PSLE - New Format for Maths

[Rason]

david59:

...Now I can imagine sudents in earlier years from P1 to P5, working very hard, learning to use Models to solve qns. Suddenly in P6, suddenly everyone starts to throw away model methods and starts practising Algebra diligently to solve all difficult qns. As always we are very kiasu mah.


This is why in my earlier post, I feel that MOE must make a stand : Totally no usage of Algebra allowed in Section C or allows it to be part of the P6 Maths Curriculum for solving problem sums( not just learning simple basic Algebra). Then it will be an even level playing field for every P6 candidate. Should we make a petition to MOE to do something? :roll:

Hi David, I know where you are coming from with that, but I can see why there's no need to constrain workings to either pure Algebra or pure model drawing. First and foremost we have to acknowledge that short workings doesn't mean correct workings (that's the \"Banker & Boy\" anecdote from blogTV), similarly, any working goes as long as it works for the student, never mind long or short (well, having it long runs the risk of time management, having it short runs the risk of weak oversight... it's like playing defense or offense in soccer - the level field is still there).

So what I'm proposing is to find the centre-line for good learning distribution and not put all firepower in either half of the court. All the risk and difficulty of Algebraic method lies in those many layers of equation construction stacked together. So I propose status quo for that to be tackled with model drawing and leave the operative part of Algebra to Algebra.

And of course if the student chooses pure Algebra or pure model drawing it is his/her own prerogative to do so - no penalising.

Acceptable?

[david59]

Rason:

david59:

...Now I can imagine sudents in earlier years from P1 to P5, working very hard, learning to use Models to solve qns. Suddenly in P6, suddenly everyone starts to throw away model methods and starts practising Algebra diligently to solve all difficult qns. As always we are very kiasu mah.


This is why in my earlier post, I feel that MOE must make a stand : Totally no usage of Algebra allowed in Section C or allows it to be part of the P6 Maths Curriculum for solving problem sums( not just learning simple basic Algebra). Then it will be an even level playing field for every P6 candidate. Should we make a petition to MOE to do something? :roll:

Hi David, I know where you are coming from with that, but I can see why there's no need to constrain workings to either pure Algebra or pure model drawing. First and foremost we have to acknowledge that short workings doesn't mean correct workings (that's the \"Banker & Boy\" anecdote from blogTV), similarly, any working goes as long as it works for the student, never mind long or short (well, having it long runs the risk of time management, having it short runs the risk of weak oversight... it's like playing defense or offense in soccer - the level field is still there).

So what I'm proposing is to find the centre-line for good learning distribution and not put all firepower in either half of the court. All the risk and difficulty of Algebraic method lies in those many layers of equation construction stacked together. So I propose status quo for that to be tackled with model drawing and leave the operative part of Algebra to Algebra.

And of course if the student chooses pure Algebra or pure model drawing it is his/her own prerogative to do so - no penalising.

Acceptable?

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:

[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'?

[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\">