Parents, not enrichment centres, are key to result
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Chenonceau:
I fully agree schools have to provide sufficient teaching/materials to enable students to achieve A/A* without tuition.
Yes indeed to your point in RED. It is wonderful you took the time to write. A perspective like yours is invaluable. We have been waiting for someone like you to come and write.Musings:
Hi I have been following this discussion not for my own kids but becos I teach a group of P4-P6 students in Sunday school and they are all underachievers who are at the borderline of Normal and Express. Maths is the perennial Archilles heel. Together with some people in church, we were wondering how to help them to at least make it to Express. And because they typically do not have parents who can coach and we assume the school is not doing a good enough job, we were hoping to fill in the gap. I have been thinking if the so called heuristics which appears to be not taught or taught adequately could help them.
However, I realise that in all likelihood their problem is one of lack of basic foundation which needs to be addressed first. Therefore, I can understand why the school or the educational system may not implement heuristics teaching to ALL students from the outset - those students stuggling at the bottom of cohort such as these Sunday school kids I know will not absorb and likely feel even more inferior and less motivated to improve.
Instead, these kids need to focus and master the basic skills before we talk about any higher order skills.
The discussion in this thread seem to be amongst parents whose kids are already rather bright and just needed to be given the right sort of materials/training to make it to A/A*. Unfortunately, there are many kids I know who do not fall into that category.
However, schools are also responsible for teaching those who CAN cope if they choose to TEST such skills. They TEST what they do not teach. You do need these heuristics to pass Paper 2 in P5. Even GOOD students need
(1) parents who CAN teach
(2) access to enrichment
The good students shouldn't even need external help. This leaves only tuition for those who really need it.
The key of course is how to do so when there are kids at both ends of the spectrum and kids who are in between.
The current Maths textbooks are definitely insufficient and seem to be pegged at the lowest common denominator. Not that this is in itself wrong because there many kids who are unable to master even such content but that it is insufficient.
Schools have dealt with this by supplementing with their own in house developed content (a colleague whose kid is in CHS shared this) or using Onsponge materials etc. I hear some schools send selected high ability kids to be given additional classes by external vendors to teach higher order thinking skills tested in exams (not out of syllabus stuff like Math Olympaid)
I would think a possible way is for Maths textbooks to be differentiated in the same way as Chinese textbooks - i.e. sections of it are only taught to high ability kids just like the enrichment part of Chinese textbooks are taught to kids doing Higher Chinese.
I had a recent conversation with a friend who is the principal of a primary school. She spoke of her predecessor who decided to 'pack' the top 2 classes to > than 40 kids leaving the bottom classes with < than 40 kids to implement differentiated teaching. So the top classes will get more teaching in heuristics, bottom classes focus on foundation and teachers can pay more attention due to smaller size of the class. This may seem very logical but it took many levels of approval to get this implemented.
But it ain't perfect either. The parents whose kids are in the top class may be happy, those whose kids in bottom class complain of discrimination. Those whose kids in the middle classes complain - neither here nor there??
Nonetheless, I am heartened there remain educators who are passionate and care deeply for their charges and seek to maximise the potential of all students despite the constraints. -
Chenonceau:
Chenon, you have summarised everything very well. If we want to target the majority to handle Math at PSLE, (1)the basics have to be taught right to set a strong foundation. After achieving that, the race is more equal at streaming time and by right, streaming should be taking care of the stretch for HA students.Some people have PM-ed me their thanks for the heads-up on heuristics. Most are parents with kids in P3 and P4. Some in P1 & P2. I am mindful of the wisdom that ksi has consistently counselled since the start of the debate - We should not have a mass stampede towards centres that TEACH heuristics... nor buy books that tout themselves as heuristic.
This post is a cautionary one to parents who are tempted to quickly jump on the heuristic bandwagon without really knowing what an heuristic is, and are tempted to do so because Chenonceau convinced them that heuristics are good.
Since I am a psychologist, the term heuristic has never been a marketing term to me. I first got to know about heuristics when reading research by Tversky and Kahneman (both are highly influential cognitive psychologists most active in research in the 1970s, 1980s and 1990s). This could explain why I was far less sensitive to the notion that the term \"heuristics\" is very much marketing hype, used by people who are trying to make money by touting a big word. Not until ksi made the comment about business-driven \"heuristics\" was I even aware of the profiteering aspect of this term in Singapore.
But now I know better, and so I feel compelled to write this post.
What is an heuristic?
In psychology, heuristics are simple, efficient rules, hard-coded by evolutionary processes or learned, which have been proposed to explain how people make decisions, come to judgments, and solve problems, typically when facing complex problems or incomplete information. These rules work well under most circumstances, but in certain cases lead to systematic errors or cognitive biases. (Direct quote from http://en.wikipedia.org/wiki/Heuristic)
Note the emphasis on the terms \"systematic errors\" and \"cognitive biases\". Read the following URL for an example of how one can make error using a heuristic http://en.wikipedia.org/wiki/Availability_heuristic.
Parents need to be aware that heuristics are short-cuts to problem-solving. A short-cut saves time but exposes you to the danger of mis-reading a problem and once you have mis-read the problem, the solution will be wrong. It is for this reason that people like ksi and wonderm caution against the possibility that teaching heuristics can lock the child in to fixed methods of problem-solving.This again is wise advice from Mommies who are themselves good at Math, and we should heed their advice.
The only way to guard against cognitive biasness is to have high volume exposure to different problem statements... i.e., a lot of practice, using multiple methods. Teaching heuristics means you need MORE practice NOT less, because you need to practise enough to get past the \"dumb application\" of heuristic to problem. You need to HAVE HAD more practice... and you need MORE FURTHER practice after you've been taught.
You need enough practice to develop a sensitivity to the different types of problems, so that you will know when NOT to use such and such a math heuristic. Of the top school papers, Math is the only subject where we actually do ALL the papers. Last year, DS completed 3 years worth of 12 top school papers. We left out many Paper 1 but we made sure we did ALL the Paper 2.
Are math heuristics good for children with a poor foundation in Math?
I am not sure but I am tempted to say \"No\". Children with poor foundation in Math are likely to be more prone to cognitive bias than another with a good feel for numbers and numerical concepts. This COULD explain why some children with POOR math foundation go into Onsponge training and Math Heuristic training in lower primary only to have their math grades drop further as the years go by. A Mommy shared with me the experience of her son who was not helped at all by heuristic.
If you try to feed lobster/eggs/nuts to a baby, the baby might get allergy. Typically, Mommies introduce such foods after age 3 or 4. There is a time for everything. So, parents need to know that just because something (such as math heuristics) has been beneficial to others for PSLE, it may not be wise to start too early. When you build a house, you must build the foundations first. The foundations of the math cognitive scaffolding is very well documented in ksi's post here - http://www.kiasuparents.com/kiasu/forum/viewtopic.php?p=691122#p691122. These are the heuristics you want your child to master in lower primary... and master well. To complete this list, I would advise to develop naturally a set of math heuristics through a LOT OF practice in numerical calculation. Addition, subtraction, multiplication, division. The schools give hardly enough practice here. I used to print out sheets of such numerical calculations and get my son to do one worksheet a day in P4. In addition, I signed him up to Kumon classes which we have since stopped in P5.
Note that my son was a 90+ math student at end-P4. He failed Paper 2 in early P5, and after skimming Onsponge 5, his grades went back up to 90s very fast. The other little boy I know who obtained such results was a GEP student who was also pretty good at Math. Both boys were not bad at Math to begin with. I am tempted thus to conclude that heuristics training is dangerous for those who have a poor Math foundation. But I am not terribly terribly sure as yet. Again, I must give ksi the credit for highlighting this point most spiritedly, and I am most sorry that in the cut and thrust of the debate, I was not sensitive, and I rode rough shod over her wisdom.
Parents need to be careful.
(1) Early exposure is not better.
(2) The word \"heuristic\" on the front page of an assessment book does not mean it is a good book.
(3) The word \"heuristic\" on the billboard of a tuition centre is no guarantee of better grades.
Will enrichment centres teaching heuristics be always useful in helping your child improve?
The answer here is an obvious \"no\". Apart from the dangers of cognitive bias, there are also issues of motivation. Practice makes perfect. An unmotivated child won't practise. My DS is very motivated. We had a discussion this morning about working on Sunday. He wants to, saying \"I can get more done\". I don't want him to. In the end, I had to tell him \"I'm sorry. You are not working on Sunday. Sunday is play day. I'm not discussing this further.\"
I think I owe it to the community to eat a bit of humble pie (because much of this post expands on what ksi has been saying all along) and sound a word of caution. So here it is. -
Musings:
I fully agree schools have to provide sufficient teaching/materials to enable students to achieve A/A* without tuition.
Yes indeed to your point in RED. It is wonderful you took the time to write. A perspective like yours is invaluable. We have been waiting for someone like you to come and write.Chenonceau:
[quote=\"Musings\"]
Hi I have been following this discussion not for my own kids but becos I teach a group of P4-P6 students in Sunday school and they are all underachievers who are at the borderline of Normal and Express. Maths is the perennial Archilles heel. Together with some people in church, we were wondering how to help them to at least make it to Express. And because they typically do not have parents who can coach and we assume the school is not doing a good enough job, we were hoping to fill in the gap. I have been thinking if the so called heuristics which appears to be not taught or taught adequately could help them.
However, I realise that in all likelihood their problem is one of lack of basic foundation which needs to be addressed first. Therefore, I can understand why the school or the educational system may not implement heuristics teaching to ALL students from the outset - those students stuggling at the bottom of cohort such as these Sunday school kids I know will not absorb and likely feel even more inferior and less motivated to improve.
Instead, these kids need to focus and master the basic skills before we talk about any higher order skills.
The discussion in this thread seem to be amongst parents whose kids are already rather bright and just needed to be given the right sort of materials/training to make it to A/A*. Unfortunately, there are many kids I know who do not fall into that category.
However, schools are also responsible for teaching those who CAN cope if they choose to TEST such skills. They TEST what they do not teach. You do need these heuristics to pass Paper 2 in P5. Even GOOD students need
(1) parents who CAN teach
(2) access to enrichment
The good students shouldn't even need external help. This leaves only tuition for those who really need it.
The key of course is how to do so when there are kids at both ends of the spectrum and kids who are in between.
The current Maths textbooks are definitely insufficient and seem to be pegged at the lowest common denominator. Not that this is in itself wrong because there many kids who are unable to master even such content but that it is insufficient.
Schools have dealt with this by supplementing with their own in house developed content (a colleague whose kid is in CHS shared this) or using Onsponge materials etc. I hear some schools send selected high ability kids to be given additional classes by external vendors to teach higher order thinking skills tested in exams (not out of syllabus stuff like Math Olympaid)
I would think a possible way is for Maths textbooks to be differentiated in the same way as Chinese textbooks - i.e. sections of it are only taught to high ability kids just like the enrichment part of Chinese textbooks are taught to kids doing Higher Chinese.
I had a recent conversation with a friend who is the principal of a primary school. She spoke of her predecessor who decided to 'pack' the top 2 classes to > than 40 kids leaving the bottom classes with < than 40 kids to implement differentiated teaching. So the top classes will get more teaching in heuristics, bottom classes focus on foundation and teachers can pay more attention due to smaller size of the class. This may seem very logical but it took many levels of approval to get this implemented.
But it ain't perfect either. The parents whose kids are in the top class may be happy, those whose kids in bottom class complain of discrimination. Those whose kids in the middle classes complain - neither here nor there??
Nonetheless, I am heartened there remain educators who are passionate and care deeply for their charges and seek to maximise the potential of all students despite the constraints.[/quote] :goodpost: Actually... it might already help if all school libraries had many copies of these expensive resources and a bibliography were given out to students organised into tiers such as Fundamentals and Stretch. This would really help students who have no money to buy the resources and CAN cope with the material.
It would certainly help the very conscientious teachers who are stressed because they find it hard to teach everyone. Let the kids have the necessary resources to learn themselves. -
ksi:
Thank you. I wanted to do justice to your sharing, and honour it for its quality. I did write an integration post earlier but it was a quick job. This one is much better.
Chenon, you have summarised everything very well. If we want to target the majority to handle Math at PSLE, (1)the basics have to be taught right to set a strong foundation. After achieving that, the race is more equal at streaming time and by right, streaming should be taking care of the stretch for HA students. -
insider:
Thanks insider, I appreciate the advice.
Musings,Musings:
.
Instead, these kids need to focus and master the basic skills before we talk about any higher order skills.
If the kids under your care do have some reasonable basic skills, you may actually try to explore using Onsponge's methods to teach them.
If you were to look through the methods, they are a bit like 'dead methods' (ę»å¦), ie, see this question, use this method, see that question, use that method, etc.
It depends on your objective in tutoring them. If your objective is to let them to have a better score for maths in PSLE, you may try, but if your objective is to let them have a more flexible brain for sec school maths, then you may have to think again whether to use this short cut. If they manage to see 'patterns' (most of the PSLE maths questions, if you see them long enough, carry 'patterns'), they have a high chance of getting the correct answer. It's a gamble to use heuristics right away with the technique of 'identifying' patterns in questions without further usual thinking process but at least they have a chance to 'gamble' and get it right.
I used to tutor some friends who were hopeless in their maths (or logical thinking skills) during my sec school days. As they were hopeless and I gauged that I was not powerful enough to make them understand concepts (I was young then at 16), I used 'patterns' to teach them (see this, do this; see that, do that; don't think of any other things). ALL did well enough for their business maths in their O levels at the end...
In some cases, we have to ę»é©¬å½ēꓻ马å». This is the same situation when last minute, many children have to memorise compositions to score for languages... (the children must be able to memorise and apply in the first place else this gamble will not work as well...)
PS:
If the children under your care really having problems with challenging sums and you assess not quite possible for them to understand (whether concepts or heuristics), then you may actually throw these about 10 marks away and focus on other topics like area & parameters, etc. For certain kids, not worth to harp on the 10% challenging problems and missing other 'trees' that maybe easier to climb. Taking exams...most of the time is about 'strategies'... -
Chenonceau:
By the way, did you notice sth up there......
Thank you. I wanted to do justice to your sharing, and honour it for its quality. I did write an integration post earlier but it was a quick job. This one is much better.ksi:
Chenon, you have summarised everything very well. If we want to target the majority to handle Math at PSLE, (1)the basics have to be taught right to set a strong foundation. After achieving that, the race is more equal at streaming time and by right, streaming should be taking care of the stretch for HA students.
Just to share a lighter moment with you about my experience, I get PM asking me to teach their children.....of course it is joking but at the end of the day, we know every parent is concerned about this issue after our debate....
-
ksi:
By the way, did you notice sth up there......
Thank you. I wanted to do justice to your sharing, and honour it for its quality. I did write an integration post earlier but it was a quick job. This one is much better.Chenonceau:
[quote=\"ksi\"]
Chenon, you have summarised everything very well. If we want to target the majority to handle Math at PSLE, (1)the basics have to be taught right to set a strong foundation. After achieving that, the race is more equal at streaming time and by right, streaming should be taking care of the stretch for HA students.
Just to share a lighter moment with you about my experience, I get PM asking me to teach their children.....of course it is joking but at the end of the day, we know every parent is concerned about this issue after our debate....[/quote]I oso want you to teach mine leh... just paiseh to ask only!!!!
Yeah... I know the debate has made the issue salient to many parents. That's why I thought I should write a proper integration post. Unfortunately, we have not had much representation from parents who work and who have no time to teach their kids, so the perspective may still be incomplete.
Yes.. I noticed the streaming. Chose not to respond because seriously, my brain works by taking in new perspectives, and I CHANGE my mind as new pesrpectives come in... At present, I have no entrenched position on streaming. What I wrote... I wrote as questions to stimulate thought and push the boundaries. I haven't thought through streaming properly so I dun really have anything sensible to say. I have questions more than objections.
I do have an entrenched position on textbooks, however. -
Chenonceau:
If you are referring to me based on my earlier post, just to clarify, my ds1 attended TLL maths in upper primary but my ds2 never attended any maths tuition before. I am grateful to TLL for helping build a strong maths foundation for ds1 but it is not always necessary.At least one parent has children who did well in Math without Onsponge. That is my other bug bear. These books are EXPENSIVE. But this parent (who did not use Onsponge)
(1) sent her kids to The Learning Lab (which is even more expensive than buying the Onsponge book).
(2) is herself good at Math. -
wonderm:
Yup! I was referring to you. Could it be that you learnt from DS1 so you could help DS2?
If you are referring to me based on my earlier post, just to clarify, my ds1 attended TLL maths in upper primary but my ds2 never attended any maths tuition before. I am grateful to TLL for helping build a strong maths foundation for ds1 but it is not always necessary.Chenonceau:
At least one parent has children who did well in Math without Onsponge. That is my other bug bear. These books are EXPENSIVE. But this parent (who did not use Onsponge)
(1) sent her kids to The Learning Lab (which is even more expensive than buying the Onsponge book).
(2) is herself good at Math. -
Chenonceau:
I want the 2 of you to teach ME! Then I can teach my kids.
I oso want you to teach mine leh... just paiseh to ask only!!!!ksi:
By the way, did you notice sth up there......
Just to share a lighter moment with you about my experience, I get PM asking me to teach their children.....of course it is joking but at the end of the day, we know every parent is concerned about this issue after our debate....
.
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