Proposed changes to the Mathematics syllabus: Thoughts? (5 Viewers)

[mreditor16]

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.

But I would only like to see matrices taught if enough time was then spent on areas which utilise interesting applications of matrices. Many HSC students imo will find matrices and some of its applications quite theoretical/conceptual, rather than real-world and applicable.

 

[InteGrand]

But I would only like to see matrices taught if enough time was then spent on areas which utilise interesting applications of matrices. Many HSC students imo will find matrices and some of its applications quite theoretical/conceptual, rather than real-world and applicable.

Since this is a maths course, the focus of matrices should probably not be on the practical / "real-world" applications, but rather on the mathematics (unless they decided to open two strands – Pure and Applied; but this is another discussion) (and besides, one can't focus on advanced applications unless having learnt a lot of theory first, and there's no room in the HSC syllabus to do both to a great level of depth). I don't think students who choose to do 4U maths can complain if what they do is conceptual-based.

That being said, there probably would (or should) be basic applications though as glittergal96 described, probably more than currently in the Conics topic, for example (which is mostly just messy/tedious algebra questions). The responsibility for delving deeply into the ''real-world'' applications of matrices etc. should be on the subjects where these are actually applied (Physics, Chemistry, Economics, etc. etc.), but I can't see them doing this in the HSC (because they've shied away from involving maths since ~ 2001).

 

[Drongoski]

The IB Diploma Maths subjects: Mathematics (SL) and Mathematics (HL) both had matrices for many years, but dropped them in 2014. Don't know the rationale behind this change. But Vectors are still in, for both.

I think the IB syllabuses could provide some useful ideas for updating the current HSC syllabuses (syllabi).

 

[Trebla]

But I would only like to see matrices taught if enough time was then spent on areas which utilise interesting applications of matrices. Many HSC students imo will find matrices and some of its applications quite theoretical/conceptual, rather than real-world and applicable.

There are lots of examples of matrices being applied in other HSC topics (especially if the foundations are built pre-HSC). Linear functions is the most obvious one but there are also potential applications in statistics and calculus as well. It's just a matter of being able to incorporate it properly in the content.

 

[eyeseeyou]

When are they going to change the maths syllabus in the future?

Are they going to shove conics in parametrics (proving parabolas and locus)?

What are the changes for 2u, 3u and 4u?

 

[Carrotsticks]

When are they going to change the maths syllabus in the future?

Are they going to shove conics in parametrics (proving parabolas and locus)?

What are the changes for 2u, 3u and 4u?

The changes have NOT been finalised, though the proposed changes are listed in the document I linked in my original post.

The idea at the moment is to begin it in 2018/2019. In other words the first teaching of it in 2018 to the Year 11's, who will then go on to do the first 'new' HSC exam in 2019.

 

[Paradoxica]

The changes have NOT been finalised, though the proposed changes are listed in the document I linked in my original post.

The idea at the moment is to begin it in 2018/2019. In other words the first teaching of it in 2018 to the Year 11's, who will then go on to do the first 'new' HSC exam in 2019.

Carrotsticks is alive!!!!

 

[eyeseeyou]

IMO, changing the maths syllabus isn't a good idea especially when you've got the syllabus and content staying the same for the last 30 years.

If they're going shove statistics in the Hsc, they might as well shove matrices

 

[leehuan]

IMO, changing the maths syllabus isn't a good idea especially when you've got the syllabus and content staying the same for the last 30 years.

If they're going shove statistics in the Hsc, they might as well shove matrices

I already mentioned in putting matrices and the comments on it are in another thread. Go find them.

 

[Carrotsticks]

IMO, changing the maths syllabus isn't a good idea especially when you've got the syllabus and content staying the same for the last 30 years.

If they're going shove statistics in the Hsc, they might as well shove matrices

But they can very well be taught independently of each other at this stage. I see no reason why if one is introduced, the other must be dragged along with it.

Statistics is a vital and pretty much new topic, which is why it is being introduced. If matrices are to be introduced, it would have to be taught as early as Year 9-10 so then students in Year 11 and 12 can -actually- learn and use the more advanced techniques and tools. Given that the new syllabus has already been made and implemented for junior years, this isn't happening any time soon.

If it is introduced in Year 11 and 12 now, then they would not get very far with them (as they'll need to be taught everything from scratch) and most likely will only scratch the surface of the topic.

 

[eyeseeyou]

I'm just amazed but when they first put conics in the syllabus, they didn't bother to think how important statistics was and just thought about using everything that was "calculus" and 30 years later, they come to think of this plan and it took them 30 years. I'm just amazed

Apparently statistics could possibly involve calculus however it would be out of the range of extension 2 maths at high school (i.e. looking at statistics of such e.g. HSC results, looking it in a bell curve graph and integrating from one end to the other)

 

[leehuan]

I'm just amazed but when they first put conics in the syllabus, they didn't bother to think how important statistics was and just thought about using everything that was "calculus" and 30 years later, they come to think of this plan and it took them 30 years. I'm just amazed

Apparently statistics could possibly involve calculus however it would be out of the range of extension 2 maths at high school (i.e. looking at statistics of such e.g. HSC results, looking it in a bell curve graph and integrating from one end to the other)

The calculus side of statistics, if you did some proper research on it, you would find IS far too beyond the capabilities of a typical MX2 student.

They focused the courses too much on calculus and neglected algebra thoroughly in my opinion.

 

[InteGrand]

The calculus side of statistics, if you did some proper research on it, you would find IS far too beyond the capabilities of a typical MX2 student.

They focused the courses too much on calculus and neglected algebra thoroughly in my opinion.

The NSW maths HSC (or equivalent) papers from 30-50 or so years ago had linear algebra in them as well as calculus (and more calculus than now). From memory, for linear algebra, the old HSC 4U papers had Q's on things like matrices operations and calculations, linear transformations (like rotations and reflections and applications to conics iirc), eigenvalues and eigenvectors, etc. These old papers can be searched up if anyone wants to see the types of Q's they had.

 

[leehuan]

The 4U papers from 30-50 or so years ago had linear algebra in them as well as calculus (and more calculus than now). From memory, for linear algebra, the old HSC 4U papers had Q's on things like matrices operations and calculations, linear transformations (like rotations and reflections and applications to conics iirc), eigenvalues and eigenvectors, etc. These old papers can be searched up if anyone wants to see the types of Q's they had.

And then they got rid of the linear algebra

 

[InteGrand]

And then they got rid of the linear algebra

Correct! In fact, many topics have been removed from the NSW high school maths curriculum over the past 100 years (including things like group theory and the Riemann Zeta function it seems). Here's a post that lists these:

It used to be in the course, but was removed.

The current 1-year 4 unit course used to be a 2-year course (Level 1). Arc length was in Level 1 and used to be taught in high schools in NSW. Other countries' syllabuses for high school maths also have arc length.

Level 1 was watered down to the 1-year course in 1981.

Many people would like the 2-year course to return.

The only excuse for why the harder Level 1 course can't be taught in high schools again, is teacher incompetence. And that's a very poor excuse.<!-- google_ad_section_end -->

Here are the topics previously in the course which have been removed, but many people want back:

Leaving Certificate (1916-1966)

• 3rd derivative test for inflections
• Substitution x=acos²θ+bsin²θ for ∫√((x-a)(x-b))dx, ∫(1/√((x-a)(x-b)))dx, ∫√((x-a)/(b-x))dx
• Euler's Formula
• Integration as a summation
• Determinants and solutions of equations
• Convergence and divergence of infinite series
• Logarithmic and Exponential series and Euler's constant
• Binomial series for fractional or negative index.

Level 1 (1966-1980)

• Euclidean algorithm
• Proof of the fundamental theorem of arithmetic
• Determinants and the solution of equations and area of triangle
• Geometry of matrices
• Geometrical transformations using matrices
• Algebra of matrices
• Rolle's theorem and mean value theorem
• Integration as summation
• Euler's formula
• Length of arc
• Group theory, isomorphism
• Applications of matrices to geometry and probability
• Work, Kinetic Energy, Potential energy
• Convergence and divergence of infinite series
• Riemann Zeta function
• Logarithmic and exponential series
• Series for sinx, cosx, tan^-1x
• Taylor's series.

Level 2F (1966-1982)

• Mid-ordinate rule
• Change of coordinate systems - transformations
• Analytical geometry in three dimensions

Quite a lot of this stuff which used to be taught in school, is now postponed till university in Australia. However, other countries are still teaching it in school. So Australia is seen as a bit behind the rest of the world, particularly in regard to school maths and 1st year uni maths.

If we bring these topics back and make 4 unit a 2-year course again, we won't have to postpone them till university, and perhaps the uni's can then focus on what they should be doing and not have to teach what should have been done in school, as they currently do.

I reckon you could also add surface area of revolution to the high school maths syllabuses as well as arc length.

Here are some past HSC questions on arc length:

• 1967 Q8(iv)
• 1970 Q3(i)
• 1972 Q7(iii)
• 1974 Q5(i)
• 1977 Q8(ii)
• 1979 Q7(iii)
• 1984 Q2(a) (note in 1984 the formula was given)

available in the files

http://www.boredofstudies.org/mirror/4u/hsc1967-1974.pdf
http://www.boredofstudies.org/mirror/4u/hsc1975-1980.pdf
http://www.boredofstudies.org/mirror/4u/hsc1981-1989.pdf

 

[tywebb]

Those old links at the end of the post you quoted don't work any more. Here are the correct links:

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

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

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

 

[eyeseeyou]

The calculus side of statistics, if you did some proper research on it, you would find IS far too beyond the capabilities of a typical MX2 student.

They focused the courses too much on calculus and neglected algebra thoroughly in my opinion.

But calculus is literally everything in maths (in that sense)

They still do have algebra, complex numbers

 

[eyeseeyou]

The maths HSC (of equivalent) papers from 30-50 or so years ago had linear algebra in them as well as calculus (and more calculus than now). From memory, for linear algebra, the old HSC 4U papers had Q's on things like matrices operations and calculations, linear transformations (like rotations and reflections and applications to conics iirc), eigenvalues and eigenvectors, etc. These old papers can be searched up if anyone wants to see the types of Q's they had.

Are these all taught in uni now?

 

[eyeseeyou]

And then they got rid of the linear algebra

I suppose it's taught in first year uni

 

[eyeseeyou]

Correct! In fact, many topics have been removed from the NSW high school maths curriculum over the past 100 years (including things like group theory and the Riemann Zeta function it seems). Here's a post that lists these:

Interesting, are these taught in uni or what?