Singapore Primary Math Explained sc-math

More than one way to solve math problems

Page 5 of 5

Observations

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There is a danger that some pupils will repeatedly use a simpler or more familiar problem solving strategy such as 'guess and check' to the exclusion of others. This is especially so at the lower levels where the math problems are necessarily simpler and could therefore be easily solved by simpler problem solving strategies. However, the pupil's favourite problem solving strategy may not always be suitable for the more varied and challenging math problems encountered at the higher levels. For example, guess and check may not be the best strategy to solve the following math problem:

Peter has a bag containing a mixture of white, blue and red marbles. The number of red and blue marbles equals 3/4 of the white marbles. 1/3 of the red marbles + 1/5 of the blue marbles equals 1/6 of the white marbles. What is the ratio of the number of white, blue and red marbles?

Pupils who neglected to develop their proficiency in the various problem solving strategies at the lower levels will find it even tougher to use these strategies for the challenging math problems.

There are also pupils who often attempt to use algebra (probably taught by parents or tutors) to solve math problems. As mentioned earlier, pupils are NOT penalised for using algebra if they get the correct answer. However, as the Singapore Primary Math syllabus only covers introductory algebra at primary six, the average pupil may not have sufficiently developed their mental skills to apply algebraic concepts to solve challenging math problems. Parents should therefore assess their child's ability to understand algebraic concepts before teaching them algebra.

As with the other problem solving strategies, algebra may not always be the best strategy for solving math problems. Pupils knowing some algebra may be tempted to solve the following math problem algebraically. Should they have considered other problem solving strategies?

The product of 4 consecutive numbers is 1608. What are the 4 numbers?

Closing remarks

At the primary level, pupils should broaden their mind by striving to be proficient in the various problem solving heuristics. The cognitive skills and knowledge gained from learning and applying the various strategies to solve math problems serves as a strong foundation for them to better understand the more advanced or complicated concepts introduced at the higher levels.

Thinking and problem solving skills are necessary and important skills not only for students at all levels, but also in the corporate world. The importance of problem solving skills was highlighted in an article in the "Today" newspaper (13 July) where Professor David N Smith, vice dean at Harvard who will become law dean at The Singapore Management University on 1 Aug 2007, was reported to have said that "When I speak to law firm partners around the world, or CEOs of companies, and I ask 'what do you look for most in your lawyer', they almost invariably say, 'the ability to solve problems'."

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page 1 of 1 1 comment

#1, 31 Jul 07 - 06:50pmbhchia

great way of looking at it.

another way of visualizing from reasoning is to start with mid-point of 150 boxes each, ie. 150 x 5 kg = 750kg and 150 x 3 kg = 450kg, which gives a delta of 300kg.but given condition is 380 kg (difference of 80kg) more of 5-kg boxes than 3-kg boxes, means more 5 kg boxes than 3-kg. since for every 3-kg box taken out we add a 5-kg, nett increase of one 5-kg and backing out one 3-kg results in a nett increase of 8kg..hence adding 10 boxes of 5-kg (10 x 8kg = 80kg) from 150 boxes, giving 160 x 5-kg and 140 x 3-kg...ie. 1220 kg in total.
160 x 5 = 800 kg
140 x 3 = 420 kg
diff = 380 kg.

cheers

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