PSLE - New Format for Maths

[ChiefKiasu]

atutor2001:

I think many people are becoming siao. Chocolate and sweets so difficult to count one meh? Just use fingers and toes when the number becomes too big. :lol:

Kekekke... I think most of us parents just want our kids to pass their exams and get into a decent Secondary school. Other than the fact that chocolates and sweets and kite angles could get in the way of their dreams, most parents probably don't give 2 hoots about the fine art of solving those problems

[Rason]

ameryeducation:

There is actually a very simple and elegant model drawing solution for this, that does away with complex algebraic solutions, or tedious model drawing.


The thing with model drawing that many parents don't get is that it's not difficult. You just have to be introduced to how easy models can be constructed before you start to realise how powerful it can be as a solution.

Please visit our website http://www.ameryeducation.com for our solution, which I think is the most appropriate solution around for the primary level.

Hi Amery, I read your company's stand on Algebra vs Model drawing and took some time to think through the controversy. Much as I applaud your initiative in making a stand, I have to say that it would be advisable to review the doctrine of using model drawing as the exclusive tool to solving \"Chocolates & Sweets\" (i.e. Simultaneous Equations). Models can be used to illustrate the concept of variables substitution after which simple Algebra should follow. Any further manipulation of drawings for replacing simple algebraic steps is literally \"adding legs to snakes\" (as the Chinese would say). I propose that P6 students ought to be taught simple algebraic operations in conjunction with model drawing because it is one way to fortify the imagery of algebraic operations - not just in shifting terms across the equal sign but also in perceiving the original concept of equation balancing. I believe the earlier they are exposed to Algebra, the more they can get used to abstract maths and essentially calculus later on in secondary school. Any purported benefits of extensive model drawings can be picked up with more targeted forms of cognitive training and should not be prescribed at the expense of desensitizing students' response towards operation-intensive maths.

p/s Say, even if you are not offering content by the open paradigm, I would wish you success in your curriculum. Just continue figuring what's right to apply.

ChiefKiasu:

Kekekke... I think most of us parents just want our kids to pass their exams and get into a decent Secondary school. Other than the fact that chocolates and sweets and kite angles could get in the way of their dreams, most parents probably don't give 2 hoots about the fine art of solving those problems

It's alright for the parent to just assume the cheerleader role I guess. After all, instructional designing and lesson delivery is the preserve of educators and teachers. Anyway consider this: if kids nowadays can go through methodical training and pick up things like speed calculating, which your generation and mine are strangers to, what surprise is there if someone manages to teach them calculus as well. By then it is not about missing the stars but keeping their feet on the ground. This applies whether the child excel as a mathematician or a musician, or any occupation that may or may not be to the parents' approval. Inspiration and support is crucial during their formative years (so the art of inspiring would apply); and celebrate when the child does bloom, no matter when, no matter how.

[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.)


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.

[david59]

Rason:

ameryeducation:

There is actually a very simple and elegant model drawing solution for this, that does away with complex algebraic solutions, or tedious model drawing.


The thing with model drawing that many parents don't get is that it's not difficult. You just have to be introduced to how easy models can be constructed before you start to realise how powerful it can be as a solution.

Please visit our website http://www.ameryeducation.com for our solution, which I think is the most appropriate solution around for the primary level.

Hi Amery, I read your company's stand on Algebra vs Model drawing and took some time to think through the controversy. Much as I applaud your initiative in making a stand, I have to say that it would be advisable to review the doctrine of using model drawing as the exclusive tool to solving \"Chocolates & Sweets\" (i.e. Simultaneous Equations). Models can be used to illustrate the concept of variables substitution after which simple Algebra should follow. Any further manipulation of drawings for replacing simple algebraic steps is literally \"adding legs to snakes\" (as the Chinese would say). I propose that P6 students ought to be taught simple algebraic operations in conjunction with model drawing because it is one way to fortify the imagery of algebraic operations - not just in shifting terms across the equal sign but also in perceiving the original concept of equation balancing. I believe the earlier they are exposed to Algebra, the more they can get used to abstract maths and essentially calculus later on in secondary school. Any purported benefits of extensive model drawings can be picked up with more targeted forms of cognitive training and should not be prescribed at the expense of desensitizing students' response towards operation-intensive maths.

p/s Say, even if you are not offering content by the open paradigm, I would wish you success in your curriculum. Just continue figuring what's right to apply.

ChiefKiasu:

Kekekke... I think most of us parents just want our kids to pass their exams and get into a decent Secondary school. Other than the fact that chocolates and sweets and kite angles could get in the way of their dreams, most parents probably don't give 2 hoots about the fine art of solving those problems

It's alright for the parent to just assume the cheerleader role I guess. After all, instructional designing and lesson delivery is the preserve of educators and teachers. Anyway consider this: if kids nowadays can go through methodical training and pick up things like speed calculating, which your generation and mine are strangers to, what surprise is there if someone manages to teach them calculus as well. By then it is not about missing the stars but keeping their feet on the ground. This applies whether the child excel as a mathematician or a musician, or any occupation that may or may not be to the parents' approval. Inspiration and support is crucial during their formative years (so the art of inspiring would apply); and celebrate when the child does bloom, no matter when, no matter how.

In the past, very few students talked about using Algebra in PSLE examinations. But it has become more prevalent as the years go by. Can I say that esp. this year, more kids are being taught to use Algebra to solve tough questions in Enrichment Centres or by tutors? My Pri 6 students in my Care Centre were never taught by their respective school teachers to use Algebra to solve difficult qns. except for the GEP student.

Using Algebra to solve problem sums has a greater advantage over other methods (IMHO). Let this unknown be 'X'. and then just create a few formulae to get to the value of 'X' and finally problem solved.

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:

[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