Syllabus development (2 Viewers)

[zeek]

f it means making a syllabus for primary schools then thats fine

I think this is an excellent idea. Encouraging students to use higher order thinking from an early age is the way to go if you want to see a high number of mathematics students in the future.

u can't teach anyone creativity

Well you aren't exactly born with creativity. Students can be encouraged to become creative.

 

[Affinity]

I think this is an excellent idea. Encouraging students to use higher order thinking from an early age is the way to go if you want to see a high number of mathematics students in the future.



Well you aren't exactly born with creativity. Students can be encouraged to become creative.

I agree in principle, but disagree with it nevertheless because if this idea is picked up by syllabus committees, it would definitely lead to a decline in mathematical ability. I think it will be implemented so that basic arithmetic will be given less prominence and there will be more and more wordy concepts... Not that I am against things which are wordy.. but they should be taught in language lessons, not maths.


More drills in arithmetic should be given in primary school and more drills in manipulating algebraic expressions should be done in high school. One must have a good foundation in these things to do any serious mathematics. Also, these exercises train the mind and increase it's processing capacity in general.


The situation now seems to be that the universities are dumbing down their math courses to cater for the weak HSC syllabus, which in turn is tied down by the earlier math courses.. one has to work from the bottom (year 1) to improve the situation.

 

[Trebla]

I read on the news somewhere that they're going to "dumb down" the HSC maths syllabus because it's too hard at the moment. Does that mean we'll lose the academic rigour and challenging nature of the current Extension 2 course (which is not found in any other state)? That would suck if that were true...sure, it might help the less able students, but for the top students, it would suck...

 

[Affinity]

It doesn't even help the weaker students.. If one applies their real motive to the extreme, then one should just give everyone 100% for every subject they take for the HSC.

Dumbing down doesn't make weaker students learn more.., it just makes everyone's mark high so everyone's happy. I guess this problem stems from the deeper problem that what most people care about are marks, university entrance, prestige and what not. many and I dare say the majority of Students Parents and teachers are exam oriented.

 

[buchanan]

Horatio Scott Carslaw did a review of mathematics in Australia in 1914 called The Teaching of Mathematics in Australia. In those days Sydney University (the only one in NSW at the time) had entrance exams and it was Carslaw's intention to replace them with a new Leaving Certificate in 1916 (at the end of Grade V (Year 11)) - now the HSC after the Wyndham Review since 1967 (at the end of Year 12). The Sydney University Senate opposed this move by Carslaw, but Carslaw eventually got his way.

According to Carslaw it's better to have a syllabus, final exams, and marking of final exams all given externally. However he was opposed to the ideas of just sticking to a syllabus or teaching to the test.

I am also opposed to it, so I'm glad Carslaw agrees with me. So if anyone who advocates just sticking to a syllabus and teaching to a test, all you have to do is mention Carslaw and such mediocrities will be forced to crawl back under their rock.

As for dumbing down, well in 2001 they did the opposite by getting rid of MIP and MIS and replacing them with General Mathematics. This is what is getting the most criticism, so I think this is what will be likely to change the most.

It's also possible to bring back the old 2-year 4 unit course as it was from 1966-1980. It'd be unlikely to be dumbed down if they do this. However if you look at what they did to HSC Physics by dumbing it down, it's fair to say they can't be trusted with 4 unit maths either. So I (and others) have made submissions to the Board advocating they do not dumb it down.

 

[blackfriday]

perhaps they should teach more stats (not only in 4u, but also in 3u and 2u) so when we get to uni its not a shock to the system when we learn stuff like regression. stats isnt so hard, just that the majority of students get panicky when they see it. the commerce students at my uni freak out when they see things like covariance.

i read a report (barrington and brown 2005) that said the nsw hsc ext 2 maths exam is the hardest in australia and contains lots of higher level pure maths questions. is that something to be proud of?

i didnt think the course was so bad, just that it seems that each year, the gap in difficulty between the 3u exam and the 4u exam is getter closer together. the vectors we learnt in complex numbers was a complete waste of time, and pretty much useless for uni. i also dont like the anal retentiveness of how proofs are required to be set out (this is more relevant to 2u and 3u). at uni you just how to show a clear logical progression from one step to the next. this may also have something to do with the extra maths notation used at uni.

 

[acmilan]

i also dont like the anal retentiveness of how proofs are required to be set out (this is more relevant to 2u and 3u)

What do you mean by that?

 

[vulgarfraction]

He means that people can get the answer right and essentially all that is necessary to do so, but still lose marks because of setting out, etc, because marking is pedantic.

 

[acmilan]

um..from my experience they're more anal about that stuff in uni than in the hsc (tbh ive never seen it as an issue in the hsc). Discrete maths has a whole subfield dedicated to setting proofs out properly and formally, and it is a very important thing. In the professional mathematics sense, when you submit a paper, even if the works right, and in your eyes you've proven what you have to, your setting out of your proofs can basically be the difference between being approved or rejected.

 

[lala2]

With the K-10 issue, I find that mathematics here is quite dumbed down. I'm not asking it to be of Asian standard or anything where Year 8s can do Year 11 or 12 stuff, but it could be more challenging. I'm shocked that my brother has just finished Year 5 and has only just been introduced to algebra (x is about the total some of his knowledge--no pun intended).

 

[aus_peter2005]

i think they should introduce harder geometry proof, algebra and probably trigonometry in years 7 -10...cos i basically just mock around not learning much at all..and get fed up every year having to do factorisation and stuff again....they should review the syllabus so that once something is done..just get over it and start sth new..instead of repeating it againg..

 

[vulgarfraction]

See, but usually if people can get to that level in uni, setting out and writing proofs is a minor issue they can easily do. You can write a proof in an olympiad getting 7 without being as pedantic as they are in school.

 

[blackfriday]

what i mean with setting out the proof in my experience has been that teachers teach a proof, they expect their students to use that proof only. im sure lots of teachers are smarter than this and can recognise good reasoning. i did discrete maths last semester and really appreciated learning logic and proofs (well appreciated jie du's logic and proof).

for example, when diff from first principles, i found the gradient of the secant first, then proceeded to find the gradient of the tangent by taking the limit. they didnt except this because 'it was not the way we taught you'. pedantic if you ask me.

 

[acmilan]

Ah, i think thats more a teacher thing though than a HSC thing. I know my teacher insisted we end induction proofs with:

"Since its true for n = 1, its true for n = 2
since its true for n = 2, its true for n =3
...therefore its true for all n"

I absolutely hated doing this because:
1. It took ages to write in an exam
2. It's not valid. By writing that, you're effectively proving something with infinite steps, where a proof requires finite steps

I preferred to simply write "Hence the result follows by induction", so i proceeded to do it. He deducted me marks for it, but i know the hsc markers wont deduct marks for it. I sort of see why he wanted me to use his conclusion - it displays that you know why the induction process works, but its wrong.

 

[Affinity]

it's valid in some sense, it shows that given any n you can write a proof under some reasonable assumptions(eg peano arithmetic or some second order logic), it's not a valid inference under the usual first order logic formulation of the natural numbers.
by the way/ My logic exam is on the 8th... >.< don't feel too good about it


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Ofcourse it's ridiculous that teachers insist one write in that form, considering that many sources do not.

the Board of studies ought to provide examples (note s) of valid solutions to each HSC question... they certainly have some from the marking process.

 

[buchanan]

A lot of teachers could only be described as amateurs and are not good mathematicians. Unfortunately, these amateurs have influence on the syllabus development process. The result is mediocrity, not good mathematics.

Several books have been written on the subject of dumbing down, my favourites being:

Donnelly, K. (2004), Why our schools are failing.
Furedi, F. (2004), Where have all the intellectuals gone? - Confronting 21st century philistinism.
Gare, S. (2006), The triumph of the airheads and the retreat from commonsense.
Smith, N. (ed.) (2004), Education and the ideal.

There will be a new one out on Feb 1, 2007, called

Donnelly, K. (2007), Dumbing down: outcomes-based and politically correct - the impact of the culture wars on our schools

I got the following message from a professional mathematician on the hsc exam committee regarding induction which shows how stupid and unmathematical some amateur teachers are when they insist on a mantra:

I would like to comment on the induction part of the question.

It has come to my attention that many teachers are training their students to write some form of the following mantra at the end of induction problems.

The statement is true for n=0 and hence is true for n=1. The statement is true for n=1 and hence is true for n=2. The statement is true for n=2 and hence is true for n=3 and so on. Hence the statement is true for all integers n≥0 (by induction).

In many cases the words 'by induction' are omitted.

It needs to be pointed out that

(a) No marks are awarded for this mantra in the marking guidelines for the HSC.

(b) Much time is wasted writing it

(c) Most importantly, the above mantra, especially if the word induction is left out, is at best misleading.

There is a logical (and subtle) difficulty in trying to argue that because the statement is true for any (finite) integer n, it follows that it is true for all non-negative integers n. The axiom of induction is needed to fix this difficulty.

It would be better both mathematically, and for the students themselves, if they ended induction proofs with the simple statement

Hence the statement is true for all n≥0 by induction.

I might add that students who persist in writing this mantra actually LOSE marks in our discrete Mathematics courses at University, so teachers are not doing their students any service, either in the short term (HSC marks) or in the long term. I (and others) have been complaining about this for a long time but without success.

The current syllabus does not insist on a mantra, and if induction remains in the syllabus I only hope the amateurs won't put one in it.

If the amateurs put a mantra in the syllabus the better teachers would instruct their students to burn it.

 

[acmilan]

by the way/ My logic exam is on the 8th... >.< don't feel too good about it

PHIL2001 or a MATH version?

 

[Affinity]

Maths version, includes the first and second incompleteness theorems. not at UNSW though, they aren't running it any more due to insufficient enrolment.

 

[acmilan]

Damn, Logic is the area i want to specialise in. I'll be taking COMP4141 and PHIL2001, but it seems to be lacking in the MATH area at unsw

 

[Affinity]

AMSI runs summer sessions now and then..

I find logic quite yucky at the moment. it really f**ks with your mind

why are you taking PHIL2001 if you are taking COMP4141, don't be lazy...

I think COMP4141 also cover the basic maths course.. but from a slightly different perspective.

sorry for the digression.