Parents, not enrichment centres, are key to result
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Chenonceau:
Please do not quote me wrongly.
I didn't know until ksi volunteered the information that GEP get taught heuristics... and that some students there don't do well despite of being taught heuristics. Why does GEP get taught heuristics and mainstream does not? Because mainstream students are too dumb to cope? But mainstream students take the same PSLE exam which needs these heuristics (Onsponge) or equivalent (from TLL).
Fact 1:
Heuristics IS TAUGHT in school otherwise how do you expect children to solve any Math problem at all? As I have mentioned, one cannot learn concepts without learning any form of techniques to solve them. There are methods taught yet some still cannot get it so more special heuristics will not help. Understanding & Mastering the concept is still the key and practising may help cement the understanding, not the introduction of more heuristics. You have been referring to special heuristics I believe cos I am not familiar with the names you have mentioned. I am not a heuristics-tagged person per se....I just solve Math problem logically. Some of the common ones are taught even at lower primary level, eg. (E)
A. Use a diagram / model
Draw a diagram / model to create a pictorial description of the problem. This helps the child to visualise and understand the problem. Drawing also enables the child to \"manipulate\" the data.
B. Make a systematic list
Organise the data such as numbers or type of objects logically into tables or lists. This helps the child identify and spot missing data asked for in the problem. Organised tabulation of data also helps the child perceive trends or patterns in the data.
Look for pattern(s)
Examine the available data for patterns or relationships. Having perceived a pattern, the child can then predict the missing data or answer.
C.Work backwards
Look at the end results and work backwards towards the beginning. This strategy can be useful in problems involving a series of steps or computations. It is also useful when the problem gives more data about the end condition and little data about its beginning.
D. Use before after concept
Compare the situation before and after the problem is solved. Sometimes the differences (or a specific difference) can shed light on the cause and lead to a possible solution.
E. Use guess and check
Make an educated guess of the answer and check to see if it is correct. Use the knowledge gained from testing an incorrect guess to improve the next guess. It is important to avoid making wild guesses. Track the guesses made and look for patterns to improve the next guess.
F. Make suppositions
Study the data given and make suppositions (assumptions without proof) about some aspects of the problem to form the basis for further thinking. This reduces the number of possibilities and makes it easier to explore the problem further.
G. Restate the problem in another way
Read the problem carefully and restate it in the child's own words. This helps the child understand the problem and identify important factors of the problem.
H. Simplify the problem
Make a difficult problem simpler. This can be done by changing complex numbers to simple numbers or by reducing the number of things in the problem. The solution to the simplified problem may help the child solve the original problem.
I. Solve part of the problem
Split a complex problem into smaller parts and solve the simpler part first.
The Singapore primary mathematics syllabus suggested the above eleven problem solving heuristics for primary students. It is important to expose your child to the various problem solving heuristics. Besides knowing the heuristics, they should also know when to use them.
Fact 2:
I DO NOT KNOW for a fact GEP teaches any special heuristics so you have interpreted wrongly. I only mentioned this mother who hired a GEP teacher to teach her kids heuristics because she was proudly declaring 2 key words, GEP and heuristics. Ok so we assume he knows how to teach ALL heuristics. Now assuming the heuristics he teaches is the common set above, the children are having problem learning as seen from their results. And assuming he teaches them the special heuristics, they are obviously not absorbing as well as seen from their results. So more heuristics help? I believe some of these special heuristics may require high order thinking. For example, algebra is one way of solving Math problems but many kids cannot master it until they are ready for it. If not, why don't we just teach algebra to all kids from P4 onwards and when they reach P6, viola, all will be ready to solve any Math problem because algebra is a powerful form of \"heuristics\". I highly recommend algebra but I trust MOE knows sufficiently about learning pedagogy to introduce them at the right time for the majority.
Coast, the discussion so far is not an emphasis on asking for more materials to be produced by MOE, we have been discussing the \"untaught\" heuristics as being a critical point to ensure better results and some of us here say \"No\". More importantly, deliver a good job in concept learning so that kids can interpret question well and solve the problems with understanding.
It is good to read about the examples of children without tuition for heuristics can still manage A/A* for PSLE Math. -
Chenonceau:
thanks for sharing.
What I would suggest is that in lower primary, you work on mechanical calculations. Build speed and accuracy with mechanics of counting - multiplication, division, addition and subtraction.Build a strong foundation in computational skills before you hit P5 and P6. I wouldn't pay attention to heuristics at all before P5. The exams don't need these.
what is 'mechanical calculations' and 'computational skills'? +-x/?
my boy's mental calculation is not so good. he is pretty visual, so need to work out on paper (affecting his speed).
i have pm-ed you. thanks.
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ksi:
Yup... I know. All you've documented were very useful up to P4. We could score well with these up to P4. The moment we hit P5, we had to use others not taught in school to manage the PSLE level difficulty. We've used stuff from Onsponge. We've used the Models documented in excellent detail by Math Heuristics. We've used simultaneous equations too. They don't teach these in school but we've found them useful for PSLE. The Learning Lab would also have some specialized approaches to cope with these challenging PSLE questions but I don't know what they are 'cos I am not willing to send my son for tuition.
Please do not quote me wrongly.Chenonceau:
I didn't know until ksi volunteered the information that GEP get taught heuristics... and that some students there don't do well despite of being taught heuristics. Why does GEP get taught heuristics and mainstream does not? Because mainstream students are too dumb to cope? But mainstream students take the same PSLE exam which needs these heuristics (Onsponge) or equivalent (from TLL).
Fact 1:
Heuristics IS TAUGHT in school otherwise how do you expect children to solve any Math problem at all? As I have mentioned, one cannot learn concepts without learning any form of techniques to solve them. There are methods taught yet some still cannot get it so more special heuristics will not help. Understanding & Mastering the concept is still the key and practising may help cement the understanding, not the introduction of more heuristics. You have been referring to special heuristics I believe cos I am not familiar with the names you have mentioned. I am not a heuristics-tagged person per se....I just solve Math problem logically. Some of the common ones are taught even at lower primary level, eg. (E)
A. Use a diagram / model
Draw a diagram / model to create a pictorial description of the problem. This helps the child to visualise and understand the problem. Drawing also enables the child to \"manipulate\" the data.
B. Make a systematic list
Organise the data such as numbers or type of objects logically into tables or lists. This helps the child identify and spot missing data asked for in the problem. Organised tabulation of data also helps the child perceive trends or patterns in the data.
Look for pattern(s)
Examine the available data for patterns or relationships. Having perceived a pattern, the child can then predict the missing data or answer.
C.Work backwards
Look at the end results and work backwards towards the beginning. This strategy can be useful in problems involving a series of steps or computations. It is also useful when the problem gives more data about the end condition and little data about its beginning.
D. Use before after concept
Compare the situation before and after the problem is solved. Sometimes the differences (or a specific difference) can shed light on the cause and lead to a possible solution.
E. Use guess and check
Make an educated guess of the answer and check to see if it is correct. Use the knowledge gained from testing an incorrect guess to improve the next guess. It is important to avoid making wild guesses. Track the guesses made and look for patterns to improve the next guess.
F. Make suppositions
Study the data given and make suppositions (assumptions without proof) about some aspects of the problem to form the basis for further thinking. This reduces the number of possibilities and makes it easier to explore the problem further.
G. Restate the problem in another way
Read the problem carefully and restate it in the child's own words. This helps the child understand the problem and identify important factors of the problem.
H. Simplify the problem
Make a difficult problem simpler. This can be done by changing complex numbers to simple numbers or by reducing the number of things in the problem. The solution to the simplified problem may help the child solve the original problem.
I. Solve part of the problem
Split a complex problem into smaller parts and solve the simpler part first.
The Singapore primary mathematics syllabus suggested the above eleven problem solving heuristics for primary students. It is important to expose your child to the various problem solving heuristics. Besides knowing the heuristics, they should also know when to use them.
Fact 2:
I DO NOT KNOW for a fact GEP teaches any special heuristics so you have interpreted wrongly. I only mentioned this mother who hired a GEP teacher to teach her kids heuristics because she was proudly declaring 2 key words, GEP and heuristics. Ok so we assume he knows how to teach ALL heuristics. Now assuming the heuristics he teaches is the common set above, the children are having problem learning as seen from their results. And assuming he teaches them the special heuristics, they are obviously not absorbing as well as seen from their results. So more heuristics help? I believe some of these special heuristics may require high order thinking. For example, algebra is one way of solving Math problems but many kids cannot master it until they are ready for it. If not, why don't we just teach algebra to all kids from P4 onwards and when they reach P6, viola, all will be ready to solve any Math problem because algebra is a powerful form of \"heuristics\". I highly recommend algebra but I trust MOE knows sufficiently about learning pedagogy to introduce them at the right time for the majority.
Coast, the discussion so far is not an emphasis on asking for more materials to be produced by MOE, we have been discussing the \"untaught\" heuristics as being a critical point to ensure better results and some of us here say \"No\". More importantly, deliver a good job in concept learning so that kids can interpret question well and solve the problems with understanding.
It is good to read about the examples of children without tuition for heuristics can still manage A/A* for PSLE Math.
I too had no problems with what the school covered up until P4. The techniques that came from school were quite sufficient. I just needed to let him practise computation skills for speed and accuracy. -
It really doesn't matter to me how other parents experience heuristics so referring to how other parents also agree with you is not convincing to me, even if it may make you feel vindicated in your opinion.
We differ in our opinions. That is all. We can agree to disagree or we can try and see if there is common ground and that the diversity means that we both see one reality and if we merge and agree, we will both be the richer. If you don't believe in heuristics, then don't use them and don't allow your child to learn them. All I am doing is sharing my own experience with these resources. I was very puzzled as to why my son failed Paper 2 in early P5 when he had mastered everything the school had taught.
I turned to a Mother whose son took PSLE in 2011. She in turn gave me the heads up on the resources her own GEP son used to pull his Paper 2 from Fail to almost full marks. I thought these resources useful and my heart ached for kids with no access to such resources. So I decided to share... and I proposed that these resources should be documented for all children in MOE textbooks.
Even if you don't agree with me, and I am perfectly willing to accept that since you're really good at Math, you see other ways that bypass the need for such resources. It's perfectly fine. But I am NOT good at Math. My DS was much helped by these heuristics, and I assumed that other kids, without Mothers good at Math would also benefit.
The intent behind the sharing is honourable. You may not agree but I hope that you will honour my sharing for what it is. Pure and selfless sharing. I have nothing to gain by sharing so much and everything to lose because I create competition for my DS. -
Chenon, at a personal level, I am confident your son will do well for PSLE. You have done a lot to get him to a good level of competency for this exam. Whatever you have done also matches his ability due to your good understanding of him so you will yield the results.
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ksi:
Chenon, at a personal level, I am confident your son will do well for PSLE. You have done a lot to get him to a good level of competency for this exam. Whatever you have done also matches his ability due to your good understanding of him so you will yield the results.
:hugs: I hope so. I really hope so.
Then again, like I said before, how well he eventually does is not important to me. Some mothers I know called me last year. They thought my DS took PSLE last year together with theirs. Their sons got into Hwa Chong or RI. The pressure is of course strong to want to set the same expectations for my son too. DD went to a top school. Husband and I have had strong academic track records. Our circle expects a lot from DS.
But I made very clear to all who called that my DS may not be as bright as their children, and I am unprepared to push him further than he can go. As long as he has tried his best, and I can tell you that he is trying his very best, whatever the result, I will still be very proud of him. I already am very very proud of him because he has matured so much... and become a real little man. In moments when I get frustrated that the school is so unhelpful, it is my son who hugs me and says \"It's ok Mom. We can do it. You just have to help me and I just have to work hard.\" And I can tell you that for sheer work ethic, I have yet to meet an equivalent of my son.
I've done some preliminary screening of secondary schools. I picked one school for each band of 10 right down to 210. This also is my way of letting DS know that it is perfectly fine to score much less than 250. This PSLE is tough... but man... it forms character. -
Chenonceau:
Treat me as playing the devil's advocate. I respect the honourable move by you for enthusiastically sharing what you have benefitted from the resources that you have chanced upon.It really doesn't matter to me how other parents experience heuristics so referring to how other parents also agree with you is not convincing to me, even if it may make you feel vindicated in your opinion.
We differ in our opinions. That is all. We can agree to disagree or we can try and see if there is common ground and that the diversity means that we both see one reality and if we merge and agree, we will both be the richer. If you don't believe in heuristics, then don't use them and don't allow your child to learn them. All I am doing is sharing my own experience with these resources. I was very puzzled as to why my son failed Paper 2 in early P5 when he had mastered everything the school had taught.
I turned to a Mother whose son took PSLE in 2011. She in turn gave me the heads up on the resources her own GEP son used to pull his Paper 2 from Fail to almost full marks. I thought these resources useful and my heart ached for kids with no access to such resources. So I decided to share... and I proposed that these resources should be documented for all children in MOE textbooks.
Even if you don't agree with me, and I am perfectly willing to accept that since you're really good at Math, you see other ways that bypass the need for such resources. It's perfectly fine. But I am NOT good at Math. My DS was much helped by these heuristics, and I assumed that other kids, without Mothers good at Math would also benefit.
The intent behind the sharing is honourable. You may not agree but I hope that you will honour my sharing for what it is. Pure and selfless sharing. I have nothing to gain by sharing so much and everything to lose because I create competition for my DS.
If you mention from fail to full marks, then it is a major issue in teaching in school, is GEP teaching so bad huh?
If you mention 80 to 90+ but with resources for those 2-3 tough questions to reach closer 100, then that is another story.
I am just being your 3rd eye to send you warning signals if some part of the debate can be taken wrongly. Personally, I have absolutely no benefit to win this argument either, my objective is never to win. In fact, I enjoy reading what you have been posting, just that when some logic fail to click in my mind, I will surface my views, I hope you don't mind my straight talking.
I am happy to close this case with agreeing to disagree.
Most importantly now is I sincerely wish your ds all the best in his PSLE with all the good efforts you have put in as a mother. I know it is hard being a mum these days. -
jedamum:
Simple calculations with big numbers. 4 digit long division. 4 digit multiplication. Long addition. As you practise these, your child will develop naturally the mental heuristics to do these fast. Focus on these in lower primary. These develop a Feel For Numbers.
thanks for sharing.Chenonceau:
What I would suggest is that in lower primary, you work on mechanical calculations. Build speed and accuracy with mechanics of counting - multiplication, division, addition and subtraction.Build a strong foundation in computational skills before you hit P5 and P6. I wouldn't pay attention to heuristics at all before P5. The exams don't need these.
what is 'mechanical calculations' and 'computational skills'? +-x/?
my boy's mental calculation is not so good. he is pretty visual, so need to work out on paper (affecting his speed).
i have pm-ed you. thanks.
If your child reaches P5 slow in these calculations, then you have a double whammy. Give a strong foundation in computation and in P1 to P4 concepts FIRST. -
Chenonceau:
It is great to see so much character in your son and even greater to see the support you are rendering to him. In fact, this will supercede whatever he can get from school. I actually believe the family plays a much much more important role in a child's success than the school.ksi:
Chenon, at a personal level, I am confident your son will do well for PSLE. You have done a lot to get him to a good level of competency for this exam. Whatever you have done also matches his ability due to your good understanding of him so you will yield the results.
:hugs: I hope so. I really hope so.
Then again, like I said before, how well he eventually does is not important to me. Some mothers I know called me last year. They thought my DS took PSLE last year together with theirs. Their sons got into Hwa Chong or RI. The pressure is of course strong to want to set the same expectations for my son too. DD went to a top school. Husband and I have had strong academic track records. Our circle expects a lot from DS.
But I made very clear to all who called that my DS may not be as bright as their children, and I am unprepared to push him further than he can go. As long as he has tried his best, and I can tell you that he is trying his very best, whatever the result, I will still be very proud of him. I already am very very proud of him because he has matured so much... and become a real little man. In moments when I get frustrated that the school is so unhelpful, it is my son who hugs me and says \"It's ok Mom. We can do it. You just have to help me and I just have to work hard.\" And I can tell you that for sheer work ethic, I have yet to meet an equivalent of my son.
I've done some preliminary screening of secondary schools. I picked one school for each band of 10 right down to 210. This also is my way of letting DS know that it is perfectly fine to score much less than 250. This PSLE is tough... but man... it forms character. -
ksi:
Dunno leh... DS not in GEP mah...
If you mention from fail to full marks, then it is a major issue in teaching in school, is GEP teaching so bad huh?
Also, I need to specify that the fail was in Paper 2 for both my DS and my friend's GEP son. Seems like the GEP also dun teach... just like mainstream.
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