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Posted on : 2011-08-10

Part 2

The word ‘heuristic’ is taken directly from the Greek verb, heuriskein which means ‘to discover’. In Mathematics, there are usually different ways to go about solving problem sums. These ways or methods are known as heuristics.

Heuristics can be divided into 4 main types, which another 2 types would be discussed in this article.

Three: Going through the process

·         The heuristic ‘act it out’ requires pupils to use physical objects or manipulatives to represent information. This skill is used to introduce new concepts and to allow pupils to explore the concepts using manipulatives.

 Example:   The figure is made of 17 sticks. Move 4 sticks to form 8 squares.     Solution:

Pupils can use matchsticks to represent the information and use the matchsticks to find the solution to the problem.

·        Pupils can apply the ‘work backwards’ method when given a problem that provides the final result and that requires them to find the initial quantit

 Example: There were some chocolates in a basket. Michael and three of his friends took 8 chocolates each. 25 chocolates were given to Shirley. There were then 11 chocolates left in the basket. How many chocolates were there in the basket at first? Solution: Using the ‘work backwards’ method, first find the number of chocolates taken away by Michael and his three friends. 4 × 8 = 32 chocolates Then, find the total number of chocolates taken away from the basket. 32 + 25 = 57 chocolates Number of chocolates in the basket at first = 57 + 11 = 68 chocolates

·        Pupils can use the ‘before-after concept’ for problems that provide information given before and after the event to find the unknown. This skill allows pupils to compare the information and relate different events together to solve the problems.

 Example: Jacky had \$56 more than Jill. When he spent \$108, Jill had thrice as much as what he had left.  How much did Jacky have at first?   Solution:       2 units → \$108 - \$56 = \$52     1 unit → \$52 ÷ 2 = \$26   \$26 + \$108 = \$134 Jacky had \$134 at first.

Four: Changing the problem

·        By restating a problem in another way, pupils can view the problem in another perspective.

 Example: Find the sum of 10 + 12 + 14 + … + 146 + 148 + 150. Solution:                    There are 75 numbers in the sum 2 + 4 + 6 + … + 146 + 148 + 150.   There are 4 numbers in the sum 2 + 4 + 6 + 8. 75 – 4 = 71 Hence, there are 71 numbers in the sum 10 + 12 + 14 + … + 146 + 148 + 150.        There are 35 pairs of 160 and a ‘80’. 10 + 12 + 14 + … + 146 + 148 + 150 = 35 × 160 + 80  = 5680

·        When facing a complex problem, pupils can split the problem into smaller parts and start by solving the simpler parts. After doing so, the problem is simplified and solving the problem is much easier.

Thus, do try to keep in mind the various heuristics and apply them when you are doing problem sums. With regular practice, you will be able to handle problem sums with ease.

Written by Gui Yan Tong

To understand more about the other 2 types covered in Part 1, please click here.

 Check out the series "Use of Heuristics in Problem Solving" by EPH and have more practice on the different types of heuristics

Extra!

For more pointers on Model Drawing and Guess and Check, check out these related articles at the Popular Community:

Posted on : 2011-08-10

Part 1

The word ‘heuristic’ is taken directly from the Greek verb, heuriskein which means ‘to discover’. In Mathematics, there are usually different ways to go about solving problem sums. These ways or methods are known as heuristics.

Heuristics can be divided into 4 main types, which will be covered in this 2-part article.

One: Giving a representation

·         Pupils can transform word problems into pictorial representations and represent information with a diagram/model. This skill helps pupils to understand the question better when they see the visual representation of the word problems.

·         A systematic list should be made for word problems that require pupils to identify patterns such as repeated numbers or a series of events that repeat. This skill helps pupils in identifying patterns easily as the list organises all possible answers systematically.

 Example:   Michele saved \$150 on the first month. On the second month, she saved \$60 more than the first month.   On the third month, she saved \$70 more than the second month. On the fourth month, she saved \$55 more than the third month. How much did she save in four months? Solution: Making a list: 1st month → \$150 2nd month → \$150 + \$60 = \$210 3rd month → \$210 + \$70 = \$280 4th month → \$280 + \$55 = \$335    Total amount saved = \$150 + \$210 + \$280 + \$335                                = \$975  She saved \$975 in four month

Two: Making a calculated guess

·         The ‘guess and check’ method is used for word problems when certain information is lacking. It requires them to make a guess first and check it, and making subsequent guesses and checks until the correct answer is derived. It is often used together with a systematic list as it helps pupils to narrow down the possibilities within a short time frame.

Example:

Jenny has a total of 7 dogs and parrots. The animals have 20 legs altogether.

How many dogs does she have?

Solution:

Using the ‘guess and check’ method,

 Number of dogs Number of legs Number of parrots Number of legs Total number of legs Check 1 1 x 4 = 4 6 6 x 2 = 12 4 + 12 = 16 X 2 2 x 4 = 8 5 5 x 2 = 10 8 + 10 = 18 X 3 3 x 4 = 12 4 4 x 2 = 8 12 + 8 = 20 √
She has 3 dogs.

·         The ‘look for patterns’ method is usually used by pupils when they have to identify a certain pattern in a number sequence.

Example:

 12 4 5 13 11 9 16 18 16 12 3 X

Solution:

Making a list of possibilities:

12 - 4 + 5 = 13

11 - 9 + 16 = 18

16 - 12 + 3 = 7

The value of X is 7.

Hence by using the systematic list, it is more effective to find the underlying pattern.

Written by Gui Yan Tong

 Check out the series "Use of Heuristics in Problem Solving" by EPH and have more practice on the different types of heuristics

Extra!

For more pointers on Model Drawing and Guess and Check, check out these related articles at the Popular Community:

Posted on : 2011-04-08

This is a tricky question that all Chinese educators in Singapore seek to answer. With the MOE’s increasing emphasis on Mother Tongue as well as the increasing usage of Chinese language over the years, Chinese educators in Singapore are striving to get more pupils to be proficient in the language. Without a doubt, the lack of general interest in Chinese language proves to be the major obstacle for pupils. However, parents can play an instrumental role in driving the interest in Chinese learning.

Pictures speak a thousand words

A pupil once told me that seeing rows and rows of Chinese characters naturally drove her to sleep. I do not quite agree with her statement, but I do agree that using pictures and graphics can definitely help to improve the attention span of a child.

Instead of forcing a child to read a story that he or she cannot comprehend, it will benefit the child more if the parent is willing to read the story to the child instead.

The key here is to read the story and interact with the child.

Interaction involves leading the child to describe the picture using a few complete sentences. In addition, parents can also motivate their child to verbalise their thoughts after reading the story.

When choosing a storybook, parents should always remember to let their child decide the choice of book. It is better to read a story that interests a child than to read a story that will benefit a child.

Thus, interaction through reading stories is an effective way to develop a child’s interest in learning Chinese.

Incorporating into interests

When children enjoy the learning process, they will be more interested to find out more. Parents should try to link their children’s key interests and hobbies together with language learning to encourage effective learning.

For example, if a child is only interested in video games, perhaps the parents can consider purchasing Chinese video games. Not only will the child be interested to play the game, it will also stir the child’s curiosity to find out more about the contents of the game. The result is that learning becomes fun.

With proper guidance and monitoring, multimedia will prove to be a useful tool for parents to make learning Chinese an enjoyable activity.

Making it relevant

Parents can also try to incorporate Chinese in their children’s daily lives. Besides encouraging them to watch Chinese television programmes and cartoons, they can also conduct some daily conversations in the language and even teach them some popular songs as well. Parents can also encourage their children to communicate in the language with their neighbours or with shop owners and other people in the neighbourhood.

When children realise how useful and relevant the language is to their daily lives, they will be more receptive towards learning the language.

Thus, through the use of these methods, children will be more exposed to the Chinese language and will gradually grow to become competent users of the language.

Written by Eric Pang

Posted on : 2011-08-10

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In linguistics, grammar refers to the rules of the language. When we learn about grammar in the English language, we learn about the set of rules which governs how a sentence or phrase is composed. Besides building up a good vocabulary, the key to speaking and writing good English lies in your ability to first understand how a sentence is formed and how it can be used.

More often than not, your child will find the process of learning grammar tedious and boring. Seeing as how children are still too young to understand the importance of grammar, trying to force them to memorise a seemingly endless set of rules will be a tiresome chore.

Here are some ways in which you can make learning grammar fun and interactive for your child.

1. Provide examples that they can relate to. Instead of textbook examples, try engaging their attention by talking about a real-life example. An example about your child’s recent trip to the zoo or aquarium will more likely capture their attention and interest.

2. Use humorous examples. You may have noticed that children find it much easier to remember situations or examples which they find funny. This also changes their mindset that learning grammar is boring and mundane.

3. Read widely and wisely. Select books which are informative and entertaining as your child will be more inclined to read them.

You can also purchase books on grammar to give your child adequate practice. Try searching for books with more illustrations, stories and examples which your child will be able to relate to.

Hopefully, with these tips, you can help your child to improve his or her grasp of the English grammar such that they will grow to be proficient users of the language.

Written by Michelle Lim

 You may want to look at the series Fun with Grammar by EPH where grammar components are skilfully weaved into the storyline and multiple illustrations are provided.

Extra!

What are some common grammar mistakes to watch out for? Find out in this related article at the Popular EduCommunity:

Posted on : 2011-04-08

Part 2

Previously, we have shared some tips on good study habits and how to tackle MCQ questions to achieve good grades for PSLE Science. Now let's explore some tips on how to take on another type of questions in the examination - Open-ended Questions

Open-ended Questions

• For open-ended questions, circle the keywords in each question to help you to focus on what is being asked. It is important that you understand the question.
 Example: What are the products formed during photosynthesis? To answer such a question, first, identify the keywords. The keywords are ‘photosynthesis’ and ‘products’.   When you see ‘photosynthesis’, you should recall what this word means. Photosynthesis is a process whereby plants make food in the presence of sunlight. The question is asking about the products of photosynthesis. This means that you have to provide more than one answer to the question.   Recall that food (sugar) is made in plants and oxygen is given out during photosynthesis to replenish the air. Hence, the answers are sugarand oxygen.
• Note the question terms used in the question. This will help you understand what answer is required of you in order to score full marks for that particular question.
 Example: When a magnet is placed near object X, object X does not move. When the magnet is placed near object Y, object Y moves away from it. (a)  Explain why object X does not move when the magnet is placed near it. (b)  State the possible materials that can be used to make object Y. For (a), the question term used is ‘Explain’. ‘Explain’ means that you have to give reasons for the observation stated.   The observation is that object X does not move. Object X does not move because it is neither a magnet nor an object made of magnetic material. If object X is a magnet or a magnetic material, it will either be attracted to or be repelled by the magnet.   Thus, the correct answer is ‘Object X is made of a non-magnetic material, hence it is not affected by the magnet.’   For (b), the question term used is ‘State’. State means that you only need to write short answers, meaning a few words or short phrases.   Since object Y moves away from the magnet, object Y is also a magnet. Magnets are made of or can be made by one of the four types of magnetic materials. Hence, the answer for (b) is ‘Iron, steel, nickel or cobalt’.
 Example: 50 cm3 of air is being pumped into a 30 cm3 container. (a)  What is the volume of air inside the container? (b)  Explain your answer in (a). For (a), the question asks about the property of air (gas). Recall that air does not have a fixed volume and a fixed shape and so the volume of air inside the container is 30 cm3 instead of 50 cm3. For (b), the question is asking for a reason. As mentioned earlier, air does not have a fixed volume and a fixed shape. We can only see the shape of the air changing when it is being transferred from one container to another of a different shape. Hence, we cannot write ‘Air does not have a fixed shape’ as the answer.   Air does not have a fixed volume, hence its volume changes from 50 cm3 to 30 cm3. Writing ‘Air does not have a fixed volume’ as the answer is not wrong, but there is a better word to use for this question. The keywords are ‘can be compressed’ or ‘compressible’. Air does not have a fixed volume and hence it can be compressed.   The concise answer to this question would be ‘Air can be compressed’ or ‘Air is compressible’.

Do note that constant revision is also essential in preparing for the examination. Hopefully, with these tips in mind, you will find that Science is not as difficult as you might think and will be on your way to achieve your ideal grade.

Written by: Tan Chiang Heng

Click here for Part 1 of the article

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