So, why do universities promote the currect syllabus? (2 Viewers)

[leehuan]

Hopefully, this will be my only venting post.

It seems that there was a syllabus that was designed in around 2008 to be implemented. It looks more appealing than the current one, except for the absence of circular motion (which is just my bias anyway). Except, it was archived.

Differential equations seem much more useful today. On the contrary, I've only heard of a few uses for conics. Personally I'd rather learn something that would be more applicable to mathematics today. To varying extents, curve sketching also doesn't seem to be too useful. Varying translations etc. of curves are a nice tool to have, but we have graphing applications to produce a graph for us now. If we keep the "tools", then I get the feeling curve sketching could be made a smaller topic, and in return start squeezing something like matrices into the syllabus.

I have heard so many good things about matrices...

In my cohort's 3u class, we were discussing this with the teacher. Apparently the universities prevented the implementation of this syllabus, acclaiming the current one is still relevant today. Are they really just making the BOSTES set out a syllabus just for them?

 

[InteGrand]

Matrices and other topics were in the syllabus about 40-50 years ago, but eventually things got taken out or watered down, apparently due to a shortage of teachers capable of teaching the material.

 

[leehuan]

That is worrying. But I suppose I can't be too surprised since the ATAR cut off to enter education is only around the 80's. Nevertheless, if teachers are incapable of teaching the content then I only question why they are 'teachers'.

I highly doubt they're gonna make something called "Mathematics Extension 3", so I still think the course needs to be stepped up. If matrices were in the syllabus all those years ago then that already makes me wish I took that 4 unit course instead.

Teaching needs to be encouraged more, and also begin to appeal to better students. I don't feel like ranting about politics right now but I'm inclined to blame them for this matter (wage etc. though some teachers beg to say their pay is good).

 

[InteGrand]

That is worrying. But I suppose I can't be too surprised since the ATAR cut off to enter education is only around the 80's. Nevertheless, if teachers are incapable of teaching the content then I only question why they are 'teachers'.

I highly doubt they're gonna make something called "Mathematics Extension 3", so I still think the course needs to be stepped up. If matrices were in the syllabus all those years ago then that already makes me wish I took that 4 unit course instead.

Teaching needs to be encouraged more, and also begin to appeal to better students. I don't feel like ranting about politics right now but I'm inclined to blame them for this matter (wage etc. though some teachers beg to say their pay is good).

http://4unitmaths.com/1916.pdf

http://4unitmaths.com/hsc1967-1974.pdf

http://4unitmaths.com/hsc1975-1980.pdf

http://4unitmaths.com/hsc1981-1989.pdf

http://4unitmaths.com/4u_1990-1994.pdf

1995-2009 are on <a href="http://www.boardofstudies.nsw.edu.au/hsc_exams/">board of studies website</a>

^Past 4U (or equivalent) papers over the years

 

[Silly Sausage]

^Past 4U (or equivalent) papers over the years

1916 wow.

 

[InteGrand]

1916 wow.

Don't think there were calculators that could be used then (according to Wiki "The first solid state electronic calculator was created in the 1960s''), so they wouldn't be able to make Q's that require computations via calculator like they can now. Hence more proof-based or theoretical problems (plus the level was generally higher the further back we go it seems).

 

[Drongoski]

Just digressing:

I was suggesting to some of my students that today's calculators like the Casio fx-82AU PLUS, selling for about $20 during the Back-to-Schools season, would have fetched $20,000 at least in 1960, were it available; that would be, perhaps around $5 million in today's money. I still carry a book of 4-figure Tables (for common logs, anti-log, sine, cosine, tangent, etc) to show my students how we used the log tables to carry out (approx) multiplication and division, to avoid having to do same by hand. I wish I have kept the slide rule I used to use.

Ah! You guys are so inundated with advanced technology, and take such things for granted. Also, one consequence is weakness with the multiplication table.

 

[Silly Sausage]

Just take out the good ol' trig and log tables.

 

[InteGrand]

Just digressing:

I was suggesting to some of my students that today's calculators like the Casio fx-82AU PLUS, selling for about $20 during the Back-to-Schools season, would have fetched $20,000 at least in 1960, were it available; that would be, perhaps around $5 million in today's money. I still carry a book of 4-figure Tables (for common logs, anti-log, sine, cosine, tangent, etc) to show my students how we used the log tables to carry out (approx) multiplication and division, to avoid having to do same by hand. I wish I have kept the slide rule I used to use.

Ah! You guys are so inundated with advanced technology, and take such things for granted. Also, one consequence is weakness with the multiplication table.

Well from 1×1 up to 12×12 at least I think students learn those off by heart. Some may forget how to multiply bigger numbers by hand though.

 

[BLIT2014]

Well from 1×1 up to 12×12 at least I think students learn those off by heart. Some may forget how to multiply bigger numbers by hand though.

They don't officially teach full timetables in lots of primary schools

 

[InteGrand]

They don't officially teach full timetables in lots of primary schools

Well I'm guessing that people who go on to do some level of maths would learn times tables by the HSC (if not in primary school, then by high school)? Although you don't need to technically, since a calculator is allowed of course. But if they ever had a maths test in high school where no calculator is allowed, they may have had to learn times tables.

 

[RealiseNothing]

The syllabus as it is now is great imo. Putting in matrices is a bad idea.

What are you going to teach high school students about matrices? Nothing of substance really.

 

[leehuan]

'67-'80 looks quite interesting. The syllabus seemed to start to correspond to the current at '81 I think from all of that.

That '16 though. I always tell my class the harder maths is the more fun for me but that looks like something I would probably fail at...

The syllabus as it is now is great imo. Putting in matrices is a bad idea.

What are you going to teach high school students about matrices? Nothing of substance really.

Can't see too much use in the conics proofs either though. The conics theorems are probably useful in their applications but I can't see anything else worth mentioning. I got matrices out of my cohort's 3u teacher, so even if matrices are pointless what about differential equations then?

(I get that eccentricity etc. of conics and their graphs may be useful too, but that could really just be M/C, seeing as though maths M/C is a thing now.)

 

[Silly Sausage]

Well simple differential equations are technically in applications of calculus, e.g. growth and decay, SHM, Newton's law of heating and cooling etc.

 

[leehuan]

Touche, can't argue that. Solving them would perhaps be a bit more interesting than the normal "verify" proofs they give in the HSC though.



I guess it does set up differential equations; just doesn't go into as much depth as possible.

 

[tywebb]

In 2008 the NSW senior mathematics syllabus development process was put on hold because of the national curriculum. This has now also been put on hold as you can see in this article: http://4unitmaths.com/nc-y11-12shelved.pdf

Nevetheless, BOSTES will revisit it according to this document from last year http://www.boardofstudies.nsw.edu.a...f_doc/senior-secondary-evaluation-2014-08.pdf in which (on page 22) the proposed topics for the calculus-based courses are as follows:

Preliminary Mathematics 2 Unit

Approximately six topics focusing on areas of Mathematics such as real numbers, algebra, functions, graphs, geometry, trigonometry, differential calculus, sequences and series, and descriptive statistics.

A number of modelling topics focusing on applications of Mathematics from other topics in the Preliminary course and utilising techniques from other topics in the course and earlier courses, such as applications involving real functions and applications of series to finance.

HSC Mathematics 2 Unit

Approximately six topics focusing on areas of Mathematics such as differential calculus, integral calculus, probability, trigonometry, exponential and logarithmic functions, descriptive statistics, and random variables.

A number of modelling topics focusing on applications of Mathematics from other topics in the HSC course, and utilising techniques from other topics in the course and earlier courses, such as applications involving probability and finance, applications to the natural environment.

Preliminary Mathematics Extension 1

Approximately six topics focusing on areas of Mathematics such as circle geometry, further algebra, polynomials, functions, graphs, trigonometry, series, elementary difference equations, random variables, and the normal distribution.

HSC Mathematics Extension 1

Approximately six topics focusing on areas of Mathematics such as mathematical induction, binomial theorem, methods and applications of integration, further trigonometry, inverse functions and the inverse trigonometric functions, and further applications of calculus.

Mathematics Extension 2

Approximately eight topics focusing on areas of Mathematics such as further inequalities, complex numbers, polynomials, functions, graphs, vectors, integration techniques, volumes, modelling with functions and derivatives, mechanics, difference equations, and statistical inference.

There was consultation on this last year, but the impetus has since shifted now that the senior national curriculum has been put on hold - so it remains to be seen how this all pans out for the calculus based courses.

On page 33 of that same document it says draft writing briefs would be released early 2015, but that hasn't happened yet.

Nevertheless one change that came from the 2008 documents is that General maths was split into 2 - General 1 and 2, and General 2 was first examined in the HSC last year.

It is unlikely however that the Board will just use the documents from 2008 for the new calculus courses. The intention so far is to start the process again as outlined on page 33 (although this seems to be delayed so far).

For 4 unit, rather than just comparing old HSC exams back to 1967, you might like to compare the actual syllabuses. So here they are:

1989

<a href="http://www.boardofstudies.nsw.edu.au/syllabus_hsc/pdf_doc/maths4u_syl.pdf">Third 4 unit syllabus (i.e., current syllabus)</a>

1980

<a href="http://www.angelfire.com/ab7/fourunit/4usyllabus2.pdf">Second 4 unit syllabus</a>

1973

<a href="http://www.angelfire.com/ab7/fourunit/4usyllabus1.pdf">First 4 unit syllabus</a>

1965

<a href="http://www.angelfire.com/ab7/fourunit/level1syllabus.pdf">Level 1 syllabus</a>

Also, you can't really call the 1916 exam an HSC equivalent exam because the leaving certificate only went to grade V (Year 11 equivalent). Grade VI (i.e., year 12) only started in NSW in 1967.

 

[braintic]

1989
<a href="http://www.boardofstudies.nsw.edu.au/syllabus_hsc/pdf_doc/maths4u_syl.pdf">Third 4 unit syllabus (i.e., current syllabus)</a>

1980
<a href="http://www.angelfire.com/ab7/fourunit/4usyllabus2.pdf">Second 4 unit syllabus</a>

1973
<a href="http://www.angelfire.com/ab7/fourunit/4usyllabus1.pdf">First 4 unit syllabus</a>

1965
<a href="http://www.angelfire.com/ab7/fourunit/level1syllabus.pdf">Level 1 syllabus</a>

Also, you can't really call the 1916 exam an HSC equivalent exam because the leaving certificate only went to grade V (Year 11 equivalent). Grade VI (i.e., year 12) only started in NSW in 1967.

The 1989 syllabus was not a new syllabus. As it says at the top of the 2nd page, it was only an amendment to the 1980 syllabus. There were no new topics and no topics were discarded. The only difference was that each topic was specified in a lot more detail. There was no hoo-hah regarding its release ...... in fact, many teachers in 1991 (the year it was actually used for the first time, despite what the document says) were not even aware of the existence of the new document.

And ... have you seen the 1916 paper? It is certainly not a trivial paper. I've seen my father's textbooks from Fifth Form 1951. He didn't do the highest level, and the content and difficulty looks pretty much the same as the current Ext 1 course. Fifth form was the equivalent of the current year 12 ... hence the feeling by many that they are treading water in junior school.

 

[RealiseNothing]

'67-'80 looks quite interesting. The syllabus seemed to start to correspond to the current at '81 I think from all of that.

That '16 though. I always tell my class the harder maths is the more fun for me but that looks like something I would probably fail at...



Can't see too much use in the conics proofs either though. The conics theorems are probably useful in their applications but I can't see anything else worth mentioning. I got matrices out of my cohort's 3u teacher, so even if matrices are pointless what about differential equations then?

(I get that eccentricity etc. of conics and their graphs may be useful too, but that could really just be M/C, seeing as though maths M/C is a thing now.)

It's not so much that matrices are pointless, it's just that for them to be useful you need to know A LOT about them. To do this as a topic in high school probably wouldn't give you enough time to learn it well enough.

Conics isn't exactly useful as a direct application, but the actual methods you use and ideas behind some of the questions I think suit the course well (everything kinda comes together). It is also useful here and there in uni I guess too.

 

[tywebb]

The 1989 syllabus was not a new syllabus. As it says at the top of the 2nd page, it was only an amendment to the 1980 syllabus. There were no new topics and no topics were discarded. The only difference was that each topic was specified in a lot more detail. There was no hoo-hah regarding its release ...... in fact, many teachers in 1991 (the year it was actually used for the first time, despite what the document says) were not even aware of the existence of the new document.

And ... have you seen the 1916 paper? It is certainly not a trivial paper. I've seen my father's textbooks from Fifth Form 1951. He didn't do the highest level, and the content and difficulty looks pretty much the same as the current Ext 1 course. Fifth form was the equivalent of the current year 12 ... hence the feeling by many that they are treading water in junior school.

Well teachers of the current course should be using the current syllabus, which is the 1989 document, not the 1980 one.

And yes. I've seen all the leaving certificate papers from 1916 to 1966. It's not fair to compare final exams from these years to the HSC final exams because from 1967 onwards, high school had an extra year.

 

[2azn4u]

Have a read of what Dr Bill Pender wrote back in 2008:

http://www.angelfire.com/ab7/fourunit/0806BOSSubmission.pdf