PSLE - New Format for Maths

[James Ang]

kiasiparent:

Rason:

Some Suggestions on previous postings...


For trigonometry functions, picture the angle and subtending sides as -

cos --> crocodile's mouth
sin --> slide
tan --> \"t\" has right angle

(Mnemonics used this way enhances visual memory. After all it's geometry we are working with.)

Are you chinese? Do you know something called 'toa cah soh'?

TOA CAH SOH is really very effective, it makes Singapore students very pro in Trigonometry! I think TOA CAH SOH has been around for more than 20 years! :!:

[HoSayLiao]

To be on the safe side, trigonometry should also be taught. Hopefully with time, AP and GP can be taught as well. P6 students can also be taught how to derive formula for the nth term in a number sequence.


I will also be teaching my students similar figure. (L1/L2)^2 = A1/A2, (L1/L2)^3 = V1/V2.

Did I miss out anything?

[HoSayLiao]

Oh by the way, (A1/A2)^1.5 = V1/V2

[Rason]

david59:

I would love to see the status quo too. But with the latest saga of the PSLE Maths, I am very sure many kiasu and kiasi parents and schools will want to make sure their kids will be drilled to use Algebra in P6 so as not to be disadvantaged in solving tough qns during PSLE next year. Seriously, a few of the PSLE qns this year would be easier to solve with Algebra than with model method. Next year I will definitely teach my students to use Algebra even though I have always prefer Models as they are not so abstract as using Algebra. Such is life. :celebrate:

In any case it can never be \"Teach Less Learn More\".

kiasiparent:

Are you chinese? Do you know something called 'toa cah soh'?

Yes, I'm Chinese and I'm in touch with my dialect. But remembering \"o\" as \"opposite\", \"a\" as \"adjacent\", etc. and relating them to the diagram is a tad slow as compared to recognizing the pictorial pattern itself.

Let me quote sight-reading of music notation as an example. We don't actually take time to count the notes from a reference space or line like we are taught in primary school music lessons. We are supposed to identify a bar of notes as a pattern. The brain can relate to visual patterns as abstract as that.

[Rason]

ameryeducation:

...At the end of the day, we must see that algebra is a step forward from the model drawing method. Whilst the model drawing method represents unknowns visually as boxes, algebra uses abstract symbols. So when algebra is being taught, it is important that (1) students are already familiar with the model drawing method and (2) the transition is smooth with the similarities of model drawing method and algebra made clear.


In other words, at the P5/6 level, only students who are clearly ahead of their cohort should learn and employ algebra, and parents and educators should not emphasise the differences between algebra and model drawing method, but rather the similarities and how algebra builds upon the model drawing method...

I concur with all the above except for \"only students who are clearly ahead of their cohort should learn and employ algebra\". Since the two methods are homologous, they should complement each other - which means learning both will help to improve the students' overall dexterity in problem solving and teachers should reorder their curriculum time for that accordingly. Like I proposed earlier, the maximum efficiency is with using models to tackle equation construction and using Algebraic operation to reduce the model, instead of planning model reduction right in the first place. By the way I'm basing this argument on the \"Chocolates & Sweets\" archetype, which happened to shift model planning into overdrive. For the conventional questions, model drawing alone does the trick.

[Rason]

Hi Amery, I tried to break down the flow of your grid method and compare against mine (call it "1D forward construction with Algebra"). My comparison draws the following conclusion -


1. The grid method typically works back to front.

2. It provides vertical axes for one-stroke division which otherwise would take multiple strokes in a 1D model.

3. The same division concept, for making LCM or otherwise, can be applied in both models nevertheless.

4. In my case I prefer to use Algebra to reduce step 3 into getting the first unknown variable. Thereon substitution into the other variable (basically the other bar diagram) becomes apparent. That said, the grid division and substitution idea is not that apparent, i.e. about as abstract as using alphanumeric representation of quantities (Algebra).

5. Like you said, for the simpler questions without the convenience of vertical axes coming into play, it becomes an overkill (probably at the expense of solution catches that are better visualised with horizontal alignment).

[Rason]

Hopefully you can picture this:


Two equal bars, \"Upper\" bar 4 units filled \"U\", \"Lower\" bar 7 units filled \"L\" + a portion \"9\" with dashed outline. Brace 3 units of \"Upper\" bar and 4 units of \"Lower\" bar as \"Boys\", the remaining as \"Girls\". Form equation 3U+4L = 2(U+3L); U = 2L. From here straight away can see that the two bars is 8L - 7L = 1L difference, which is 9. Now, note that in my diagram, 9 is visible, there's only one degree for direct equality reference, so it becomes pretty smooth flow towards getting the final answer.

Update (27 Oct): Step by step guide appended below. Established Simultaneous Equations standard as 7 steps.

http://rason.brinkster.net/psle/UpperLower.gif\">

[david59]

ameryeducation:

David,


MOE's stand is actually very clear. Whilst they recommend the use of Model Drawing Method in problem solving, they will not penalise students who use Algebra or any other mathematically sound method to derive the solution.

David and Rason,

The problem is, yes, algebra can be effective in solving questions, but MOE recommends the Model Drawing Method as opposed to algebra because it is also concerned with students' learning. This takes time, effort and patience, but I believe, as surely does the MOE, that it pays off eventually. Algebra can probably get quicker results, but switching to algebra too quickly and abruptly may be bad for a child's mathematical understanding in the long run.

As I have shared before, I know what Moe stands for in regard to using Algebra. However, there is no level playing field since most schools would always frawn at their students for using Algebra to solve qns. I personally think that one who is not good with model method might be capable of solving tough questions using Algebra.

Personally, I have always insisted n preferred students to appreciate the logical process of solving qns using models. But then, if the need calls for helping a kid in P6 to perform better with Algebra, I won't hestitate to help him achieve it. Afterall, he will be using a great deals of Algebra and a whole lots of abstract mathematical equations once he steps into secondary school. So, how can it be bad for a child's mathematical understanding in the long run if he starts using Algebra in P6? :?

[atutor2001]

Not sure if anybody remembers a report in ST in 2008 on \"Teaching of Mathematics - Students learn better with symbols\"


In the report, US researchers carried out several experiments: teaching maths using \"abstract symbols and various formulae\" against teaching math using \"real-world examples such as story problems\"

An example cited in the article was teaching students commutativity - that you can switch the order of elements and still get the same answer, as in 3 + 2 or 2 + 3 equals 5.

Some students learned the concepts using generic symbols. Others were taught with examples such as pictures of measuring cups filled with liquid or slices of pizzas in a container.

Their finding :

While all of the students were able to master these concepts easily, the students who first learned maths concepts using abstract symbols were better able to transfer the learning to other problems when tested. The danger with teaching using measuring cups as example is that many students only learn how to solve the problem if the questions involves measuring cups or related objects.

Which is better? You decide

[atutor2001]

Model method is unique to Singapore. The feeling I get is that our educators are very proud of it believing that they have come out with an ingenious method.


Whenever I think of Model method, it reminds me of the handheld "grass cutting machines in the early days (which I think some of us here may have forgotten)

In those days, such machines came with a rotating blade. There were many accidents involving flying blades or stone sent flying by the rotating blades, injuring passer-bys.

Many great inventors came out with many ideas. One even patented his collapsible blades. There were much fanfare and the invention was published in the paper and the inventor interviewed on TV.

Today we don’t see any collapsible blades. All that is needed is a plastic strip (for tying wires) to solve the problem. The strip is strong enough to cut the grass but not strong enough to send a stone flying at great speed. When the strip breaks change a new one, it costs only a few cents.

The moral of the story is, we like to make things very complicated where the simple solution is already there.