Parents, not enrichment centres, are key to result
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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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Chenonceau:
The go-to person can be the teacher in school. If we keep thinking no point asking them, then we are under-utilising the teachers as a resource in school. It is nice to know that when my child misses any lesson in school, the teachers, especially Math ones, would always ask if she has any problem doing the homework sheet for Math for the lesson learned. Albeit my child typically needs no help but it is nice to know the teacher asks. For children without much parental help at home or tuition/enrichment and yet perform well, I believe their guidance are the teachers in school, otherwise, where else?
Yes... flexibility... I quite agree. But when the tools are numerous, the potential for flexible solutionning increases.wonderm:
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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