Math - How to teach problem sums
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Striker09:
How is \"abacus\" related to problem sum. I have seen girls who are excellent in arithmetic but are miserable in problem sum because of poor English comprehension.Because of my 6 yrs old son, I have personally spending times exploring 3G Abacus & Traditional Abacus.
After completing the 3G ABACUS instructor course, I have applied the methods to teach my son. It is very simple & easy to understand. As such, he has shown more interest in mathematics than before.
I am planning to let him take part in the INTERNATIONAL Grading Exam this coming DEC 09. If possible, I will let him take part in year 2009 competition.
Currently, I am teaching kids & parents the 3G Abacus.
If you are interested in 3G ABACUS, please email me. -
Topic selected for http://www.kiasuparents.com/kiasu/content/teaching-problem-sums%22.
Problem sum is always a problem to most children :lol: (pun intended).
Well before we even talk about problem sum, the child needs to have a strong foundation in what is called mechanical calculation questions. These are simply questions which deals with straight forward calculation. These are what I would call simple mini problems.
Then we go to what used to be called story sums or now known as problem sums.
Problem sums have it's own funny mathematical language. A child needs to be able to decode the language. IN most cases, the language is simple for everyone to understand but in some cases it is tricky. Once the child is able to decode the language, they would then have decoded the question.
A mathematician named George Polya came about with the Polya approached to problem solving. If you google George Polya, you will be able to read what he says.
I think I have been a bit long winded with this. Let's get back on track.
To teach problem sums, we need to take small steps first.
What I would do would be to start with simple problems which are straight forward. Once the child is able to solve this, here is where it differs, I will make the child write out her own questions based on that sum or concept. This would allow the child to understand the way how a question is being asked and allow them to explore how else that question can be asked.
Next, once they are comfortable with these simple problem sums, I will then exposed them to the mid-difficulty problems. Here is where I will try to equip the child with the various different heuristic approaches. In this case, the approaches are like model method, using a table, guess and check, act it out and etc.
This would help the child to gain confidence in using these heuristic approaches.
Finally, when they are comfortable with the mid difficulty questions, then I will move them to the difficult ones, knowing that the child has the confidence for easy and mid-difficulty.
The important thing to take note is that, we should let the child develop their skill step by step. Sad to say the duration may be slower than what we may like but the reward would be greater.
The common mistake is to jump to the difficult questions and if the child could not do it, we would simply kill their interest and create a fear for math in them.
Phew!..Hope I did not confuse all of you.
Regards. :oops: -
NIEtrainedTEACHER:
Not sure if you have encountered kids who, by nature, just has no \"logic sense\". After spending hours explaining the logic, they finally understood it and we thought hurray, he/she finally understand - only to find that 1 day later, everything is forgotten and we need to explain again and again. When the question is re-phrased, the poor kid will also not be able to apply the same logic......
The important thing to take note is that, we should let the child develop their skill step by step. Sad to say the duration may be slower than what we may like but the reward would be greater..... :oops:
The cycle goes on and the time needed to get them to understand becomes longer and longer as the problem sum becomes more difficult. Before we realise, the poor kid has already reached P6 and the final result is obivous.
My guess is that about 50% of those kids who do badly for math are in this category. It is a real heartache.
The remaining 50% are either just plain lazy or poor in English. Kids in the lazy group would not be bothered to think when the problem gets too complex and just simply give up. The English Problem group doesn't even understand the question. Teaching in steps cannot help the lazy group to overcome the need to think or the English Problem group to understand the language used when many problem steps are combined into 1 complex question. -
atutor,
I agree with you. On the other hand, the exam paper is created in such a way that the higher order questions quota according to the TOS is always 30% of the total. For those whom are not sure what this mean, it means that a paper will be split into 3 parts, 30% for Knowledge questions - the easy ones, 40% Comprehension questions - the mid difficulty ones and 30% Higher Order, the difficult ones.
In view of that aspect, the initial goal would be to clear the 70% of the paper. this goal should be clear starting from P1 and then build up to P6.
In most cases, the child is so obsessed with the Higher Order questions that they couldn’t even see and realise that the other 70% has not been fully achieved. this would then make the child lose marks from the two parts which they should score.
I mean if the child is already having problems with the mechanical questions, then what else would it be with problem sums?
What usually happen is that the formative years of the child are sometimes being taken lightly and the panic starts at upper primary. At this junction, the child would have a tremendous amount of knowledge gap which at times is not easy to be filled. This would also go for the Language aspect. Language is something that most people take lightly without realising that language is another area that needs to be developed continuously through regular usage and practices.
However, for the child who is lazy, what they need is to see the benefit of not being lazy. Hopefully that would create a realisation for them to snap out of it. But like what the cliche saying goes, you can bring the horse to the stream but you cant force the horse to drink.
Regards. -
NIEtrainedTEACHER:
Problem sum is always a problem to most children :lol: (pun intended).
Well before we even talk about problem sum, the child needs to have a strong foundation in what is called mechanical calculation questions. These are simply questions which deals with straight forward calculation. These are what I would call simple mini problems.
Then we go to what used to be called story sums or now known as problem sums.
Problem sums have it's own funny mathematical language. A child needs to be able to decode the language. IN most cases, the language is simple for everyone to understand but in some cases it is tricky. Once the child is able to decode the language, they would then have decoded the question.
A mathematician named George Polya came about with the Polya approached to problem solving. If you google George Polya, you will be able to read what he says.
I think I have been a bit long winded with this. Let's get back on track.
To teach problem sums, we need to take small steps first.
What I would do would be to start with simple problems which are straight forward. Once the child is able to solve this, here is where it differs, I will make the child write out her own questions based on that sum or concept. This would allow the child to understand the way how a question is being asked and allow them to explore how else that question can be asked.
Next, once they are comfortable with these simple problem sums, I will then exposed them to the mid-difficulty problems. Here is where I will try to equip the child with the various different heuristic approaches. In this case, the approaches are like model method, using a table, guess and check, act it out and etc.
This would help the child to gain confidence in using these heuristic approaches.
Finally, when they are comfortable with the mid difficulty questions, then I will move them to the difficult ones, knowing that the child has the confidence for easy and mid-difficulty.
The important thing to take note is that, we should let the child develop their skill step by step. Sad to say the duration may be slower than what we may like but the reward would be greater.
The common mistake is to jump to the difficult questions and if the child could not do it, we would simply kill their interest and create a fear for math in them.
Phew!..Hope I did not confuse all of you.
Regards. :oops:
NIEtrainedTEACHER,
Thank you very much for sharing :goodpost: -
NIEtrainedTEACHER:
There are many kids who become lazy only when it comes to math. Adults think that it is because they simply don't like numbers.
.....However, for the child who is lazy, what they need is to see the benefit of not being lazy. Hopefully that would create a realisation for them to snap out of it. But like what the cliche saying goes, you can bring the horse to the stream but you cant force the horse to drink....
Is it true or does the real cause lies with the way math is thought in school?
It is a fact - kids hate to draw model. Yet model is presented to them as the generic method to solve problem sum. In the past, teachers even questioned the child if they don't use model to solve problem sum. (I used to meet math teachers over this silly issue)
Reasons on why kids hate model :
1. Drawing models is tedious
For example, given that 7/8 of A is equal to 8/9 of B, try using model to show that the ratio of A : B = 64 : 43. We would need to divide 7 and 8 units into 56 parts. (of course such extreme case won't come out but less extreme case did come out before)
2. Developing model need many different specific knowledge
For example, ratio of apples of A : B = 3U : 2U and after 4 more apples are given to A and 4 more apples are given to B, the ratio becomes 5V : 3V. To develop this model \"quickly\" we need to know and remember that the \"difference\" of the 2 ratios represent equal amount. Therefore, the model can only be easily understood if we develop it from \"differences are equal i.e. 1U = 2V\".
There are even kids trying to cut the model on \"ratio of the no. of stamps\" to get the model on \"ratio of the cost of the stamps\" - which is impossible.
Until the day where model is thought correctly, problem sum will remain a big problem for the average kid. -
Atutor,
Good point. I have that experience in my previous school. In fact, it turned out into an argument between me and a senior teacher during our Math Com meeting.
one of the things that lead to the argument was regarding the use of model. my take was that model is not the only way to solve problem sums and this has been agreed by the Curriculum Department Personnel. That discussion lead me to ask the MOE personnel why is it that the textbooks are advocating model drawing when Curriculum Department approved the whole range of heuristics. That will be another issue.
So, for me I believe that the child should be exposed to the whole range of heuristics. I even went to the extend of making my students solved one problem sums using various different heuristics. They were happy with it as they are able to see and experience that there are other ways beside model drawing.
I also agree that model drawing is a good preparation for secondary school as it is actually a simplified derivative of algebra.
But just like what you have said, until model drawing is being taught correctly in schools, the children will have problems using it.
Regards -
hmm… For me the reasons why a child do badly in section b and c is
1. they are very careless.
To improve on this I think we need to instill a habit of checking the workings immediately after finishing the question instead of finishing the whole paper and than go back and recheck it.
2. They have misconception
As a tutor most of the students cannot do well is not because they cannot add minus multiply or divide. Is because they DO NOT KNOW WHEN TO USE WHICH!!! Try to help them by getting rid of habit of "see more= add" "see less = minus" make them understand the whole sentence rather then recognize "key words"
3. They do not read the question.
This is the most wasted case. Why? They know how to the the entire question but they did not answer to what is ask.(simple example: tom has 2 times more sweet then jack. jack has 6 sweets. how many sweets they have altogether?) In this example they know tom has 12 sweets and THEY IMMEDIATELY USE IT AS THE ANSWER!! when they can get the full more by just reading and find out they are actually asking the TOTAL.
To improve on this just emphasize by telling your children to read the ENTIRE questions. -
Guan Hui:
But some children are very lazy to check their working, they just want to finish quickly their work and hand in. They do not care whether correct or wrong.hmm... For me the reasons why a child do badly in section b and c is
1. they are very careless.
To improve on this I think we need to instill a habit of checking the workings immediately after finishing the question instead of finishing the whole paper and than go back and recheck it. -
angela:
my boy's checking is often not thorough enough. checks of the same question can yield the same wrong answer!! :x
But some children are very lazy to check their working, they just want to finish quickly their work and hand in. They do not care whether correct or wrong.
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