Primary school maths: A vicious circle (from TODAY May 8)
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atutor2001:
yes, I must agree with you. Just take a look at the Maths problems in the Primary Maths threads where parents post their problems and are presented with modelling solutions. That didn't really solve their problems because they didn't learn how to fish. Few do by just looking at the solutions. Just look at how many parents came back again with similar problems. If they had learnt how to solve those problems, they wouldn't be back with the exact same problem types. This is so sad.....which means their children didn't learn anything as well.
Yes model is only 1 of the many heuristic approach. However, it is ironical to draw model because if someone can understand the logic/approach, he/she can solve without the models. Why spend time drawing the model? If one does not have the slightest idea of how to solve, drawing the models the wrong way will not help either. There are many ways to draw models but weak students usually only know how to draw simple comparison model of A & B. They can stare at them for the entire duration of the exam and nothing will surface.blessed777:
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Dont be confused, model drawing is only 1 of Heuristics approach. N if im not wrong MOErecommended 11 problem solving Heuristic for primary school level. As for my dd school p6 sa1 there are 7 problem solving Heuristic to be tested including MD....
....Onsponge bk shows solution for complex more/less than (using model drawing) but i find it easier to teach dd using tabulation..... \"
The impression given by many teachers and tutors is that drawing model will show us the way to the solution for most problem. To make matter worse, many teachers go to the extent of threatening their students that marks will be deducted if they don't use model. (because they only know how to determine if working is correct or wrong as answer keys used model).
To further complicate matter, many innovative individuals would do their best to apply/promote \"model method\" to all kinds of problem sum, including those that can be easier solved with other methods. A typical example is to represent the value of money in 4 units of $10 notes, with a rectangle divided into 4 rows and 10 columns.
Model concept has been abused. I have experimented with kids who failed miserably using model. Just teach them simple algebraic manipulation and simultaneous equations, they can solve most, if not all, the conventional problem sums by P6.
They had the fish caught for them and now they can only hope the exact same fish comes along in the exam, so that they can catch it. If the fish changes it's color, or it's size, they would not know how to catch it again. The same people are asking similar questions, again and again and again. It has become a vicious cycle.
The parents fail to understand that the presented solution is just a presentation, neatly packaged into nicely aligned boxes, the actual analysis of the problem was never explained. Why did they choose the particular heuristic as opposed to some other heuristic is never explained, it just is. The more astute students might form their own conclusions on a defining logic that links to that particular problem type. Most will just accept without questioning and move on. Such is life in the Maths underworld. -
Nebbermind:
I don't think it is a \"one method fits all questions\" type of teaching for Maths. Most schs / tuition centres teach by \"drilling\" - you practise more, recognise the question style and apply the methology to the same type of questions. I know of kids who have been drilled to do this, and score well in Maths when the questions are what they are exposed to. These kids will fail miserably in years when MOE came out with unconventional PSLE questions (which luckily did not happen in the last 2 years). I know, those kids who are very strong in Maths are all crying \"unlucky\" for the last 2 years. One man's meat is another man's poison - can't please all!
I think the main problem is that the kids don't try to analyzing the questions and try to solve it. Instead, they try to find a suitable heuristic to fit the qns. Like someone mentioned, the difficult qns can involve a couple or more heuristic...and the kids goes into mental block state. Math is not something u can solve with some standard prescribed steps.atutor2001:
Yes model is only 1 of the many heuristic approach. However, it is ironical to draw model because if someone can understand the logic/approach, he/she can solve without the models. Why spend time drawing the model? If one does not have the slightest idea of how to solve, drawing the models the wrong way will not help either. There are many ways to draw models but weak students usually only know how to draw simple comparison model of A & B. They can stare at them for the entire duration of the exam and nothing will surface.
The impression given by many teachers and tutors is that drawing model will show us the way to the solution for most problem. To make matter worse, many teachers go to the extent of threatening their students that marks will be deducted if they don't use model. (because they only know how to determine if working is correct or wrong as answer keys used model).
To further complicate matter, many innovative individuals would do their best to apply/promote \"model method\" to all kinds of problem sum, including those that can be easier solved with other methods. A typical example is to represent the value of money in 4 units of $10 notes, with a rectangle divided into 4 rows and 10 columns.
Model concept has been abused. I have experimented with kids who failed miserably using model. Just teach them simple algebraic manipulation and simultaneous equations, they can solve most, if not all, the conventional problem sums by P6. -
cherryc:
I dont know whether there is any book where you can find all the methods. All I hv just 2 heuristic math assesment bks n onsponge, which I hardly use due to time constraint. dd only done few pages of one bk n the other 2 left untouched. dd bring home tons of daily hw, so I use her hw to help her instead of assesment books & I only emphasize methods she learn at school. You dont have to master all methods to solve a problem, but mastering more methods will help to hv flexibility in problem solving. School text bk use drawing model method, but teacher also compliment some heuristics. She brings home good variety of math hw, not necessarily all challenging all the time. I would pick and teach questions which she is weak or which can help her to understand better. Sorry if I can't recommend u any book, some parents here recommend OnSponge. Make sure yr kids understand the concept well so they will be able to use any method they learn.Finally I got a better understanding of the model method . I was groping in the dark for the last few years . Different schools have different approaches and even in a given school , the better classes are taught more than the weaker classes. My DS took
PSLE, I realise that many methods taught by the assessment books are not taught in school, neither were they documented in the textbooks. When I finally sent him to tuition, it was too late as he was bombarded with even more model methods. We were so frustrated then.
By the way, which book would you recommend to study comprehensively all the model methods?? Where can I find the 11 methods which I don't even know after so many years. -
TheBluePapa:
At the very least, such free resources help these astute students... which is better than having no one to ask... I guess. Have you in mind other ways to help such students who may have nowhere else to ask their questions when schools test what they don't think they need to teach?
The parents fail to understand that the presented solution is just a presentation, neatly packaged into nicely aligned boxes, the actual analysis of the problem was never explained. Why did they choose the particular heuristic as opposed to some other heuristic is never explained, it just is. The more astute students might form their own conclusions on a defining logic that links to that particular problem type. Most will just accept without questioning and move on. Such is life in the Maths underworld. -
Frankly speaking, I won’t recommend onsponge unless the child already had a very strong and good foundation. If not, it will create confusion. The basic concept must be there before inputting more.
To me, Andrew Er’s books are good enough. -
Mychildren:
heh, heh, everyone have their own pet books.Frankly speaking, I won't recommend onsponge unless the child already had a very strong and good foundation. If not, it will create confusion. The basic concept must be there before inputting more.
To me, Andrew Er's books are good enough.
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Mychildren:
Only had onsponge and agree that the kid need to have strong foundation or else it's just a waste of time. I find the GEP qns still easier than the more difficult onsponge qns.Frankly speaking, I won't recommend onsponge unless the child already had a very strong and good foundation. If not, it will create confusion. The basic concept must be there before inputting more.
To me, Andrew Er's books are good enough. -
Chenonceau:
don't get me wrong. The free resources are great. It is just that it not used to it's fullest potential. The problem solvers are great people who are interested in helping children. The issue is that the parents or sometimes, the children are not asking the right questions to the problem solvers. They just take the solution, say their thanks and off they go. Only to return in a few days later with more questions on the same topic. So much for fishing on their own.
At the very least, such free resources help these astute students... which is better than having no one to ask... I guess. Have you in mind other ways to help such students who may have nowhere else to ask their questions when schools test what they don't think they need to teach?TheBluePapa:
The parents fail to understand that the presented solution is just a presentation, neatly packaged into nicely aligned boxes, the actual analysis of the problem was never explained. Why did they choose the particular heuristic as opposed to some other heuristic is never explained, it just is. The more astute students might form their own conclusions on a defining logic that links to that particular problem type. Most will just accept without questioning and move on. Such is life in the Maths underworld.
If they had asked the pertinent questions, why this heuristic, why not that heuristic ? what defines this particular question type ? how would they recognize such question type again, what are the possible permutations of this particular question type ? why is it that when the question is phrased this way, it means ....., why doesn't it mean ...... ask the questions, so that you know how to fish on your own.....
It is only by asking such questions, it shows that the student is actively analyzing the question as opposed to just accepting it. The problem solvers have experience in handling hundreds of such problems and can give you insights into their world, if you only ask. I have yet to see such questions, most just ask why is 1 + 1 = 2 type of questions, if at all. -
TheBluePapa:
don't get me wrong. The free resources are great. It is just that it not used to it's fullest potential. The problem solvers are great people who are interested in helping children. The issue is that the parents or sometimes, the children are not asking the right questions to the problem solvers. They just take the solution, say their thanks and off they go. Only to return in a few days later with more questions on the same topic. So much for fishing on their own.
At the very least, such free resources help these astute students... which is better than having no one to ask... I guess. Have you in mind other ways to help such students who may have nowhere else to ask their questions when schools test what they don't think they need to teach?Chenonceau:
[quote=\"TheBluePapa\"]
The parents fail to understand that the presented solution is just a presentation, neatly packaged into nicely aligned boxes, the actual analysis of the problem was never explained. Why did they choose the particular heuristic as opposed to some other heuristic is never explained, it just is. The more astute students might form their own conclusions on a defining logic that links to that particular problem type. Most will just accept without questioning and move on. Such is life in the Maths underworld.
If they had asked the pertinent questions, why this heuristic, why not that heuristic ? what defines this particular question type ? how would they recognize such question type again, what are the possible permutations of this particular question type ? why is it that when the question is phrased this way, it means ....., why doesn't it mean ...... ask the questions, so that you know how to fish on your own.....
It is only by asking such questions, it shows that the student is actively analyzing the question as opposed to just accepting it. The problem solvers have experience in handling hundreds of such problems and can give you insights into their world, if you only ask. I have yet to see such questions, most just ask why is 1 + 1 = 2 type of questions, if at all.[/quote]I agree. Thanks for clarifying.
I post on average 3 questions a month in that thread and I don't bother to understand the working directly. I get my son to log on and explain the why to me... and to brainstorm alternative methods of solving.
Maybe this helps? I'm a math idiot so this is the best I could think of to help DS to mastery. But I will bear in mind your advice. Thanks for sharing. -
atutor2001:
When my dd was in P3 her school conducted parent's workshop introducing model drawing, they told us that the children are required to use MD in their exam up till P4 if i remember correctly. It is because they are expected to understand MD before using other method, so I did not teach dd other method as not to confuse her n also MD is the only method which is allowed in exams. Only when dd in p5 I go ahead helping her with other method when I see her teacher introduced her class many other ways in solving problems.
Yes model is only 1 of the many heuristic approach. However, it is ironical to draw model because if someone can understand the logic/approach, he/she can solve without the models. Why spend time drawing the model? If one does not have the slightest idea of how to solve, drawing the models the wrong way will not help either. There are many ways to draw models but weak students usually only know how to draw simple comparison model of A & B. They can stare at them for the entire duration of the exam and nothing will surface.
The impression given by many teachers and tutors is that drawing model will show us the way to the solution for most problem. To make matter worse, many teachers go to the extent of threatening their students that marks will be deducted if they don't use model. (because they only know how to determine if working is correct or wrong as answer keys used model).
To further complicate matter, many innovative individuals would do their best to apply/promote \"model method\" to all kinds of problem sum, including those that can be easier solved with other methods. A typical example is to represent the value of money in 4 units of $10 notes, with a rectangle divided into 4 rows and 10 columns.
Model concept has been abused. I have experimented with kids who failed miserably using model. Just teach them simple algebraic manipulation and simultaneous equations, they can solve most, if not all, the conventional problem sums by P6.
ppl tend to forget that technics/methods are meant to help in solving problem, NOT learning technics for the sake of technics and become a prisoner of technics. I learnt it at school when my math teacher asked the class on hw to solve a problem, none can come up with answer & when he finally asked me n I answered with simple calculation the whole class mumbled :\" oh.. its only like that...\" as if its only a simple answer that everyone can come up with but none came up with answer just showed that they dont hv enough understanding of the concept therefore their imagination gone to the most difficult technic that they can come up with and ended up with no answer.
When i helped dd in solving a math hw problem she told me \"mom, u r using branch method ! \" I was like \"huh? it has a name ?? I didnt know that\" ÿes mom i learned it at school\" \"is it in yr text bk ? \" \"no, but the p1 text bk has almost similar thing called number bonding\" ok you can call it whatever, mommy just call it logical thinking later on I found out onsponge bk has it & it called part-whole relationship... 
I understand that assesment bks has terminologies for the technics to help students in identifying which problem sum & which technic to apply, it does not meant to be rote learning... the students still need to understand the concepts,
when you really understand the concepts, no matter what name it will be in next 10yrs you still be able to identify and even solve it...
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