IB Further Mathematics A level vs CIE A level Further Mathematics Watch

Mathfreak3455
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Which is better— IB further maths HL or CIE A level Further Maths? Which covers more content— in terms of depth and breadth?

Which is better for learning? I want to study Mathematics and physics in university, therefore I want to make sure I choose the best math course.

Which is harder?

I will also be taking STEP papers for University of Cambridge Mathematics. Will IB Further Math HL be better or CIE A level Further Mathematics HL? Thank you in advance.
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Zacken
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(Original post by Mathfreak3455)
I will also be taking STEP papers for University of Cambridge Mathematics. Will IB Further Math HL be better or CIE A level Further Mathematics HL? Thank you in advance.
Without a doubt, CIE A-Level FM.
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dpm
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(Original post by Zacken)
Without a doubt, CIE A-Level FM.
I wouldn't be able to agree there.

The HL maths + HL Further Maths combination covers one heck of a lot of material. Just considering one module, eg FM Calculus option is very analytical in nature and covers topics met often in a 1st year undergrad Analysis course.

(all manner of sequences, series, convergence tests, proofs associated with the aforementioned; MVT, L'hopital, Rolle, Taylor including a proper analysis of error functions etc ..)

The bottom line is that the approaches to Maths are very different, both cover a good whack of content, but there is a different emphasis.

I teach them both and would say that either route would set you up in good stead for a UK based degree in Math .. If I really had to choose the "harder" route then I would say the IB double Math route is possibly the more challenging.
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Zacken
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(Original post by dpm)
I wouldn't be able to agree there.

The HL maths + HL Further Maths combination covers one heck of a lot of material. Just considering one module, eg FM Calculus option is very analytical in nature and covers topics met often in a 1st year undergrad Analysis course.

(all manner of sequences, series, convergence tests, proofs associated with the aforementioned; MVT, L'hopital, Rolle, Taylor including a proper analysis of error functions etc ..)

The bottom line is that the approaches to Maths are very different, both cover a good whack of content, but there is a different emphasis.

I teach them both and would say that either route would set you up in good stead for a UK based degree in Math .. If I really had to choose the "harder" route then I would say the IB double Math route is possibly the more challenging.
I think the IB Futher maths is horribly taught. You are taught advanced university level material in a formulaic and secondary-school natured way that you end up having to unlearn at uni and re-learn properly.

Plus, IB misses out on a fair bit of content that is covered by CIE and is used in the STEP examinations. Things like polar coordinates, parametric equations, and a bunch of stuff that I've forgotten. But none of the stuff the CIE misses out on but is taught in IB is part of the STEP syllabus.

I would argue that CIE is the better route as it sets you up better for getting into uni (doing well in STEP) and you'll be able to learn advanced maths there than learning a bunch of advanced maths in IB FM HL which is taught horribly, missing out on STEP and then if they manage to scrape into uni, having to unlearn the bad unrigorous habits taught at IB and relearn them properly and rigorously at uni.

Like you said, the IB FM Calculus option covers a heck of the analysis first year course, but all the rigour is missing, which is a fundamental part of analysis.
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dpm
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(Original post by Zacken)
I think the IB Futher maths is horribly taught. You are taught advanced university level material in a formulaic and secondary-school natured way that you end up having to unlearn at uni and re-learn properly.
That certainly isn't the way I teach it!
As far is possible, all content is dealt with thoroughly and with rigor/ proof.

the reality is, the same argument could be leveled at the same way many unfortunate students are taught GCE Mathematics.
Don't get me wrong, I do like and enjoy teaching both courses, but in fairness, the rigor required in GCE is often less than in the IB .. this is especially so with examination questions.

Plus, IB misses out on a fair bit of content that is covered by CIE and is used in the STEP examinations. Things like polar coordinates, parametric equations, and a bunch of stuff that I've forgotten. But none of the stuff the CIE misses out on but is taught in IB is part of the STEP syllabus.
Again, STEP is something that I tutor when a student needs grades in (II) and (III).
I agree, there are differences in the Syllabi, but to some degree, that is why there are 15 questions on the papers. I could also argue that the Stats component of IB FM is so advanced that it gives a significant advantage compared to GCE stats. The nature of the series covered also helps with specific proof style questions on STEP.

I would argue that CIE is the better route as it sets you up better for getting into uni (doing well in STEP) and you'll be able to learn advanced maths there than learning a bunch of advanced maths in IB FM HL which is taught horribly, missing out on STEP and then if they manage to scrape into uni, having to unlearn the bad unrigorous habits taught at IB and relearn them properly and rigorously at uni.
Your idea that IB FM HL is "taught horribly" is an awful generalization and simply untrue.
I really cannot agree with you here.. I have taught standard HL students who have coped very well with step.
In general, the IB HL + IB FM find the STEP much more accessible than their GCE FM counterparts ... (please note this is only based on relatively few students with whom I have worked over the years, and is certainly not statistically safe!)

Like you said, the IB FM Calculus option covers a heck of the analysis first year course, but all the rigour is missing, which is a fundamental part of analysis.
No it isn't!
It is full of proof and rigour, especially when taught correctly.
I hope this doesn't turn unpleasant, because we simply have a difference of opinion and I do note that helpful posts that you frequently make.

all the best
d.
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Zacken
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(Original post by dpm)
...
It's not unpleasant at all, I very much appreciate you sharing your opinion. I will have to admit that I'm slightly biased against the IB system given that I was in it for a year and thoroughly disliked my experience.

It's just that I can't quite imagine the IB FM Calculus course (and it wasn't at my old school) being anywhere near as thorough a proper analysis courses where you construct the rationals and then construct the reals and talk about convergence and what not whereas the IB course (in the way that I was taught it, at least) was more "this is true and this is true and we're going to assume the reals exist btw forget about dedekind cuts m8".

I will have to defer to your experience and expertise, of course. Most of my friends who took IB HL and the few that then took on IB HL FM where horrible mathematicians compared to the standard of the other offer holders that I've met, although that might (given your experience) just be a product of my school rather than a reflection of the IB system. I can also see that having to study 4 other subjects alongside the IB maths would be a bit of a disadvantage (not much of one, but still a minor pullback) to someone who wants to focus on maths.
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Mathfreak3455
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So basically, as someone who loves maths and want to learn as much as possible, I should choose IB further maths HL as it's more challenging? It covers more content right?I heard CIE further maths covered contents from undergrad first and second years as well. So as an aspiring Mathematician, I definitely should go for IB Further math HL right?Why not CIE specifically? How is one specifically better than the other in terms of content and rigour?I could study go through CIE content from their books for STEP papers, no problem with that. No reason why I should go for CIE further math only because of STEP.I am more concerned about what I learn — how much I learn and to what depth. Does CIE further math cover more content or IB further math HL? What about depth? Which is better for learning?

Note. I am not familiar with STEP preparation. I will post about it later on. But as far as I know CIE does't have any book for further math. How should I prepare for STEP in case I decide to go for IB Further Math HL and self study the missing CIE further Math topics for STEP?
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dpm
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(Original post by Mathfreak3455)
So basically, as someone who loves maths and want to learn as much as possible, I should choose IB further maths HL as it's more challenging? It covers more content right?I heard CIE further maths covered contents from undergrad first and second years as well. So as an aspiring Mathematician, I definitely should go for IB Further math HL right?Why not CIE specifically? How is one specifically better than the other in terms of content and rigour?I could study go through CIE content from their books for STEP papers, no problem with that. No reason why I should go for CIE further math only because of STEP.I am more concerned about what I learn — how much I learn and to what depth. Does CIE further math cover more content or IB further math HL? What about depth? Which is better for learning?

Note. I am not familiar with STEP preparation. I will post about it later on. But as far as I know CIE does't have any book for further math. How should I prepare for STEP in case I decide to go for IB Further Math HL and self study the missing CIE further Math topics for STEP?
Either set of Qualifications will meet your needs.
The best thing that you can now do is some research.
Get the CIE FM syllabus and get the IB HL+IBFM Syllabus .. print them all out and spend some time comparing and contrasting the materials; see which appeals to you more. If you have a talent for Maths, then either direction will work.
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Mathfreak3455
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(Original post by dpm)
I wouldn't be able to agree there.

The HL maths + HL Further Maths combination covers one heck of a lot of material. Just considering one module, eg FM Calculus option is very analytical in nature and covers topics met often in a 1st year undergrad Analysis course.

(all manner of sequences, series, convergence tests, proofs associated with the aforementioned; MVT, L'hopital, Rolle, Taylor including a proper analysis of error functions etc ..)

The bottom line is that the approaches to Maths are very different, both cover a good whack of content, but there is a different emphasis.

I teach them both and would say that either route would set you up in good stead for a UK based degree in Math .. If I really had to choose the "harder" route then I would say the IB double Math route is possibly the more challenging.
Can you be specific why one is better than the other? Which topics are covered better in which course?

Will I learn more Mathematics if I do IB Further math HL or CIE further mathematics?

Which is better for an aspiring mathematician?
Lastly which is better for learning? Which one goes in more depth? I don't want to learn more material by being bad at the ones I am studying. Eventually I will be studying those topics in university. Therefore I care about the depth as well.

Does CIE further math cover less content? I am actually more interested in CIE qualifications as I can take 8 subjects in A level here, whereas in IB I can only take 3-4 HL subjects?

So bottomline: which do you recommend and why exactly?
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Mathfreak3455
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(Original post by dpm)
Either set of Qualifications will meet your needs.
The best thing that you can now do is some research.
Get the CIE FM syllabus and get the IB HL+IBFM Syllabus .. print them all out and spend some time comparing and contrasting the materials; see which appeals to you more. If you have a talent for Maths, then either direction will work.
Tbh I have been googling for IB FM HL syllabus for last few hours but haven't found it. Can you post the link here?

As a former teacher, can you tell me briefly which is better and more suited to someone who cares about both depth and breadth and dreams of getting a field medal someday
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dpm
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(Original post by Mathfreak3455)
Tbh I have been googling for IB FM HL syllabus for last few hours but haven't found it. Can you post the link here?

As a former teacher, can you tell me briefly which is better and more suited to someone who cares about both depth and breadth and dreams of getting a field medal someday
IB HL link: http://highered.colorado.gov/academi...um%20Guide.pdf

you need to be able to do the rest of the research yourself.

all you will get here is opinions ... there is no right and wrong, just differing opinions..

good luck
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Mathfreak3455
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That means IB further maths is about taking all of the optional papers from IB math HL right? I actually thought that the components had different syllabus topics for IB further Maths HL. Thank you.
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