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

I was casually browsing through the SISTIC programme booklet on the way back to class when Teri ran up to me and  exclaimed excitedly that she will be performing in one of the events. She pointed me to ‘Tiger Burning” and the synopsis read,  ‘The production is inspired by the real life escape of a three-legged Sumatran tiger from a poacher’s snare… captures urban street dance alongside traditional dance in a young people’s production that calls awareness to the themes of environmental concern, cultural appreciation, and communal empowerment.’

Wow! My student performing at the Esplanade! So I bought tickets for my whole family to support her.

We almost didn’t make it for the show. My boys were not well and I was pretty worn out taking care of them. The performance was great! Teri looked so cute in her tiger costume. Unfortunately, she changed out of them before we could take a photo.

A relative commented, “Wah, these days be teacher not easy huh? Must work on Sunday! Some more come out with your own money!”

True enough, money and time was spent but it goes along way to build good rapport with students and to encourage co-corriculum activities among the young. It was also a family outing for us and I took the opportunity to educate my boys on concert etiquette. My boys sat through and enjoyed the perfomance very much.

So, I would say, it was well worth the money. Well worth the time.