Parents, not enrichment centres, are key to result
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ksi:
It is too much to expect to develop heuristics on your own when the skills component of the syllabus is so heavy. If you're looking at the standards of performance of the past, yes... not now.
So concepts are important to grasp, heuristics can develop on your own if the concept is strong.
In the same way, if you're just looking to cook well enough to get by daily then it's fine to potter around by just figuring out from recipes, and not really knowing which part of technique you're getting wrong unless you grope around some more. The moment you up the standards really high (and the stakes are high) AND you're looking at world class standards of performance very early, then it is important that your cook book teach you also the essential basic techniques of roasting, steaming etc... so you need not re-invent the wheel. It's the difference between James Peterson and Shermay Lee. You learn to cook faster and with better results with James Peterson's book.
The PSLE Math paper is packed so full of heuristics (that aren't taught) that our kids have no time to grope and re-invent each one. That is the problem with the system today. It is STILL assuming that the children will develop the How (the heuristics) naturally. The truth is, the enrichment centres make good money teaching the How, and those students who pay to learn the How, learn faster... do better and have more time to play. My son too gained in play time once he had completed skimming Onsponge in one week. Onsponge 5... one week. Onsponge 6... one week. Grades buoyed up to 90+. See how much time you save by not re-inventing the wheel?
It's working efficiently by having the right resources.
Schools still maintain that they are doing enough by teaching only the What. This is an MOE cop out, and a refusal to acknowledge that their textbooks are written by novices who had no clue how to document heuristics... whether in Science nor in Math. This gap has been left to the enrichment centres to fill.
Times have changed. The PSLE demands have changed. I have no intention to waste my son's time by getting him to figure out his own heuristics when I know that resources exist that will make his learning very much more efficient in very short a time. Added to that, all his friends are getting these heuristics TAUGHT to them by enrichment centres. Why should I shortchange my son? It's bad enough that I insist that he pick it up without a tutor's help.
When I started my PhD, one still had to run around libraries photocopying material. Today, electronic research databases provide all manner of access to high quality material at the click of a button. Not surprisingly, standards of research have gone up greatly. Expectations of research quality too have gone up vastly. Time to publication is much shorter. Research is faster and better now. If Singaporean universities today still believed that researchers can just naturally pick up knowledge without the productivity e-tools of the e-databases, then the research standards in Singapore will simply fall further and further behind.
The MOE expects a lot from our kids. I cannot refute the argument (though I would like to) that standards must not be diluted. We SHOULD expect a lot from our kids because our economic survival depends on it (or so the argument goes). Yet, the MOE expects very little of itself. It contents itself with teaching concepts only and expects the children to bridge the gap of heuristics on their own. Times have changed. It is time to up the standards of teaching to cover heuristics, not just concepts.
The only reason that enrichment has now become a necessity is that the schools test heuristics but don't teach them, and thus, they leave a humongous gap for enrichment centres to fill. These enrichment centres fill the gap with much gusto and make a lot of money too because there is NO WAY to do well in school if you don't pay for enrichment.... or source for materials that bridge the gap.
The bright kid with no access to enrichment stands no chance at all because the school teaches less than half of what he needs to know (only the What), and tests more than twice what it teaches (the heuristics too). -
Once the basic foundation of heuristics has been mastered, my DS tends to evolve his own methods. He has strange ways of approaching problems that none of us can fathom… a sort of hodge podge of the various tools he has been exposed to.
It truly shortcuts the learning by a lot, and stimulates creativity.
Same with cooking. Once you master the basic technique, your creativity is much enhanced if you have the bent for it. But the technique is still important to teach and to learn if high standards of performance are what is required. -
The thing is \"Concepts are taught by teaching techniques!\". Tell me how to teach concepts without teaching techniques and you can be a Nobel Prize winner.
There are new things I can learn daily, pray share.
Maybe not all the possible techniques are taught in school but certainly techniques are required. I believe MOE in the past have been accused of 'spoon-feeding' education as well. -
ksi:
Concepts are...The thing is \"Concepts are taught by teaching techniques!\". Tell me how to teach concepts without teaching techniques and you can be a Nobel Prize winner.
There are new things I can learn daily, pray share.
Maybe not all the possible techniques are taught in school but certainly techniques are required. I believe MOE in the past have been accused of 'spoon-feeding' education as well.
(1) Ratio
(2) Percentage
(3) Fractions
Heuristics (techniques are )...
(1) Repeated identity
(2) External unchanged
(3) Unchanged total
(4) Constant difference
The first lot are taught. The 2nd lot are not. The 2nd lot are heuristics that apply to problems of ratio, percentage and fractions. These categories are the work of an expert like Ammiel Wan. The 1st lot are traditional math concepts that are in every Math textbook, the work of novice writers unable to see past the obvious topics to the underlying problem-solving principles.
In Science...
Topics are
(1) Cycles
(2) Systems
(3) Interations
The heuristics are...
(1) Linking
(2) Specificity
(3) Comparison/Contrast
The 1st lot is taught explicitly in school. The 2nd lot is not, but forms a large part of the Science PSLE exam performance. Indeed, I was only able to find good documentation on scientific thinking skills from resources imported from USA. Principles such as Occam's Razor are useful when thinking about the questions in the SCIENCE PSLE paper, but you can't find it in any assessment book. So too is evidence-based concluding not explicitly taught nor documented... but tested.
The line between spoon feeding and NOT teaching was crossed sometime in the past 7 years. Why do we expect our under-12s to bridge gaps that took adults centuries to formulate without explicitly teaching them? Maybe it is true that my DS isn't bright and needs to be taught things other children are born knowing. Then again, there are a lot of children who aren't bright taking the PSLE exam too... and doing well because someone taught them. And then they had the requisite practice.
It is a mainstream exam after all. Should it be that those who do well GET taught because they have parents like me... or parents with money? Schools should teach everyone these basic heuristics and then may the best child win. -
Actually I sometimes fight the other battle, ironic it may seem.
Schools teach model diagram but there are some questions that can be solved without using model diagram and some schools penalise the children. Model diagram is a technique. My peeve is children are forced to use techniques prescribed, and not allowed to present a solution logically from their thought process. To me, that is even more wrong than not teaching some sophisticatedly-named heuristics. They are forced to conform to prescribed methodologies which I am so glad PSLE does not do that. -
ksi:
Yup... I dun like that either. It's like teaching the child just to Roast... and force the child to just Roast. I get my son to skim for techniques/heuristics from various sources... I teach my son to distill method from solution and store away the problem-solving principle.Actually I sometimes fight the other battle, ironic it may seem.
Schools teach model diagram but there are some questions that can be solved without using model diagram and some schools penalise the children. Model diagram is a technique. My peeve is children are forced to use techniques prescribed, and not allowed to present a solution logically from their thought process. To me, that is even more wrong than not teaching some sophisticatedly-named heuristics. They are forced to conform to prescribed methodologies which I am so glad PSLE does not do that.
School only teach Models.
THEN I encourage him to use any combination of techniques he has seen to get to the answer in the shortest time possible. I can't do what he does, he has to figure these out himself.
Heuristics is not just some sophisticated sounding thing. Don't let tutors make you believe otherwise. They are just very useful problem-solving techniques that are tested but not taught. I don't believe in tutors. And I am hard to bluff when it comes to teaching and learning.
The proof of the pudding is in the eating, really. When my DS was stuck only with models, he had little opportunity to be really creative. Now that he has collected a toolbox of quick and dirty heuristics, things are much faster and he can approach questions with a greater bandwidth of creativity. These other heuristics are not taught in school. So, if you listen to teacher and only know models... then that's too bad.
A carpenter with more tools in his toolbox, can do more in less time. A mathematician with more heuristics in his mental toolbox can similarly do more in less time. How can schools just teach modelling only?
It is possible we are disagreeing because you're not seeing what I mean by heuristics. Before P5, I had no idea either. Can't talk about ice cream if you haven't tasted it.
The worst thing is that after penalizing you left right and centre in lower primary for not using models, a large void appears for the obedient child in the PSLE where questions need solutions that are not model dependent (if you want speed and accuracy). Some problems take forever with models. -
Chenonceau and ksi, thanks for the interesting discussion.
I have heard about "short cuts" taught by tutors but I am worried that my boys will blindly apply the techniques without fully understand the concept. I was from science stream and am still the "come to person" for my Sec 2 and Sec 4 boys for their maths and science questions including Maths Olympiad questions, yet I don’t know any of the heuristics Cheononceau mentioned. I guess that’s because I learnt the concepts in schools with MOE materials. To me, having to learn all those heuristics could be more confusing than figuring out the solution from the concepts. -
wonderm:
Chenonceau and ksi, thanks for the interesting discussion.
I have heard about \"short cuts\" taught by tutors but I am worried that my boys will blindly apply the techniques without fully understand the concept. I was from science stream and am still the \"come to person\" for my Sec 2 and Sec 4 boys for their maths and science questions including Maths Olympiad questions, yet I don't know any of the heuristics Cheononceau mentioned. I guess that's because I learnt the concepts in schools with MOE materials. To me, having to learn all those heuristics could be more confusing than figuring out the solution from the concepts.
I don't even bother to learn them. I'm still as clueless about Math before we started P5. The advantage of being really lousy at Chinese and Math is that I encourage my child to go beyond me. I don't let me put a lid on what they are capable of.
I let my DS mess with as many heuristics as he can find... from wherever he might find them because I have no idea how to help him solve his Math questions even in Paper 1, let alone the Math Olympiad questions. He has only his Dad to go to... and Dad is often busy, and very confused by the various heuristics. Often, after they sit together for a while, it is my son who hashes together an approach with some strange technique and then explains to his Dad.
But if he didn't have them in the toolbox already, he wouldn't have been able to figure it out.
Most people think more is confusing, without realizing that the human brain comes alive with complexity. It is when we simplify everything that we get under performance because the larger part of the brain has gone to sleep. Teachers used to get my DD to write out a word 10 times to learn it. The more she learnt, the more mistakes she made in spelling test. I got fed up and I said \"Go to MSWord. Type out the word. Copy and paste 9 times. Print. I expect you to learn your spelling at ONE glance and I expect full marks.\" The next spelling test was full marks.
It is intuitive to teach by simplifying. But like what ksi mentioned once, you really dunno how efficiently your brain can learn until you push the envelope and start to wake it up. So, I teach by complexifying. No assessment books. Just real and exciting learning... dynamic and unpredictable exposure to knowledge, and then I get my DS to distill to principles for me.
I dunno if it works for all kids but it worked for both mine. -
Chenonceau:
You are right. There is no harm learning more techniques if one does not get confused by them. I just wanted to share it is not a \"must\" to know the heuristics. When my boys approach me with a question, I would guide them towards the solution but not just give them the answer. I always remind them not to \"remember\" a fixed way of doing a certain kind of question even if that is tempting and seemed to save time. By doing that too often, they will forget the concept behind.wonderm:
Chenonceau and ksi, thanks for the interesting discussion.
I have heard about \"short cuts\" taught by tutors but I am worried that my boys will blindly apply the techniques without fully understand the concept. I was from science stream and am still the \"come to person\" for my Sec 2 and Sec 4 boys for their maths and science questions including Maths Olympiad questions, yet I don't know any of the heuristics Cheononceau mentioned. I guess that's because I learnt the concepts in schools with MOE materials. To me, having to learn all those heuristics could be more confusing than figuring out the solution from the concepts.
I don't even bother to learn them. I'm still as clueless about Math before we started P5. The advantage of being really lousy at Chinese and Math is that I encourage my child to go beyond me. I don't let me put a lid on what they are capable of.
I let my DS mess with as many heuristics as he can find... from wherever he might find them because I have no idea how to help him solve his Math questions even in Paper 1, let alone the Math Olympiad questions. He has only his Dad to go to... and Dad is often busy, and very confused by the various heuristics. Often, after they sit together for a while, it is my son who hashes together an approach with some strange technique and then explains to his Dad.
But if he didn't have them in the toolbox already, he wouldn't have been able to figure it out. -
wonderm:
Yes... flexibility... I quite agree. But when the tools are numerous, the potential for flexible solutionning increases.
You are right. There is no harm learning more techniques if one does not get confused by them. I just wanted to share it is not a \"must\" to know the heuristics. When my boys approach me with a question, I would guide them towards the solution but not just give them the answer. I always remind them not to \"remember\" a fixed way of doing a certain kind of question even if that is tempting and seemed to save time. By doing that too often, they will forget the concept behind.
Also, your kids dun need these heuristics because they have a go-to person. My DS does not... many other kids don't.
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