intuitionist1:Are you referring to mathematical intuitionism
Yes.
What were you referring to?
I leave you with Dag's thread for now - it goes into things in a very challenging way.
intuitionist1: Karvol: I would much rather have a student who can plot a curve on a calculator and actually understand what it all means, rather than have a student who can sketch a curve, work out maxima and minima without any real understanding of the mathematics behind it. Naturally a combination of both worlds would be idealAs for myself, I would much rather have a student who can sketch a curve, work out maxima and minima and actually understand what it all means, rather than have a student who can plot a curve on a calculator without any real understanding of the mathematics behind it. Naturally, throwing the graphical calculator in the bin would be ideal.- Sabbir
Karvol: I would much rather have a student who can plot a curve on a calculator and actually understand what it all means, rather than have a student who can sketch a curve, work out maxima and minima without any real understanding of the mathematics behind it. Naturally a combination of both worlds would be ideal
I would much rather have a student who can plot a curve on a calculator and actually understand what it all means, rather than have a student who can sketch a curve, work out maxima and minima without any real understanding of the mathematics behind it. Naturally a combination of both worlds would be ideal
As for myself, I would much rather have a student who can sketch a curve, work out maxima and minima and actually understand what it all means, rather than have a student who can plot a curve on a calculator without any real understanding of the mathematics behind it. Naturally, throwing the graphical calculator in the bin would be ideal.
- Sabbir
er...Did you actually read what I wrote?
DM: They should be able to do it if they have studied roots of polynomials in AS further maths david. The allocation of topics to units has changed, that's all.
They should be able to do it if they have studied roots of polynomials in AS further maths david. The allocation of topics to units has changed, that's all.
There is a big difference between having the potential to do something and actually being able to do it.
intuitionist1: DM: They should be able to do it if they have studied roots of polynomials in AS further maths david. The allocation of topics to units has changed, that's all.There is a big difference between having the potential to do something and actually being able to do it.
Sabb, that question is easy. I have just finished teaching roots of polynomials with my Year 12 further mathematicians so I will give it to them on Tuesday and report back on how they get on. They are not particularly able by the way - more than half did not attain A* at GCSE.
Actually, I should also ask whether you can provide any examples of questions from a 1957 further maths paper that a present day GCSE student might be expected to be able to do?
DM: intuitionist1: DM: They should be able to do it if they have studied roots of polynomials in AS further maths david. The allocation of topics to units has changed, that's all.There is a big difference between having the potential to do something and actually being able to do it.Sabb, that question is easy. I have just finished teaching roots of polynomials with my Year 12 further mathematicians so I will give it to them on Tuesday and report back on how they get on. They are not particularly able by the way - more than half did not attain A* at GCSE.
intuitionist1: DM: They should be able to do it if they have studied roots of polynomials in AS further maths david. The allocation of topics to units has changed, that's all.Actually, I should also ask whether you can provide any examples of questions from a 1957 further maths paper that a present day GCSE student might be expected to be able to do?- Sabbir
Now you are confusing me. I thought this was an A Level question? Hardly any GCSE students would be able to do it.
Ok, my turn to make a typo - I should have written "x/(1+x^2)" ! :-)
Nevertheless the basic point stands.
Best wishes,
Sabbir.
P.S. I hope you did not use a graphical calculator or other computing aid to reach your conclusion! ;-)
DM: Now you are confusing me. I thought this was an A Level question? Hardly any GCSE students would be able to do it.
It was a 1957 O level question. The topic is covered thoroughly in Chapter X of Durell's "School Certificate Algebra" textbook which I mentioned earlier.
intuitionist1: P.S. I hope you did not use a graphical calculator or other computing aid to reach your conclusion! ;-)
Surprising as it seem, I was able to use my brain to deduce what might happen in the neigbourhood of the vertical asymptote. I have an excuse though, I am nearly as ancient as you so did not experience the present-day excuse for an education system*.
* sarcasm meter is set to moderate.