Q&A - PSLE Math
-
rains:
Right you are, rains...It's interesting how outsiders perceive teachers as ignorant when outsiders are ignorant of how teachers and the education system work.
Teachers in Singapore have been through the compulsory education of primary school and have advanced beyond secondary school education. Most teachers are graduates and even for those who are not, I'm very sure they have learnt algebra in secondary school.
Teachers do know how to use algebra to solve problems. The real problem is: primary school students' maths syllabus does not require them to use algebra to solve problems. Sure, teachers can teach them to use algebra as a heuristic, but we're sure to see more confused students than enlightened ones, given that the majority are struggling with the current number of problem-solving strategies.
And to teach students to use algebra as a heuristic, the content of the topic needs to be more in-depth than what we have at present, and algebra is perceived to be of a higher level maths. Most of our children are not ready for it.
So, teachers do not show students how to use algebra to solve problems. Teachers do use algebra to solve problems, but as teachers, they need to devise a method other than algebra to solve the problem before they demonstrate it to students. From what I know, some teachers use algebra to solve the problem first, if it's difficult, then work backward to find a heuristic familiar and easier for students to use. In fact, many teachers are adept at using algebra to solve mathematical problems, but they spend alot more time on how to use a 'simpler' method so that students are able to use what they are taught and are familiar with to solve the problems.
So please don't assume that teachers do not know their algebra.
Most teachers just see algebra as an alternative way of solving problems, like, instead of climbing a wall, you just walk around it? That is an easier way, but the teachers want you to scale that wall, to make it over, to know what you are doing!
Just in that way, the teachers aren't entirely REFUSING to teach in-depth algebra, they just want to see their students using the methods taught to them in school, so they don't feel their efforts are being wasted talking on and on about methods that are blatantly being ignored because of the \"easier\" algebraic method... -
Muffins:
I think you didn't get my point. Teachers are not so inflexible as to want students to use the methods taught for the sake of not wasting their effort in teaching the methods. Teachers have many constraints in teaching. If any teacher dares to challenge the syllabus and teach algebra as a heuristic, any parent can jump up to the teacher's face and get the teacher sacked because it's out of syllabus. Most of our children are NOT ready for algebra and the topic is out of syllabus. If teachers teach algebra, they are asking for trouble.Right you are, rains...
Most teachers just see algebra as an alternative way of solving problems, like, instead of climbing a wall, you just walk around it? That is an easier way, but the teachers want you to scale that wall, to make it over, to know what you are doing!
Just in that way, the teachers aren't entirely REFUSING to teach in-depth algebra, they just want to see their students using the methods taught to them in school, so they don't feel their efforts are being wasted talking on and on about methods that are blatantly being ignored because of the \"easier\" algebraic method...
To adults, algebra is easy. To kids, algebra is greek. It's very abstract for children to associate algebra with numbers and problem-solving. It's definitely not an 'easier' way to solve problems.
Our syllabus is not plucked out of thin air. Teachers teach only certain things and not other things because of the cognitive level of children. I'm sure there isn't a teacher who wants to confine his students to what he teaches. Teachers are human beings like you and I. Teachers also been through schools. Teachers also have kids themselves. Teachers think as parents. They just hope that parents can, for a moment, think as teachers. -
rains:
..... Teachers have many constraints in teaching. If any teacher dares to challenge the syllabus and teach algebra as a heuristic, any parent can jump up to the teacher's face and get the teacher sacked because it's out of syllabus..
I don't think most parents here are asking the teachers to change the syllabus on their own. We just want the teachers to accept algebra as an alternative method for solving math problem - don't just say no or mark wrong.rains:
Most of our children are NOT ready for algebra
Totally disagreed. Most of my friends and myself have taught our kids algebra on our own from as early as P4. We don't face any problem with teaching algebra to our kids. The only problem we face is the teacher. But we long learned to tell the teacher to leave our kids alone - sound arrogant but that was what I did to 1 silly lady teacher who insisted in using model. No problem with the other teachers though (mostly male :oops: )rains:
Our syllabus is not plucked out of thin air. Teachers teach only certain things and not other things because of the cognitive level of children. ..
Forgive me for being rude in what I am going to write here because I felt passionately about the too many wrongs that have been going on. To me, our syllabus are drawn up by a group of DREAMERS who do not touch base with the real world. They have no idea how difficult the PROCESS of developing a model is. Just to list a few of the difficulties :
1. Can't draw straight line free-hand
2. Can't divide models into correct number of equal parts
3. Don't know what to compare - comparing A to B or their totals or ...
4. Don't know in which direction to add or remove from the model to show the changes
Those DREAMERS were probably conned into believing that model is wonderful because they were shown only the final product - a beautifully computer-drawn model (everything to scale) showing clearly the relationship of the different parameters. They failed to try DEVELOPING a model on their own. See what a model looks like if you use free-hand (don't suggest using ruler, no time for such luxury during exam). If any of the DREAMERS had tried solving a complex question using model, they would probably be as agitated as me. It took me 3 years to understand the various tricks in developing models. (don't laugh - I am quite stupid but not that stupid you know :P) After mastering the skill of model drawing, I am totally not impressed by it at all. However, I must still concede that model is the most power tool for questions with \"minimum information given\".
Lets look at the other subject - English, the DREAMERS thought that \"Thematic approach\" is the right way because they saw Ang Mo teaching it that way. They failed to understand that most parents here don't speak proper English at home. As a result, we end up with many batches of students who don't know basic grammars and can't write simple reports.
The DREAMERS realised their mistakes and tried to make amendments by re-introducing grammar in the text book (I think last year). However, being DREAMERS, they overkilled again. I was shocked to find the level of grammar so very chim that even adults have problem doing - aren't they DREAMERS? -
atutor2001:
Hi atutor2001,rains:
..... Teachers have many constraints in teaching. If any teacher dares to challenge the syllabus and teach algebra as a heuristic, any parent can jump up to the teacher's face and get the teacher sacked because it's out of syllabus..
I don't think most parents here are asking the teachers to change the syllabus on their own. We just want the teachers to accept algebra as an alternative method for solving math problem - don't just say no or mark wrong.rains:
Most of our children are NOT ready for algebra
Totally disagreed. Most of my friends and myself have taught our kids algebra on our own from as early as P4. We don't face any problem with teaching algebra to our kids. The only problem we face is the teacher. But we long learned to tell the teacher to leave our kids alone - sound arrogant but that was what I did to 1 silly lady teacher who insisted in using model. No problem with the other teachers though (mostly male :oops: )rains:
Our syllabus is not plucked out of thin air. Teachers teach only certain things and not other things because of the cognitive level of children. ..
Forgive me for being rude in what I am going to write here because I felt passionately about the too many wrongs that have been going on. To me, our syllabus are drawn up by a group of DREAMERS who do not touch base with the real world. They have no idea how difficult the PROCESS of developing a model is. Just to list a few of the difficulties :
1. Can't draw straight line free-hand
2. Can't divide models into correct number of equal parts
3. Don't know what to compare - comparing A to B or their totals or ...
4. Don't know in which direction to add or remove from the model to show the changes
Those DREAMERS were probably conned into believing that model is wonderful because they were shown only the final product - a beautifully computer-drawn model (everything to scale) showing clearly the relationship of the different parameters. They failed to try DEVELOPING a model on their own. See what a model looks like if you use free-hand (don't suggest using ruler, no time for such luxury during exam). If any of the DREAMERS had tried solving a complex question using model, they would probably be as agitated as me. It took me 3 years to understand the various tricks in developing models. (don't laugh - I am quite stupid but not that stupid you know :P) After mastering the skill of model drawing, I am totally not impressed by it at all. However, I must still concede that model is the most power tool for questions with \"minimum information given\".
Lets look at the other subject - English, the DREAMERS thought that \"Thematic approach\" is the right way because they saw Ang Mo teaching it that way. They failed to understand that most parents here don't speak proper English at home. As a result, we end up with many batches of students who don't know basic grammars and can't write simple reports.
The DREAMERS realised their mistakes and tried to make amendments by re-introducing grammar in the text book (I think last year). However, being DREAMERS, they overkilled again. I was shocked to find the level of grammar so very chim that even adults have problem doing - aren't they DREAMERS?
You are right in saying that some children take to algebra like a chocaholic to Cadbury, but rains in right in saying that some children in some schools break their heads over an algebra problem, both of you make valid points...
As for the models, you are SO right, atutor2001, the teacher usually get perfect, computerised versions of the models that makes them think it is so \"easy\" to understand, but they cannot grasp the concept that some students draw free-hand, and try to understand the problem from there...
For the English, you could not be a more correct person. The grammar that some students use is \"not applicable\" in some of the textbook problems, but when the teachers don't have the \"all revered\" answer sheet with them, they suddenly are blank, not understanding the problem themselves, saying \"wait!\" and making excuses themselves... The should at least give english and maths problems that the teachers themselves understand without the answer sheet, right?!
Quite miffed by this problem in schools... :x [/img]
-
atutor2001:
Hi atutor2001,rains:
..... Teachers have many constraints in teaching. If any teacher dares to challenge the syllabus and teach algebra as a heuristic, any parent can jump up to the teacher's face and get the teacher sacked because it's out of syllabus..
I don't think most parents here are asking the teachers to change the syllabus on their own. We just want the teachers to accept algebra as an alternative method for solving math problem - don't just say no or mark wrong.rains:
Most of our children are NOT ready for algebra
Totally disagreed. Most of my friends and myself have taught our kids algebra on our own from as early as P4. We don't face any problem with teaching algebra to our kids. The only problem we face is the teacher. But we long learned to tell the teacher to leave our kids alone - sound arrogant but that was what I did to 1 silly lady teacher who insisted in using model. No problem with the other teachers though (mostly male :oops: )rains:
Our syllabus is not plucked out of thin air. Teachers teach only certain things and not other things because of the cognitive level of children. ..
Forgive me for being rude in what I am going to write here because I felt passionately about the too many wrongs that have been going on. To me, our syllabus are drawn up by a group of DREAMERS who do not touch base with the real world. They have no idea how difficult the PROCESS of developing a model is. Just to list a few of the difficulties :
1. Can't draw straight line free-hand
2. Can't divide models into correct number of equal parts
3. Don't know what to compare - comparing A to B or their totals or ...
4. Don't know in which direction to add or remove from the model to show the changes
Those DREAMERS were probably conned into believing that model is wonderful because they were shown only the final product - a beautifully computer-drawn model (everything to scale) showing clearly the relationship of the different parameters. They failed to try DEVELOPING a model on their own. See what a model looks like if you use free-hand (don't suggest using ruler, no time for such luxury during exam). If any of the DREAMERS had tried solving a complex question using model, they would probably be as agitated as me. It took me 3 years to understand the various tricks in developing models. (don't laugh - I am quite stupid but not that stupid you know :P) After mastering the skill of model drawing, I am totally not impressed by it at all. However, I must still concede that model is the most power tool for questions with \"minimum information given\".
Lets look at the other subject - English, the DREAMERS thought that \"Thematic approach\" is the right way because they saw Ang Mo teaching it that way. They failed to understand that most parents here don't speak proper English at home. As a result, we end up with many batches of students who don't know basic grammars and can't write simple reports.
The DREAMERS realised their mistakes and tried to make amendments by re-introducing grammar in the text book (I think last year). However, being DREAMERS, they overkilled again. I was shocked to find the level of grammar so very chim that even adults have problem doing - aren't they DREAMERS?
You are right in saying that some children take to algebra like a chocaholic to Cadbury, but rains in right in saying that some children in some schools break their heads over an algebra problem, both of you make valid points...
As for the models, you are SO right, atutor2001, the teacher usually get perfect, computerised versions of the models that makes them think it is so \"easy\" to understand, but they cannot grasp the concept that some students draw free-hand, and try to understand the problem from there...
For the English, you could not be a more correct person. The grammar that some students use is \"not applicable\" in some of the textbook problems, but when the teachers don't have the \"all revered\" answer sheet with them, they suddenly are blank, not understanding the problem themselves, saying \"wait!\" and making excuses themselves... The should at least give english and maths problems that the teachers themselves understand without the answer sheet, right?! Quite miffed by this problem in schools... :x
-
Sorry, I still don't get it. :? Can someone explain with working please? Thanks.
atutor2001:
I also get $380, tianzhu also get 380 so I think it should be correct. :lol:[/quote]
Hi atutor2001,Muffins:
[quote=\"atutor2001\"]This question is actually a prelim question from a neighbourhood school. It is very interesting because it tests the kids understanding of fractions and multiples. For those who love using model, it is the easiest way to understand.
Is the answer $380? -
KSP:
The working goes something like this :Sorry, I still don't get it. :? Can someone explain with working please? Thanks.
A man spent 1/5 of his money on clothes and a few sevenths on food. He has $152 left. How much did he spend on food?
Since the money is divided into 1/5 and sevenths, so we divide the money into 35 units (LCM of 5 and 7)
1/5 = 7 units
1/7 = 5 units
After spending 7 units (1/5) on clothes the man has 35 - 7 = 28 units left
These 28 units is the total of amount spent on food and $152.
However, the amount spent on food is in \"sevenths\" that is it must be in multiples of 5 units.
So the amount spent on food and remaining money left can be :
Food - 5 units Left - 23 units
Food - 10 units Left - 18 units
Food - 15 units Left - 13 units
Food - 20 units Left - 8 units
Food - 25 units Left - 3 units
The amount left is $152 and the only combination where the amount \"left\" can be divided without recurring decimal is \"Left - 8 units\". Those with recurring decimal has to be rejected because money cannot be broken down into recurring decimal.
Therefore 8 units = 152 so 1 unit = 152/8 = 19
Food = 20 units = $380
Hope the explanation is ok -
atutor2001:
I don't think most parents here are asking the teachers to change the syllabus on their own. We just want the teachers to accept algebra as an alternative method for solving math problem - don't just say no or mark wrong.
Teachers do accept algebra as a problem solving method. They mark wrong probably bcos they are not sure if the children did the sums themselves or were helped by parents. Being untaught, it's only reasonable to assume that the sum was done by the parents.atutor2001:
Yes. You teach YOUR OWN kids. Individually. Teachers teach a class of 40. I also have no problem getting my kid to read Charlotte's Web at kindy, or Harry Potter or Roald Dahl's books at P1. You go look at the kids in our neighbourhood schools. They read the same books as my kid when she was in kindy when they are at P6. Will I be able to get 40 kids to read Roald Dahl at P1? I really doubt so. It doesn't make me a good teacher just becos I'm able to get my kid to read earlier. I'm able to teach my kid to solve questions using simple algebra too, but I doubt I can train even 20 kids who fail their Maths to use algebra to do anything. If you really feel strongly that you're able to teach algebra to 40 P6 kids, try teaching as a job.Totally disagreed. Most of my friends and myself have taught our kids algebra on our own from as early as P4. We don't face any problem with teaching algebra to our kids.
atutor2001:
Er ... there's this thing called 'model ruler' which is meant to fix the motor skills related problems (no. 1 and 2). And teachers are supposed to teach No. 3 and 4.They have no idea how difficult the PROCESS of developing a model is. Just to list a few of the difficulties :
1. Can't draw straight line free-hand
2. Can't divide models into correct number of equal parts
3. Don't know what to compare - comparing A to B or their totals or ...
4. Don't know in which direction to add or remove from the model to show the changesatutor2001:
English - I agree. But you must admit that they did have good intentions. They were probably imitating the British, American and Australian style which did not teach Grammar explicitly, but built Grammar into their conversational. They probably thought it could work if done at an early age.Lets look at the other subject - English, the DREAMERS thought that \"Thematic approach\" is the right way because they saw Ang Mo teaching it that way. They failed to understand that most parents here don't speak proper English at home. As a result, we end up with many batches of students who don't know basic grammars and can't write simple reports.
The DREAMERS realised their mistakes and tried to make amendments by re-introducing grammar in the text book (I think last year). However, being DREAMERS, they overkilled again. I was shocked to find the level of grammar so very chim that even adults have problem doing - aren't they DREAMERS?
They are also human beings what. Not saints right? To err is human. Must forgive and forget lah.
I think I've this tendency to make people sidetrack horribly in the threads. I don't mean to do that. Teaching is one of the most misunderstood job in the whole world. I just want to give a voice to a thankless job. -
:celebrate: :udawoman: :udaman: :thankyou:
atutor2001:
The working goes something like this :KSP:
Sorry, I still don't get it. :? Can someone explain with working please? Thanks.
A man spent 1/5 of his money on clothes and a few sevenths on food. He has $152 left. How much did he spend on food?
Since the money is divided into 1/5 and sevenths, so we divide the money into 35 units (LCM of 5 and 7)
1/5 = 7 units
1/7 = 5 units
After spending 7 units (1/5) on clothes the man has 35 - 7 = 28 units left
These 28 units is the total of amount spent on food and $152.
However, the amount spent on food is in \"sevenths\" that is it must be in multiples of 5 units.
So the amount spent on food and remaining money left can be :
Food - 5 units Left - 23 units
Food - 10 units Left - 18 units
Food - 15 units Left - 13 units
Food - 20 units Left - 8 units
Food - 25 units Left - 3 units
The amount left is $152 and the only combination where the amount \"left\" can be divided without recurring decimal is \"Left - 8 units\". Those with recurring decimal has to be rejected because money cannot be broken down into recurring decimal.
Therefore 8 units = 152 so 1 unit = 152/8 = 19
Food = 20 units = $380
Hope the explanation is ok -
How do you become a "class monitor"?
Hello! It looks like you're interested in this conversation, but you don't have an account yet.
Getting fed up of having to scroll through the same posts each visit? When you register for an account, you'll always come back to exactly where you were before, and choose to be notified of new replies (either via email, or push notification). You'll also be able to save bookmarks and upvote posts to show your appreciation to other community members.
With your input, this post could be even better š
Register Login
Online Users
Statistics
Popular Topics
