Syllabus development (2 Viewers)

[blackfriday]

mr. buchanan, i see the name 'donnelly, k.' as someone who has written about dumbing down. i agree that postmodernism and the rejection of absolute truth has pervaded some aspects of the hsc syllabus, but surely not for maths. i know what you're getting at, but the difficulty of the maths course probably reflects the lack of application of students (lots of students hate maths and dont feel compelled to take it for the hsc if they dont like it) and lower university entrance marks to get into maths teaching. this is the same guy who wrote an essay called 'john howard and the art of democratic leadership' or some garbage like that.

 

[Slidey]

There's a very good logic summer school here at the ANU for honours+.

http://lss.rsise.anu.edu.au/index.php?module=ContentExpress&func=display&ceid=59

A bit too late to register, though.

 

[Affinity]

They might still accept ppl. I mean.. in practice there's no problem admitting an extra person when a course is running

 

[buchanan]

The review of Stage 6 Mathematics commenced in March this year with the first phase of the project - the Syllabus Review phase - due to be completed in December 2006.

The Syllabus Review phase will review the full NSW Stage 6 Mathematics provision, taking into account the needs of less able students as well as those who would undertake the higher-level calculus-based mathematics courses. It will also evaluate the current Stage 6 Mathematics syllabuses and any implications of their revision, as well as establishing a plan for revision or development.

The Syllabus Review phase has involved a range of opportunities for organisations, schools and individuals to submit their feedback on the current Stage 6 Mathematics syllabuses and to identify what may be required in any revision of the syllabuses.

The main data-gathering strategies used earlier in the review comprised oral submissions and written submissions from key organisations and individuals, and a symposium attended by more than 80 participants, including teachers, academics, parents and students.

More recently, surveys were sent to a random sample of 100 NSW schools to gain feedback on the current Stage 6 Mathematics syllabuses and Stage 6 Mathematics education in NSW generally.

A literature and curriculum review by Dr Mary Coupland of the University of Technology, Sydney has also been completed. The purpose of this research was to report on issues relevant to the teaching and learning of Stage 6 Mathematics in NSW.

Dr Coupland reviewed relevant literature and other Australian and international mathematics syllabuses for post-compulsory years of secondary schooling. Her research included the analysis of syllabuses from Australian States and Territories, the mathematics curricula of Finland, Hong Kong, Singapore, the United Kingdom and the United States of America, and the International Baccalaureate (IB) Diploma Program.

The data obtained through the analysis of the survey responses and the findings of the literature and curriculum review, together with the other information collected this year, are currently being used to establish broad directions for the revision or development of the Stage 6 Mathematics courses. The broad directions will guide the development of syllabus writing briefs in the next phase of the project, due to begin in January 2007.

- Board Bulletin v. 15 No. 6, December 7, 2006

 

[Affinity]

So nothing has been done yet?

 

[buchanan]

Yes. A lot has been done - in the context of the current phase (review phase).

The purpose of the review phase is to submit feedback on the current Stage 6 Mathematics syllabuses and to identify what may be required in any revision of the syllabuses.

<a href="http://users.tpg.com.au/nanahcub/submission.pdf">Here is my submission</a>

The writing brief phase begins next month.

Here is a more detailed timeline (although this may be changed a bit soon):

Syllabus review: evaluate, consult, research, recommend. (Mar – Dec 2006)

Writing-brief development: write brief, consult, identify issues, revise brief. (Jan – Jul 2007)

Syllabus development: draft; consult; address issues; report on meeting Board criteria; modify; to Curriculum Committee, then Board, then Minister; brief schools; distribute. (Aug 2007 – Nov 2008)

Implementation (Probably from 2010)

 

[buchanan]

A literature and curriculum review by Dr Mary Coupland of the University of Technology, Sydney has also been completed. The purpose of this research was to report on issues relevant to the teaching and learning of Stage 6 Mathematics in NSW. Dr Coupland reviewed relevant literature and other Australian and international mathematics syllabuses for post-compulsory years of secondary schooling. Her research included the analysis of syllabuses from Australian States and Territories, the mathematics curricula of Finland, Hong Kong, Singapore, the United Kingdom and the United States of America, and the International Baccalaureate (IB) Diploma Program.

The Coupland review was released today in 2 parts:

http://www.boardofstudies.nsw.edu.au/manuals/pdf_doc/maths_st6_lit_curr_rev_pt1.pdf

http://www.boardofstudies.nsw.edu.au/manuals/pdf_doc/maths_st6_lit_curr_rev_pt2.pdf

as well as the full symposium proceedings:

http://www.boardofstudies.nsw.edu.au/manuals/pdf_doc/maths_st6_symposium_06.pdf

and a Report on Syllabus Review Phase:

http://www.boardofstudies.nsw.edu.au/manuals/maths_s6_rev_dev_2006.html

 

[buchanan]

And it made it to today's Sun-Herald, page 34:

Outdated HSC maths no longer adds up

Hannah Edwards Education Reporter
February 4, 2007

Sections of the Higher School Certificate maths syllabus are out of date and the course should not be so exam-focused, a new report says.

Conducted by University of Technology Sydney academic Mary Coupland, the analysis is part of a broad review of the senior maths syllabus by the NSW Board of Studies.

While subjects are typically reviewed every five to six years, HSC maths - or stage six maths - has not been overhauled for about 20 years.

The review began late last year and a new curriculum is expected to be introduced for study in schools in 2010, with students examined on it the following year.

Dr Coupland, senior lecturer in the department of mathematical sciences, analysed the non-compulsory maths study options in Australian states including Victoria and Queensland and countries including England, the US, Finland and Singapore.

She found that senior maths in NSW was set at an appropriate level for students hoping to go on to university when compared with other states, but the syllabus had not kept up with trends.

"The current NSW mathematics courses provide an appropriate level of challenge but have not changed in content to reflect current uses of technology, and contemporary applications of mathematics," the report says.

Fewer students were studying higher level maths, with more enrolling in the easier course options.

The senior maths course could also shift from being so exam-focused.

"In schools the focus could be nudged from the tests towards the solving of interesting problems.

"This is a time for evaluating, preserving the best, and incorporating the better of the new," Dr Coupland said.

The study's findings, as well as the results of a survey of 100 schools and a symposium of mathematics experts, will now be analysed by the Board of Studies.

http://www.smh.com.au/news/national...-longer-adds-up/2007/02/03/1169919577628.html

 

[buchanan]

Of course great things come from individuals. They do not come from committees.

Or as Bertrand Russell puts it, "One should as a rule respect public opinion in so far as is necessary to avoid starvation and to keep out of prison, but anything that goes beyond this is voluntary submission to an unnecessary tyranny".

And so we must see the syllabus as minimum requirements. If you want a good education though, you'll have to spend most of your time persuing mathematics outside the syllabus.

 

[buchanan]

The syllabus is the floor, not the ceiling.

This week an Asian teacher told me that students in Asia see education as the only way forward. And an Asian student told me that he thinks that education in Asia is very competitive. I don't however think that it has to be an approach to education peculiar to Asia. If all cultures have this approach they can all be successful.

Syllabus documents should facilitate this success. So even though a syllabus should only specify minimum requirements, it is imperative that it is also of the highest possible standard. Unfortunately this is not the case with many syllabuses. They've been dumbed down. So the warning to the Board of Studies which I sent to them in my submission is that if the Board cannot produce syllabuses of the highest standard, then students will find someone else who will.

 

[buchanan]

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.
- Michael G Cowling (Head of the School of Mathematics and Statistics, UNSW)
- <a href="http://www.review.ms.unimelb.edu.au/UNSWsubmissionRevised.pdf">Submission</a> to the <a href="http://www.review.ms.unimelb.edu.au/index.html">National Strategic Review of Mathematical Sciences Research in Australia</a>

Last week, I became a signatory to the open letter petition to the Prime Minister about it at http://www.review.ms.unimelb.edu.au/OpenLetter.html in opposition to the rapid depletion of Australia's university mathematics departments and have encouraged others to do the same. There have been articles in The Australian recently about this petition:

http://www.theaustralian.news.com.au/story/0,20867,21458323-12332,00.html (last Wednesday)

http://www.theaustralian.news.com.au/story/0,20867,21476027-13881,00.html (today)

I don't want a syllabus written by amateurs. I have already written a paper on <a href="http://users.tpg.com.au/nanahcub/pmvam.pdf">professional mathematics versus amateur mathematics</a> and will not be very forgiving of the BOS if they stuff up the maths syllabus, as they have done in the past with so many others.

 

[buchanan]

The call for signatories for the petition has now closed, but there is a new media release about it at http://www.review.ms.unimelb.edu.au/OpenLetterMRApril07.pdf

 

[Slidey]

Bit concerned about this. There's no need for a new syllabus; especially given the fuck-ups they've made re the physics syllabus and such.

 

[buchanan]

Here are the writing briefs and surveys.

<a href="http://www.boardofstudies.nsw.edu.au/syllabus_hsc/pdf_doc/maths-st6-calculus-dwb.pdf">Calculus Writing Brief</a>

<a href="http://www.boardofstudies.nsw.edu.au/syllabus_hsc/pdf_doc/maths-st6-calculus-survey.pdf">Calculus Survey</a>

<a href="http://www.boardofstudies.nsw.edu.au/syllabus_hsc/pdf_doc/maths-st6-non-calculus-dwb.pdf">Non-Calculus Writing Brief</a>

<a href="http://www.boardofstudies.nsw.edu.au/syllabus_hsc/pdf_doc/maths-st6-non-calculus-survey.pdf">Non-Calculus Survey</a>

You can respond to the BOS by June 1.

 

[UnIqUe PrInCeSs]

What's with the presupposition that the 2 unit course and extensions have to be overwhelmingly filled with calculus?

I wouldn't mind seeing a linear algebra based course myself

EDIT: meaning, "multiply by the power and reduce it by one" or "change sin to cos" is hardly calculus is it? They don't teach you the formal definition of a limit or even state the FTC as such. You can go through the highest level of mathematics in NSW without knowing what a set is, what a vector is, or even what a function is, really.

 

[buchanan]

The introduction of data analysis and statistics, without a solid grounding in Calculus first, can only be at a fairly superficial level.

That's right. There is repeated reference in the draft writing brief to a submission from Paul Ayres, et. al from UNSW which was about a survey done of mathematicians and statisticians in the universities. Paul did a presentation on it at last year's MANSW conference which I attended in which he said that statisticians didn't want more statistics in school. They want more calculus! They don't want "back box" maths - a fact the Board conveniently leave out of the draft writing brief. Others will of course remind them and make this happy fact abundantly clear.

For example, now the Board want the central limit theorem, presumably without proof. So on my website on May 2 I put a <a href="http://mathworld.wolfram.com/CentralLimitTheorem.html">link</a> to a proof (using an inverse Fourier transform). If the Board don't like it, I'll remind them that they said in the draft writing brief that they will maintain rigour. So we'll have the central limit theorem WITH PROOF - replete with inverse Fourier transform - in 2 unit(!), now won't we?

This is just one example of mediocrity masquerading as excellence within the new draft writing brief. To say something is maintaining rigour (providing assurances, etc.) but just provide Mickey Mouse content will expose the Board of Studies for the frauds that they truly are. They are not good mathematicians and their draft writing brief is not good mathematics.

Good teachers will ignore the Board of Studies and do it properly.

 

[buchanan]

Following SGS, do Harder 3 Unit - in 3 Unit - and "Harder 4 Unit" in 4 Unit.

An example of Harder 3 Unit in 3 Unit is the extension questions in the Cambridge 3 unit exercises.

As for "Harder 4 Unit", an example is to prove Wallis' Product following for example, the 1995 4 Unit HSC Q7a:

- a solution of which is attached below -

and then let n--->&infin; thereby obtaining

[maths]{\pi\over2}=\prod_{n=1}^\infty{(2n)^2\over{(2n-1)(2n+1)}}[/maths]

Of course you don't have to do it this way. You can do it by elementary methods not requiring any calculus. See <a href="http://community.boredofstudies.org/showpost.php?p=3217933&postcount=73">this post</a> of mine explaining the situation.

As for the IB, sadly public selective schools in NSW won't have it - so in NSW the only way to do the IB is in the private schools that run it.

 

[buchanan]

An extract of my response is <a href="http://www.angelfire.com/ab7/fourunit/response-extract.pdf">here</a>

 

[buchanan]

One criticism I made was that there is too much emphasis on applications.

 

[buchanan]

Here are the new documents (writing briefs, etc.):

http://www.boardofstudies.nsw.edu.au/syllabus_hsc/pdf_doc/maths-stg6-writbrief-general.pdf

http://www.boardofstudies.nsw.edu.au/syllabus_hsc/pdf_doc/maths-stg6-consult-general.pdf

http://www.boardofstudies.nsw.edu.au/syllabus_hsc/pdf_doc/maths-stg6-consult-append-general.pdf

http://www.boardofstudies.nsw.edu.au/syllabus_hsc/pdf_doc/maths-stg6-writbrief-advext.pdf

http://www.boardofstudies.nsw.edu.au/syllabus_hsc/pdf_doc/maths-stg6-consult-advtext.pdf

http://www.boardofstudies.nsw.edu.au/syllabus_hsc/pdf_doc/maths-stg6-consult-append-advext.pdf