Syllabus development (2 Viewers)

buchanan · Jan 23, 2008

A syllabus motivated entirely by applications will be substandard.

As Bernardo Recamán Santos said on <a href="http://www.ams.org/notices/200707/tx070700822p.pdf">page 823 in the American Mathematical Society's Notices, August, 2007 issue<a/>: “Mathematics is what is lost in its applications.”

A more balanced approach is needed.

It's OK to have applications, but that shouldn't be the main motivation for the syllabus.

One of the non-negotiable <a href="http://www.boardofstudies.nsw.edu.au/manuals/maths_s6_rev_dev_2006.html">Broad Directions</a> set by the BOS is that "any revision or development of the calculus-based courses maintain the current rigour and level of challenge of the courses."

If the final syllabus is anything like the latest <a href="http://www.boardofstudies.nsw.edu.au/syllabus_hsc/pdf_doc/maths-stg6-writbrief-advext.pdf">writing brief</a>, it is a widely held view that they will be failing to comply with this directive - eg., with no Component B or Harder 3 Unit.

darkliight · Jan 23, 2008

We both know that the writing brief you linked has a good amount of pure maths in it and could not say it's motivated entirely by applications.

I hate the idea of stats, it bores the hell out of me, but I also fully respect that it's something that a lot of people will need and use, and support its inclusion.

I get the impression the DE's component is going to be a lot more developed and explicit than what is currently included - for some reason they like to skirt around the fact that you're dealing with DE's, or poorly develop it, in the current syllabus. I love my pure stuff (and in a sense DE's are pure), but again I respect that DE's are one of the most useful sets of tools to come out of mathematics. The topic is massive, I like it, it's powerful, and puts a bit more of an edge on the answers to the recurring question "why are we doing this?"

Maybe you can suggest what you would remove to make way for harder 3 unit or number theory?

In all seriousness, I would fully support a seperate stats course, then pack the current maths subjects with pure + DE's + a set of optional pure and applied topics that students/teachers could choose a couple of eg. coding theory, number theory etc.

buchanan · Jan 23, 2008

darkliight said:
I would fully support a seperate stats course

This was also suggested to the BOS and some people agree that this would be better. But unfortunately they decided against it due to staffing issues. Whilst some schools have teachers well qualified to teach such a separate stats course, many schools do not. So they decided against it and incorporated it into the main calculus courses instead.

But in a review of expectations of academics by Paul Ayres et. al., from UNSW, it was found that statisticians want more calculus to be taught in schools, not more statistics.

Reference:

Ayres, P., Brown, P., Pahor, M., Wong., C., The Value of HSC Mathematics Courses in Preparation for Tertiary Study, 2006.

buchanan · Jan 26, 2008

darkliight said:
teachers should teach the syllabus

That's OK if the syllabus is interesting. But only boring people would want to teach a boring syllabus.

And that's the problem with both the current senior syllabus and the new one. They both are pretty boring. The same can also be said of the 7-10 syllabus.

So kids go to school, go to boring lessons on a boring syllabus taught by boring teachers and come out saying maths is boring. Although we might not agree with their conclusion, I think we can nevertheless forgive them for it.

They might be convinced their conclusion is wrong by looking at the large amount of maths on the internet, much of which is quite interesting.

So what is happening in most schools is really not representative of mathematics as something interesting.

We end up with 50% doing General Maths and 5% doing 4 unit. After Year 10 most students are really not interested in maths or have given up on it. This imbalance is more to do with teacher's failure to make it interesting in junior years than the ability of the students.

An interesting syllabus might attract more interesting people to the teaching profession. Lessons in junior years can be made more interesting and maybe the imbalance can be improved. We need more people doing 4 unit, not less.

I'm actually a bit fed up with boring people dominating the teaching profession. This is what desperately needs fixing.

Trebla · Jan 26, 2008

So according to you, people find General Mathematics more interesting than the Calculus-based courses which is the reason why more people take it? lol

I don't think the large candidature in General Mathematics is just due to Mathematics being not interesting. As far as I am aware, General Mathematics is far more boring than the calculus-based courses. I reckon it is more the difficulty to the average student which makes 2 unit Maths or higher unattractive to some. The average student in NSW tends to take the easier courses because he or she wants to get good marks with the least difficulty. In this day and age, the HSC course seems to be all about getting marks.

Also, I think another factor is the shortage of teaching staff with competent Mathematical abilities. Many public schools refuse to allow students to study higher level Mathematics because they simply do not have the teachers/resources to handle such a "difficult" course. Since public schools make up the majority of schools in NSW, this can also be said to contribute to the high candidature in General Mathematics.

When you typically ask around why some people don't take 4 units of Maths or why some people drop out of 2 unit Maths to General Maths, it's mainly beacuse it's "too hard" not because it's "too boring".

I agree that there is a problem with the junior syllabus in terms of making Maths interesting, but I think the greater flaw here is the expected standards - they are too low in Years 7 - 10. I mean look what is expected in the Mathematics School Certificate exam, it's almost a joke. Compare that to the HSC and there is a great gap in the requirements. This leads to the average student conforming to a low degree of mathematical abilities. Over time this leads to a lower expected standard from future teachers as well.

A higher standard in Years 7 - 10 may force the average student to adopt to that standard in order to gain the same good marks.

Whilst there is the worry that the new HSC syllabus will be less interesting, I think the bigger concern is the fact that the new syllabus may lead to lower standards. The removal of Harder 3 Unit in particular leads to a large deficiency of the challenging nature the current Extension 2 course offers. In the past there were some pretty high standards in 4 unit papers. However, recent Extension 2 HSC papers seem to exhibit a decline in those expected standards. Is this an attempt to attract more students into higher level courses? Who knows.........

I also think that should a national curriculum be introduced (which seems inevitable), these standards would be screwed anyway.....lol

Anyway, that's my opinion....

buchanan · Jan 26, 2008

Trebla said:
So according to you, people find General Mathematics more interesting than the Calculus-based courses which is the reason why more people take it?

No. They take General Maths because they are not interested in maths. They have become disinterested in it due to the reasons you indicated about the standards of 7-10.

7-10 can and should be made more interesting, as should the senior syllabuses. They should not be dumbing down 4 unit by writing easier exams, removing Harder 3 unit or Component B.

As far as the national agenda is concerned, if ACER or the CC have anything to do with it, it will likewise be dumbed down. They tried it in 1994 and it failed. I think it was best put by Michael Cowling in his submission to the Strategic Review of Mathematical Sciences in 2006:

The academic standards of high school mathematics have declined in most states, as state
Departments of Education have distanced themselves from academic mathematicians in
the preparation of syllabuses and relied on “education experts” with little knowledge of the
subject; we are particularly concerned that NSW may be about to follow this trend, as
there is a review of HSC mathematics underway. But even if the quality of the current
syllabuses is maintained, the other trends mean that the number of our students who have
been exposed to quality high school advanced mathematics is likely to decrease.

- Michael G Cowling

http://www.review.ms.unimelb.edu.au/UNSWsubmissionRevised.pdf

buchanan · Jan 26, 2008

On the other hand by contrast to the boring sludge produced by the ACER and CC in 1994, and the NSW BOS in 2003 for 7-10, there currently is an attempt by Garth Gaudry's (the guy who taught Terry Tao, no less!) ICE-EM to improve 7-10:

http://www.icemaths.org.au/

But unfortunately since the teaching profession is dominated by boring people this will probably have limited impact.

Teachers should spread Terry Tao's message, challenging though that may be. We should not pigeonhole him. He is unique.

Any maths syllabus would be deficient if it does not include something about Terry Tao, Wiles' proof of Fermat's Last Theorem and also something about the Riemann Hypothesis.

buchanan · May 5, 2008

Affinity · May 5, 2008

ok. so they took out conics and placed in DEs

Trebla · May 5, 2008

Omg, they changed the external examination format as well....

me121 · May 6, 2008

Trebla said:
Omg, they changed the external examination format as well....

looks like some multiple choice for advanced mathematics.

pLuvia · May 6, 2008

Which is bit stupid imo esp for maths. Unless they put in negative marking so that expected mark from guessing will be 0

tacogym27101990 · May 6, 2008

回复: Syllabus development

multiple choice and a formula sheet in advanced maths
that ridiculous
way to dumb shit down

foram · May 6, 2008

glad i'm getting out before 2010.

buchanan · May 7, 2008

Sample HSC questions:

http://www.boardofstudies.nsw.edu.au/syllabus_hsc/pdf_doc/maths-sample-hsc-draft-st6.pdf

pLuvia · May 7, 2008

Ridiculous. Buchanan do you know if there will be negative marking for the MC questions for the exams?

Btw is there two general maths now?

tacogym27101990 · May 7, 2008

thats bloody terrible
multiple choice in 4 unit??
why do they have to make the tests so much easier??
its good how it is now

buchanan · May 7, 2008

pLuvia said:
Buchanan do you know if there will be negative marking for the MC questions for the exams?

Btw is there two general maths now?

I don't think they will use negative marking.

It is proposed that there is to be 2 courses for General Maths, called General 1 and General 2.

Boxxxhead · May 20, 2008

tacogym27101990 said:
thats bloody terrible
multiple choice in 4 unit??
why do they have to make the tests so much easier??
its good how it is now

Well I didn't do 4unit (I was merely a kick ass 3uniter LOL) but I agree with you. I did a fair bit of 4unit first year of uni, and I thought it was at a good difficulty level for HSC students.

Boxxxhead · May 20, 2008

pLuvia said:
Which is bit stupid imo esp for maths. Unless they put in negative marking so that expected mark from guessing will be 0

LOL Jimmy Farmer has gotten to you, has he?

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