of minutes, how many minutes will each person get to play? Ans: 100 minutes

Sally baked some cookies to sell. 3/4 of them were chocolate cookies and the remaining were almond cookies. After she sold 5/6 of chocolate cookies and 210 almond cookies, she had 1/5 of the cookies left. How many cookies did she sell? Ans: 960

Curry puff shop sells puffs at $0.80 each. Offer:Buy 3 get 4th half price. If customer has $50, how many puffs can he buy if he buys as many as he can. Ans: 71 puff

Read : Parents up in arms again over PSLE Mathematics paper.

My two cents – Firstly, if all the smart students can solve all the problems then who will be the smarter and who will be the smartest ? Secondly, the question mentioned in the article is ‘nothing new’ as similar ones can be found in exam papers from ‘top ten schools’. (The most recent – ACS Prelim 2009 Q16)

In my classes, we call this type of questions, ‘Before – After’. Typically, an initial ratio, percentage, fractions is given (Before). Then something happen – sweets eaten, marbles lost, wateva! Finally, the end ratio, percentage, fractions is given. (After).

For my students, I teach them both methods but I highly recommend the ‘X-method’ (Algebra) for solving ‘Before-After’ questions. Modals can be time consuming!

There are two ways to solve the problem.

1) Modal Method (Step-by-Step Solution)

Step 1 : Jim bought some chocolates and gave half of it to Ken. Ken bought some sweets and gave half of it to Jim.

Step 2 : Jim ate 12 sweets and Ken ate 18 chocolates.

Step 3 : The ratio of Jim’s sweets to chocolates became 1:7 and the ratio of Ken’s sweets to chocolates became 1:4

Step 4 : Focus on the two BLUE parts. Both the BLUE parts (Jim’s Sweets & Ken’s Sweets) are the same because from the question, ‘Ken bought some sweets and gave half of it to Jim’. This means Ken and Jim have equal share of the sweets.

The modal can be redrawn to look like this:

Step 5 : Focus on the GREEN parts. Both GREEN parts (Jim’s chocolates and Ken’s chocolates) are the same because from the question, ‘Jim bought some chocolates and gave half of it to Ken’. This means Ken and Jim have equal share of the chocolates.

7u = (12 + 1u) + (12 + 1u) + (12 + 1u) + (12 + 1u) + 18

7u = 48 + 4u + 18

7u – 4u = 48 + 18

3u =66

1u = 22

Ken bought : (12 + 1u) + (12 + 1u) = (12 + 22) X 2 = 68

Ans : 68 sweets.

2) Algebra

Step 1 : Jim bought some chocolates and gave half of it to Ken. Ken bought some sweets and gave half of it to Jim.

This means Jim and Ken both has 1 unit of chocolate and 1 unit of sweets.

Jim                       Ken

1s :  1c                1s  :  1c

Step 2 : Jim ate 12 sweets and Ken ate 18 chocolates

Jim                       Ken

1s – 12 : 1c          1s : 1c – 18

Step 3 :   The ratio of Jim’s sweets to chocolates became 1:7 and the ratio of Ken’s sweets to chocolates became 1:4

Jim                       Ken

1s – 12 : 1c          1s : 1c – 18

X                   X           (This is what I coined the ‘X’-method, a common lingo in my class)

1 :  7             1 : 4

Equation 1 : 7s – 84 = 1c

Equation 2 :  4s = 1c – 18 or 4s + 18 = 1c

Solving the two equations simultaneously

7s – 84 = 4s + 18

7s – 4s = 18 + 84

3s = 102

s = 34

2s = 34 x 2 = 68

Ans : 68 sweets

ORAL carries a weightage of 15% of the PSLE English examination.

Oral components

• Reading Aloud (10 marks)

• Picture Discussion (10 marks)

• Conversation (10 marks)

Guidelines for Reading

1. Read the text throgh silently to determine the text type. For stories, read expressively. For exposition, read authoritatively and for advertisements, read in a light-hearted and engaging manner.
2. Read aloud to yourself at least twice during the silent reading time before entering the examination room. This helps to reduce word recognition errors and increases expression and fluency.
3. Bring your voice down at the end of a sentence. Keep your voice up when there is a question mark.
4. Read lou enough for the examiners to hear you.
5. Read fluently, with appropriate pauses and without hesitation.
6. Some common errors in pronunciation : mother not mader, thing nor ting, time not tam, however not howrever
7. Pay attention to word endings. Do not drop them. collect, watched, just, loves, took.
8. Do not rush through the passage. Read clearly and calmly. If you trip over a word, just read it again.
9. For words you cannot pronounce, settle on one pronunciation and stick to it.
10. Do not point at the words with your finger as you read. If you need to keep track of what you read, place your finger at the edge of the paper and move it down the page as you read.

Guidelines for Picture Discussion

1. Describe the SETTING, action and people. Eg : Five children are performing on the stage. One of the performers dropped his musical instrument. In the front row of the audince, a man is tanding up and he looks anxious.
2. Interpret with your one OPINION. Eg This man is probably the boy’s father. From his gestures, he seemed to be giving words of encouragement to his son.
3. EXPLAIN further. Eg Given the situation, I am sure any parent would be anxious. If I were the boy’s father, I would be anxious too.
4. Do not say, “I finish” at the end of your task. Give a short wrap-up to the discussion. Eg: Withe the encouragement given by the father, I think the boy will pick up his trumpet and carry on with his performance.
5. In your discussion, use the PRESENT TENSE. Use past tense only when you cite past incidences or experiences.
6. Do not point at the details in the picture with your finger. Use suitable phrases to describe their location.
7. Suggested expressions to show tentativeness of observations. Eg probably, likely, perhaps, possibly, could be, maybe, seems, looks as if, looks like.
8. Suggested expressions to introduce ideas when intepreting and explianing. Eg I believe, I wonder why, It is likely that, This may lead to, I imagined that, I think I would, I can almost, This may cause, If I were.

Conversation

1. Do not look down. Establish eye contact with the examiner.
2. Listen carefully to the question asked. Respond relevantly and appropriately.
3. Speak in complete sentences. Do not use slang.
4. Do not stop at “Yes” or “No” in your answers. Elaborate on your responses wthout prompting from the examiners.
5. Smile and show interest. Respons enthusaitically. Eg: Yes, I would like to …, In Fact, I have just …..
6. When in doubt, clarify by asking, Could you please repeat your question?
7. Use dialogue fillers such as “Well….”, when you need time to process your thoughs.
8. If you are given a topic you know nothing about, do not panic. Draw ideas from the picture stimulus to help elaborate on your points. Or think about how you can talk around the topic. Eg : No. I do not own a pet but my mom used to keep a pet dog ….
9. Conversation is not a test ho how much you know about a topic. It is to test your fleuncy in the spoken language. Interact with examiners and keep the converstaion alive by introducing ideas as you go along. Do not depend on examiners to promt you.

Download : Oral Examination score sheet for pratices