Q&A - PSLE Math

[rains]

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:

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.

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.

atutor2001:

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

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.

atutor2001:

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?

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.

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.

[KSP]

:celebrate: :udawoman: :udaman: :thankyou:

atutor2001:

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?

The working goes something like this :

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

[Muffins]

How do you become a "class monitor"?

[ChiefKiasu]

Muffins:

How do you become a \"class monitor\"?

Class monitor positions are on an invitation basis. We study the contribution and savvyness of specific members and if we deem they are suitable for the class monitor position, we invite them to take up the challenge.

[atutor2001]

Hi KSP


Glad that you agree with my working. I am not sure of it myself.

There is a very interesting story behind this question. It happened at the market. My favourite vegetable stallholder was scolding her son for his poor math marks. The son protested claiming that some of the questions were so difficult that he still didn’t understand after the teacher’s explanation. So I kay poh volunteering to help. Her son show me the question and I was so embarrassed - I also don’t know how to do.

Math is very scary. I wonder what other new variations they will come up next to torture the poor kids.

[atutor2001]

rains:

..... You teach YOUR OWN kids. Individually. Teachers teach a class of 40.... You go look at the kids in our neighbourhood schools..... but I doubt I can train even 20 kids who fail their Maths to use algebra to do anything....

I agree that not all kids who fail their Maths will be able to do algebra. However, there is a group of kids (especially boys) who failed math because they hated drawing models. Personally, I have helped a number of my relatives' sons from neighbourhood schools who failed math through the use of algebra.

I feel that the authority needs to relook at the usefulness of model and give algebra a try instead of sticking to model for so many years despite hearing all the complaints.

rains:

atutor2001:

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

Er ... there's this thing called 'model ruler' which is meant to fix the motor skills related problems (no. 1 and 2).

My apology. I am outdated. During my kids' time model ruler is banned from exam. Didn't know that it can be used now. Even then, the ruler is of no help for problem like this one :

7/8 of A's apples is the same as 8/9 of B's apples. Find the ratio of A's apples to B's apples

rains:

atutor2001:

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

... And teachers are supposed to teach No. 3 and 4.

I wish I have your optimism. To develop a model, one of the most basic consideration before we start drawing is to look for 2 parts that remained the same. Then we start drawing from there. For example :

1. If equal amounts are added to A and B then the \"difference remained the same\". So we develop the model from the \"difference\"
2. If A gives to B than the total of A & B remains the same. So we develop the model by comparing the total of A & B

Those are just 2 of the most basic skills of model drawing. There are many many more. I have not come across teachers teaching the students such skills. Maybe there are some extra-ordinary teachers who do impart such knowledge. Even then, model is not a generic method. We need to understand, remember and apply certain prerequisite conditions before we can develop a meaningful model. How many conditions do we want the kids to remember and to learn to identify so that they can be proficient in developing the correct model?

The model itself cannot show us that the difference or the total did not change. However, if algebra is used, we need not care which part did not change. The problem can still be solved.

In conclusion, model method is a shortcut that looks so simple and short when one knows how to draw. For all shortcuts, vast knowledge is needed before one can apply it efficiently. Comparatively, the knowledge needed for forming 2 equations and solving is so much simplier.

[rains]

atutor2001:

In conclusion, model method is a shortcut that looks so simple and short when one knows how to draw. For all shortcuts, vast knowledge is needed before one can apply it efficiently. Comparatively, the knowledge needed for forming 2 equations and solving is so much simplier.

I'm not sure if it's your biasness towards model-drawing that makes model method look like a shortcut. I always thought it a problem-solving method while algebra is more of a shortcut.

Like what you said, vast knowledge is needed before one can apply to a shortcut effectively. If algebra is a suitable method for problem-solving, children will need to start learning simple algebra at P2 or P3 onwards in order to lead them to the abstract at P6. Learning Maths is a spiral process. Just like model-drawing. It doesn't start at P6. Children learn the concrete at P2, move on to pictorial (drawing) at later part of P2 and advance to abstract (drawing models as representation) from P2 to P3. And thereafter, they are required to employ model-drawing as one of the heuristics, from simple sums to complex ones.

The way I see it, algebra is a shortcut in itself, which is why it is reserved as a heuristic at secondary level.

As to model-drawing is not a 'generic method', I can only say that there isn't a heuristic that's 'generic'. Even for simple addition and subtraction, we don't add or minus the moment we see the words 'altogether' and 'fewer'. We also need to make careful consideration before we decide if it's really addition or subtraction and the 'keywords' may very well be a distractor.

Have parents really wrote in to MOE to complain about the model method? You would need to have a substantial number of educated parents to vote against this I believe. If it's just complaints on the ground level, MOE probably wouldn't have heard it.

[James Ang]

rains:

atutor2001:

The way I see it, algebra is a shortcut in itself, which is why it is reserved as a heuristic at secondary level.

I use model and heuristics to teach primary level Maths but students will start learning algebra to solve problems in secondary level Maths. There is almost no limit in the use of algebra which is not just a heuristic. Algebra is an extensive field of study in Maths and algebra is applied in Add Maths and Physics as well as in some social science such as Economics and even Marketing.

[lego]

rains:

Er ... there's this thing called 'model ruler' which is meant to fix the motor skills related problems (no. 1 and 2).

Hi, may i ask - how does a model ruler looks like :oops: and where can i get it? Dd is poor in her fine motor skills. Is it allowed to be used in exam?

[James Ang]

lego:

rains:

Er ... there's this thing called 'model ruler' which is meant to fix the motor skills related problems (no. 1 and 2).

Hi, may i ask - how does a model ruler looks like :oops: and where can i get it? Dd is poor in her fine motor skills. Is it allowed to be used in exam?

It looks like a stencil except that the shapes are drawn in squares, rectangles, bars and circles of different sizes. They used to be available in bookshops but now is rather hard to find. Do ask around for it at bookshops and find out if they still sell it.