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Discussion in 'Mathematics' started by Karvol, Dec 11, 2011.
The draft versions of the new syllabi are now available on the OCC. Any thoughts?
I have only skimmed through, and have probably missed aome of the crucial additions/omissions.
However I was struck by the changes to the Stats option. A lot of the discrete rv distributions seem to have gone, which is fine by me (I'd never even heard of some of them by name before teaching this option) and Bivariate stuff has come in.
This make a lot of sense to me as I could never really understand why Maths Studies was the only course to include this (personally I think it should be in the core syllabus, possibly at the exclusion of Expected Value stuff and/or Poisson.)
I am just hoping that what has come in, does not exceed in content what has been taken out.
My other observation is that this may well mark yet another pay day for publishers who will be falling over themselves to throw out brand new text books that will be 'specially written' to cover the new changes (i.e. same rehashed A level style text books with some old IB exam paper q's included and some oblique references to ToK)
Incidentally, how many major changes have there been recently? Or am I just being a grumpy old man?
I just had a look at the syllabi earlier today but I haven't done a comparison with the old syllabi yet to see what actual changes there are.
Off the top of my head, Studies now includes Normal Distributions. SL has got rid of matrices and introduced Pearson's Product-Moment Correlation. Higher also seems to have got rid of matrices but I am not sure what has been included in lieu of this. FM is now HL.
The biggest worry is going to be the new coursework or EE-lite. I am not sure how that is going to pan out in reality and what the different requirements will be separate HL and SL.
I have still not gone through it in real detail, but I did notice that the Algebra hours have gone from 20 up to 30. Matrices have slipped into this section under the guise of sim. equations with 3 unknowns. I also noticed that 'forming a conjecture' has been dropped from the Proof by Induction unit.
Volumes of revolution have been dropped, and I think they have been replaced by partial fractions, though I may have that wrong.
I am also a bit worried about the 'Exploration' (''EE-Lite' ) I am hoping there will be a heck of a lot more guidance from the IB as to how to direct students towards a worthwhile piece of work. And I don't much fancy having to mark this if each student has chosen to do a completely different exploration.
It sounds to me like the IB were running out of portfolio questions to set, and have handed this issue back to the schools. On the plus side, they have indicated that 12 sides should be a max, and there is only one of these during the course.
My overall impression is that they have tried to maintain the rigour, but reduce the workload a little.
I'm glad to see that the IB online workshops advertised today include courses for the new Maths Syllabi.
I need to do some reading on that. Thanks for the news guys.
Cor! I hadn't noticed that. I was preparing myself for a v. expensive trip to Berlin in Feb (which would have meant me missing my daughter's b'day ) Thanks for the info.
The on-line course could answer my worries.
I followed an on-line workshop for ToK a while ago, run by a contracted team (Triple A or something), and I was quite impressed. Obviously it's not the same as face-to-face chats and after session beers with other teachers, but it is a hell of a lot cheaper.
Glad to be of service!!
Good luck with these changes! If you are interested in proof by induction please take a look at the free downloads on my website www.pbperth.com There is quite a different take on this type of proof.
All the best,
Yes, lots of interesting examples. My concern is that the IB examiners are quite keen on the formal logical structure of proof by induction. Your proofs would not, as they stand gain full marks!
Just a small point regarding the solution to Q4 in the 'Proof by Induction Test'. The solution objects to the form of induction that supposes the truth of a proposition for all n < = k. This is, of course, a well known logically equivalent form of the method of induction - known by variouis names, strong induction, general induction or second-kind induction. The reason why the example is of a false application of induction is not that strong induction is inherently wrong, but that there is clearly something wrong with the way it has been applied in this example. No prizes for spotting the invalid step!
Indeed, and since Doctor Brown is good enough to give the source people might as well take a more direct route to the examples and solutions.
Yes, but the examples are rather pathetic
No one would think that the statements are true.
Thank you ?Polecat? for mentioning that my website gives lots of interesting examples of proof by induction. That is the aim, not comprehensive analysis of the topic.
If we are pedantic enough we can fault any expression of mathematical communication. Unspecified criticism of the rigour of my solutions does not really advance us. The key components are there, even if not formalised to the level you desire.
Two questions of the many given are based on faulty ?proofs?. These tackle assertions which, as you note, no-one would think are true. That?s just good teaching. My website acknowledges the source of these ideas. When I tried it, the link to this source supplied by ?Null? did not work. I do not claim, as you imply, that strong induction is incorrect.
We are teachers as well as mathematicians. We have to maintain student interest and understanding and not be completely distracted by formal symbols and setting-out.
All the best,
Strange that. I tried it at the time and it worked but now it doesn't. The link is still there on this page but the page seems to have been removed very soon after I posted the link.
I don't have a problem with assertions which no one would believe are true. After all no one would believe 2=3 but those "proofs" can still be useful.
Polecat did give a specific point which you might address. In your comments on example 4 you say
"Induction requires that the truth of one case establishes the truth of the next case, not that the truth of all preceding cases establishes the truth of the next case."
As polecat mentioned, the solution made use of strong induction. There is, of course, nothing wrong with strong induction. The problem lies in the fact that the algebra given is not valid for k=0.
I don't teach or mark IB and I didn't find your examples but what I think polecat was referring to would be things like:
A clear statement of the proposition being proved.
Explicitly checking the basis case.
The inductive step.
A conclusion which mentions that you have used the principle of mathematical induction.
It's not a matter of being pedantic, for our students it's a matter of getting all the marks.
I didn't notice this part of your post earlier. I'm afraid I got the same impression as polecat.
The solutions given are not the marking schedule for a general examination. It is an assignment and test specifically on proof by induction. In this context to require students to write ?proof by induction? on each of their proofs would be unwarranted. I see the point made by ?Polecat? and ?Null? about strong induction ? thank you ? and have rephrased the solution to Q4 on www.pbperth.com
All the best,