Proposed changes to the Mathematics syllabus: Thoughts? (2 Viewers)

[Carrotsticks]

As you all know, the gears are now moving to work towards constructing the new Mathematics syllabus, for all levels of Mathematics.

Here is the Draft Writing Brief for the calculus-based courses (Advanced, Extension 1 and 2 Mathematics). The proposed course contents are listed starting from Page 17.

I will be attending a BOSTES face-to-face consultation meeting tomorrow to pass on my feedback on the proposed syllabus with regards to the calculus-based courses (won't be saying what I think here though, it would be an entire paper in itself!).

What are your opinions on the changes? I would be happy to pass on any relevant feedback that you may have as part of my submission.

 

[photastic]

Huge fan of the changes particularly implementing statistics which is very useful for many courses at university like commerce and actuarial studies. Also the addition of several calculus topics like first-order linear differential equations which also appear at uni. If these changes were for my HSC, I would definitely transition into university mathematics a lot easier tbh.

 

[InteGrand]

Can you tell us the changes in brief?

No more conics, DE's (differential equations) and difference equations coming in, as well as statistics / statistical inference. There might be some more, didn't read it too thoroughly.

Edit, this was for 4U.

 

[BLIT2014]

Option 2 – changes to both course and examination structures and BDC/CEC status of current HSC Mathematics General 1 course

Preliminary
Mathematics General 2
(BDC)
(revised Preliminary
Mathematics General)
Moderate revision. The course will have significant overlap with the Mathematics
course to assist student movement and to obtain appropriate course relativity in
ATAR scaling. Overlap would include rates of change (without getting to the stage
of formally calculating derivatives) for stronger tertiary preparation.


I'm interested in seeing how they plan to incorporate rates of change into the general 2 course.

~~~~~~~~~~
HSC Mathematics General 2
(BDC)

The examination will have some questions in
common with the Mathematics examination so
UAC can obtain appropriate course relativity in
ATAR scaling.


I'm not so sure about this, I mean I think its important to have fairly different course ( General Mathematics) and may further discourage people from undertaking from mathematics course during the HSC.

 

[BLIT2014]

Mathematics General 1 -> Mathematics Studies
Mathematics General 2 -> Mathematics Standard
Mathematics (‘2 Unit’) -> Mathematics Advanced
Mathematics Extension 1 -> Mathematics Extension 1
Mathematics Extension 2 -> Mathematics Extension 2

The proposed name changes will probably make it easier to understand the different levels :/

 

[InteGrand]

I'm interested in seeing how they plan to incorporate rates of change into the general 2 course.

Average rates of change could easily be done without needing calculus (e.g. average speed etc.). Instantaneous rates of change would require calculus though.

 

[BLIT2014]

Average rates of change could easily be done without needing calculus (e.g. average speed etc.). Instantaneous rates of change would require calculus though.

http://www.boardofstudies.nsw.edu.au/syllabus_hsc/pdf_doc/maths-general-2-formulae-14.pdf

They already use average speed formula (It's in the data sheet)

 

[InteGrand]

http://www.boardofstudies.nsw.edu.au/syllabus_hsc/pdf_doc/maths-general-2-formulae-14.pdf

They already use average speed formula (It's in the data sheet)

They could generalise it to things other than speed (I don't know whether this is already done).

 

[Trebla]

Huge fan of the changes particularly implementing statistics which is very useful for many courses at university like commerce and actuarial business. Also the addition of several calculus topics like first-order linear differential equations which also appear at uni. If these changes were for my HSC, I would definitely transition into university mathematics a lot easier tbh.

Pretty much this.

Also I would personally reallocate more of the applied topics to fall under the advanced and ext1 course (as the intent of these courses are for a broader audience using maths at uni) and have more of the pure stuff in the ext2 course (aimed at those more interested in the actual mathematics than how it is used). Unfortunately, some of the applied stuff can be pretty difficult to understand so that might not be feasible.

Would love to see linear algebra and matrices in there somewhere but I personally think basic matrices (at least the computation of them) should be taught around Year 9 or Year 10 first before we can even start thinking about how to apply them (eg in solving linear equations).

 

[InteGrand]

The old 4U syllabuses had vectors+matrices and their applications (e.g. rotations of coordinate systems and other transformations).

 

[mreditor16]

Pretty much this.

Also I would personally reallocate more of the applied topics to fall under the advanced and ext1 course (as the intent of these courses are for a broader audience using maths at uni) and have more of the pure stuff in the ext2 course (aimed at those more interested in the actual mathematics than how it is used). Unfortunately, some of the applied stuff can be pretty difficult to understand so that might not be feasible.

Would love to see linear algebra and matrices in there somewhere but I personally think basic matrices (at least the computation of them) should be taught around Year 9 or Year 10 first before we can even start thinking about how to apply them (eg in solving linear equations).

I'm actually content that matrices didn't end up being what they're thinking of introducing. I think it's fine to introduce them in first year uni maths.

Besides that, I agree with your post.

 

[Trebla]

The old 4U syllabuses had vectors+matrices and their applications (e.g. rotations of coordinate systems and other transformations).

Do you know whether students back then had to learn the foundations of vectors and matrices during the HSC course or beforehand?

 

[mreditor16]

The old 4U syllabuses had vectors+matrices and their applications (e.g. rotations of coordinate systems and other transformations).

Idk how to best articulate it, but for me personally, it doesn't feel right to have it in high school maths. I feel its best left for university mathematics.

 

[InteGrand]

Do you know whether students back then had to learn the foundations of vectors and matrices during the HSC course or beforehand?

I don't know for sure. One can see what types of matrix questions they had though here: http://4unitmaths.com/hsc1967-1974.pdf

 

[InteGrand]

Idk how to best articulate it, but for me personally, it doesn't feel right to have it in high school maths. I feel its best left for university mathematics.

I think bringing in some linear algebra would be good, because currently the syllabus is mostly just calculus and no algebra.

 

[Trebla]

I think bringing in some linear algebra would be good, because currently the syllabus is mostly just calculus and no algebra.

Yeah I feel like operations of matrices for example would be more suited to high school (especially pre-HSC) rather than have universities teach us how do things like add, multiply or transpose a matrix.

 

[InteGrand]

Yeah I feel like operations of matrices for example would be more suited to high school (especially pre-HSC) rather than have universities teach us how do things like add, multiply or transpose a matrix.

Yeah; the only possible downside would be that high school students would find it really tedious and think matrices are pointless or get put off from studying them. But of course one needs to learn the tedious stuff before one can get to the fun stuff.

Edit: oh right, pre-HSC. Yes, they should do that, although maybe some would get put off from higher levels of maths for HSC?

 

[glittergal96]

Some linear algebra and matrices could definitely slot into the HSC courses in terms of level of difficulty. It is just a matter of what one would replace with them.

And there are plenty of basic applications that would seem interesting to some students (and provide motivation):

-The first one everyone learns, solving simultaneous equations.
-Solid geometry.
-Solving recurrences in a systematic way.
-Solving simple Markov chain type problems.
etc.

It would be a bit much to introduce abstract vector spaces to HS students by comparison to the current level of abstraction in the syllabus, but mechanical calculations on R^n and C^n would definitely be fine.

 

[Carrotsticks]

Fell sick today so I wasn't able to attend the consultation unfortunately.

However, I will be attending the one in two weeks' time so that'll give me time to perhaps share my thoughts on the changes and the reasoning behind it. I'll write a short document for this.

For the mean time, I'd love to see any more opinions on this matter!

 

[leehuan]

Despite wanting to enter actuarial, which I'm sure will be overloaded with statistics, I'm still glad I didn't have to cope with it for the time being. I started to reduce hatred for it but when I was first beginning Year 11 I rejoiced over their absence.

No conics is always beautiful.

Q: With algebra, at the university level, what exactly does that comprise of anyway?