Q&A - PSLE Math

[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 I am outdated.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.

[atutor2001]

rains:

.....while algebra is more of a shortcut....

Thanks for enlightening me. Math has been my hobby and I learnt something new today. I rest my case.

[rains]

lego:

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?

I thought teachers would ask the kids to buy one at P2 or 3 bcos most of them are not able to draw models properly or equally. You may want to check with your kid's school bookshop first. If don't have, check out Popular? I always assume they are able to use it during their exams. I haven't read a rule that's against model rulers.

Actually, I have also been to a secondary school, and studied subjects other than P6 Maths, so yeah, I do know that algebra is used elsewhere besides being a heuristic. :roll:

[Full.010894Cream]

hi rains


were u ever a IJ girl? :lol:

[rains]

Full.Cream:

hi rains


were u ever a IJ girl? :lol:

Oh no. Never. This is strange. Even in real life, a colleague insisted that I'm from a girls' school. I always thought that it has good implications if someone thought you're from a girls' school. I take it as a compliment, even if you never intended it that way.

Why? You are huh?

[MoonFlower]

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?

You can get model rulers from Popular or yr dd's bookshop. Its about $1.80 i used to get a few cos, my ds either lost it or it kind of break easily.