Channel 8's drama serial \"Daddy At Home\" last night spurred this analogy...


I imagined a number problem departing from \"Peanuts and Candies\" to teach kids about wealth management:

In 2008, The Economist reported that Morgan Stanley had estimated the Singapore Government Investment Corporation (GIC) fund's assets to be at US$330 billion. Wall Street Journal reported that the GIC suffered a loss of around 59 billion Singapore dollars in the fiscal year ended March 31, 2009, and its portfolio currently stands at around S$265 billion after drops in equity investments and property valuations.http://en.wikipedia.org/wiki/Government_of_Singapore_Investment_Corporation The Singapore National Research Foundation (NRF) under the charge of http://www.singaporebudget.gov.sg/expenditure_overview/pmo.html typically awards university research projects at S$2 million each. If both Morgan Stanley and Wall Street Journal estimations/reports are accurate, find the total number of local university research projects that can otherwise be funded by the GIC's loss starting from 2008.

Or more elementary -

Last year, the Sing family had $450,000 in foreign investments for retirement and household development. Unfortunately this year, it lost 40% in the foreign stocks market. If the Sings are affording public education for children at $2 per student, how many more schooling kids could it have had if the head of family cashed out earlier on the market?


Disclaimer: Just food for thought from all over the internet in a hypothesis, no presumption or endorsement of facts and figures on the author's part to construe misrepresentation and malice.

tutormum:

I agree totally. I have sent in numerous complaints, suggestions etc and see things done. If nothing is done, I even send a copy to my MP and get immediate response. :lol: It's just a myth that you be black marked. How to make them improve their services if we don't feedback. :heresmyfish:

Hi Tam and Tutormum, the simpler cases may take a simpler route towards plaintiff's satisfaction, however there are the more complex situations that require case studies and extraordinary hearings. It is the lack of convenient / public access to these that increases the risk of unilateralism and group-think - a phenomenon whereby decisions are reached without sufficient deliberation of issues / ideas.

In short, feedback, complaints and suggestions alone are barely enough for arresting some of our (national) problems.

Joy:

I remember clearly, just this mock exam, she scored 35/50 for paper two, and five marks were deducted just cos the teacher cannot understand her model when the reason is that it looks different from her answer key.

There's a moral to every story so here's an extension to our side discussion -

Conformity holds down constructivist (heuristic) learning and has about rule (our) society to counter-productivity. Every divergence from the norm and challenge of the status quo can be a learning point and opportunity for greater heights - it all depends on how the case responders engage in intellectual discussion for the best of (learning) outcomes.

Joy:

I like the answer that MOE replied.

Naturally, the authorities will try to quell complaints by saying that \"things are fair\", \"things are in proper order\" etc, but I think it is our civic responsibility to drive home the demand for public checks to the system (government). More open and targeted protocols have to be in place to bridge the gap between government and populace for policy review and recourse - that's my ultimate recommendation.


p/s Parallel to above post subject: it's our maths-marking today that will affect our money-making tomorrow.

david59:

...there is no level playing field since most schools would always frown at their students for using Algebra to solve qns...

So a directive from MOE is required after all. Anyway we should have no worries regarding the intrinsic results once Algebra is given the go to be taught in schools alongside model drawing.

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\">

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).

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.

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.

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?

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.)


How to actually explain off the Mei and Lin bicycle race question... using what we call Logical Induction, the mental flip-flop goes (as underlined) -

When Lin completed half the race, Mei was 3.5km ahead.
By the time Lin completed the race, Mei would have been 7.0km past the finishing line.

Mei's speed is 20km/hr so it takes 21 minutes for Mei to ride 7.0 km.
If Mei did not ride 7.0km past the finishing line, she would be waiting there for 21 minutes before Lin reaches the finishing line.

Mei would be waiting from 10.45 am till 11.06 am before Lin reaches the finishing line.

Ans: Lin completed the race at 11.06am.