Proposed changes to the Mathematics syllabus: Thoughts? (1 Viewer)

[leehuan]

Circular motion is useful if your interested in studying mechanical engineering. physics or aerospace engineering. Anyone who wants to study actuarial
or pure maths might think otherwise.

I'm doing both of the latter. But if you let statistics be a means of replacing circular motion then you're just saying screw the engineers/physicists its all about the actuaries.

I disagree.

Conical sections can be used to trisect arbitrary angles and are used in multi-lateration.

Of course, the HSC doesn't teach any of that...

Forgetting the fact we have computing software now anyway, I am pretty sure there's no need to specifically use conics when mere origami is enough to trisect angles.

 

[Paradoxica]

I'm doing both of the latter. But if you let statistics be a means of replacing circular motion then you're just saying screw the engineers/physicists its all about the actuaries.

Forgetting the fact we have computing software now anyway, I am pretty sure there's no need to specifically use conics when mere origami is enough to trisect angles.

Convince the board that Origami should be in Mathematics and then we'll talk.

 

[leehuan]

Convince the board that Origami should be in Mathematics and then we'll talk.

Why would the board even care about how to trisect angles anyway when that knowledge isn't beneficial at all for a Yr 12 kid?

I thought we were talking about real world applications when you mentioned trisecting angles, not Yr 12.

 

[Paradoxica]

Why would the board even care about how to trisect angles anyway when that knowledge isn't beneficial at all for a Yr 12 kid?

I thought we were talking about real world applications when you mentioned trisecting angles, not Yr 12.

If you want real world application, multi-lateration.

 

[leehuan]

Ok.

In that case, evidence that stats and/or circular motion is used less in the real world than conics will do.

 

[Paradoxica]

Ok.

In that case, evidence that stats and/or circular motion is used less in the real world than conics will do.

Never claimed that.

 

[Carrotsticks]

I'm doing both of the latter. But if you let statistics be a means of replacing circular motion then you're just saying screw the engineers/physicists its all about the actuaries.

Not quite 'all about the actuaries'. Many branches of Science also require statistics. For example, one of my mates is currently doing his PhD in Psychology, and statistics is an integral part of his research. To give you an idea of how vital it is in psychology, there is a statistics unit at USYD solely dedicated to statistics within psychology (mostly more advanced forms of hypothesis testing).

Also, conics (as it currently is) is fairly useless and only really serves as a way for HSC students to exercise their coordinate geometry muscles (when was the last time you saw a conics question that required you to actually THINK about what was going on?).

The closest thing, in the current course, to a more formal study of conics would be PS=ePM, PS+PS'=2a and perhaps the reflective property. If we wanted to study conics at a more practical level, then it should probably include it's connection to astrophysics (obvious use) and maybe polar equations (useful for some regions in vector calculus: engineering + physics). Otherwise, it's not a terribly huge loss.

Circular motion would be somewhat useful for a first year undergraduate engineer, but it's so restrictive at the moment so that the entire 4U topic can be safely condensed into a two or three hour lecture.

 

[leehuan]

Meh. I've always been in favour of removing conics. Mostly for that reason as well - its relevance to astrophysics isn't really touched on. Plus I'm pretty sure hardly anyone in the MX2 course would actually remember that the theorem is called the "reflective property" of ____conic___.

Could probably say that most of the HSC course can be condensed into a 2-3hr lecture though. Integration by parts takes up one full lesson during high school but in my uni lecture he only went over it for 10-15 min before he was like yep ok improper integrals now.
_________________

I suppose fair enough though. It always slips past me about how certain fields of science actually uses statistics to such an extent. Sometimes it's just not obvious enough as to why and I have to actually think about it to realise it.
(Because my biased hatred towards statistics is being eliminated this year I also don't feel annoyed by its re-introduction either.)

 

[Trebla]

I suppose fair enough though. It always slips past me about how certain fields of science actually uses statistics to such an extent. Sometimes it's just not obvious enough as to why and I have to actually think about it to realise it.
(Because my biased hatred towards statistics is being eliminated this year I also don't feel annoyed by its re-introduction either.)

Any field that requires analysis of data would involve statistical concepts. This includes any quantifiable results of scientific experiments or quantitative business data.

 

[eyeseeyou]

Okay lets see the "usefulness" of 4U topics:

Complex numbers: complete the whole number system
Graphs/Curve Sketching: Used in engineering iirc
Polynomials: I have no idea
Conics: Useless
Integration: ...unsure exactly although I know integration is about measuring the area under a curve (a.k.a. opposite of differentaition where differentiation is finding the gradient of the tangent)
Volumes: Not so familiar with this topic
Mechanics: As said above it is useful in engineering
Harder 3u: Don't know how this is useful given that harder 3u is just 3u except a million times harder. In essence it's just a recollection of 3U questions

 

[eyeseeyou]

I disagree.

Conical sections can be used to trisect arbitrary angles and are used in multi-lateration.

Of course, the HSC doesn't teach any of that...

That's why its useless...

 

[eyeseeyou]

Not quite 'all about the actuaries'. Many branches of Science also require statistics. For example, one of my mates is currently doing his PhD in Psychology, and statistics is an integral part of his research. To give you an idea of how vital it is in psychology, there is a statistics unit at USYD solely dedicated to statistics within psychology (mostly more advanced forms of hypothesis testing).

Also, conics (as it currently is) is fairly useless and only really serves as a way for HSC students to exercise their coordinate geometry muscles (when was the last time you saw a conics question that required you to actually THINK about what was going on?).

The closest thing, in the current course, to a more formal study of conics would be PS=ePM, PS+PS'=2a and perhaps the reflective property. If we wanted to study conics at a more practical level, then it should probably include it's connection to astrophysics (obvious use) and maybe polar equations (useful for some regions in vector calculus: engineering + physics). Otherwise, it's not a terribly huge loss.

Circular motion would be somewhat useful for a first year undergraduate engineer, but it's so restrictive at the moment so that the entire 4U topic can be safely condensed into a two or three hour lecture.

If conics is deemed useless wouldn't parametrics be deemed useless as well?

Also what was the point of putting conics in the first place in the maths syllabus given that it has no usefulness other than "exercising their coordinate geometry muscles"?

If conics would include astrophysics and polar equations, wouldn't that be outside the scope of the extension 2 maths syllabus (think of it like the calculus side of statistics)?

 

[eyeseeyou]

By the way Carrotsticks, given that statistics is a broad topic, to what extent would they...you know...make us spend time on it? (I hear people take a while to learn complex numbers)

 

[leehuan]

If conics is deemed useless wouldn't parametrics be deemed useless as well?

Also what was the point of putting conics in the first place in the maths syllabus given that it has no usefulness other than "exercising their coordinate geometry muscles"?

If conics would include astrophysics and polar equations, wouldn't that be outside the scope of the extension 2 maths syllabus (think of it like the calculus side of statistics)?

Nah, parametrics aren't bound to conics. You can have various parametrised curves.

 

[leehuan]

Okay lets see the "usefulness" of 4U topics:

Complex numbers: complete the whole number system
Graphs/Curve Sketching: Used in engineering iirc
Polynomials: I have no idea
Conics: Useless
Integration: ...unsure exactly although I know integration is about measuring the area under a curve (a.k.a. opposite of differentaition where differentiation is finding the gradient of the tangent)
Volumes: Not so familiar with this topic
Mechanics: As said above it is useful in engineering
Harder 3u: Don't know how this is useful given that harder 3u is just 3u except a million times harder. In essence it's just a recollection of 3U questions

Harder 3U feels half distinct from 3U if you ask me.

It's not like harder 2U. Its a seperate topic cause it does teach new concepts

And the difficulty of it is necessary given that the HSC course is still pretty dumbed down over the years; first year maths is still harder than harder 3U (although I can't say for sure by how much)

Eliminating harder 3U basically means the HSC course is no longer worth mentioning in the real world.

 

[Carrotsticks]

Okay lets see the "usefulness" of 4U topics:

Complex numbers: complete the whole number system
Graphs/Curve Sketching: Used in engineering iirc
Polynomials: I have no idea
Conics: Useless
Integration: ...unsure exactly although I know integration is about measuring the area under a curve (a.k.a. opposite of differentaition where differentiation is finding the gradient of the tangent)
Volumes: Not so familiar with this topic
Mechanics: As said above it is useful in engineering
Harder 3u: Don't know how this is useful given that harder 3u is just 3u except a million times harder. In essence it's just a recollection of 3U questions

I really wouldn't be judging the usefulness of topics at this level too critically. I always tell my students that it's akin to analysing the usefulness of a hammer by itself, or a staple by itself, or a piece of wood by itself, or some rope by itself.

Individually, you can achieve little with these components. But when you start mixing them up together, these tools start being useful and you can construct complex things. Just because you are ignorant of their uses (and I admit I too am sometimes ignorant of the uses of various methods/techniques) it doesn't mean it is useless. Chances are, there exists some use of it out there.

For example, last night in actual fact, I found a solution to a nice probability question using Extension 2 volumes techniques. Volumes by slicing to be specific, though I had to generalise to R^n instead of working in the usual R^3.

If conics is deemed useless wouldn't parametrics be deemed useless as well?

Also what was the point of putting conics in the first place in the maths syllabus given that it has no usefulness other than "exercising their coordinate geometry muscles"?

If conics would include astrophysics and polar equations, wouldn't that be outside the scope of the extension 2 maths syllabus (think of it like the calculus side of statistics)?

The parametrisation of the conics is a very tiny part of the course and can be taught in quite literally 1 minute or less. I would not link it very closely with 'parametrics' (though despite the name, the focus really on parametrisations of curves). And I wouldn't label parametrics anywhere near useless. In actual fact not too long ago I was teaching vector calculus and introducing line integrals. A lot of the teaching was slowed down due to a lack of knowledge of how parametrisations really work and how to construct a convenient one.

Lastly yes strictly speaking it is outside the scope of the course. But if you want to stick strictly to a syllabus course, then don't expect interesting/useful things to be introduced into the course. These two things are almost mutually exclusive at this level.

By the way Carrotsticks, given that statistics is a broad topic, to what extent would they...you know...make us spend time on it? (I hear people take a while to learn complex numbers)

Yes.

 

[AusHam]

I'd say conics is useful for studies of satellite orbits and astrodynamics, but even when those subjects cover conics, its only
at the definition level (x^2/a^2 + y^2/b^2 = 1) and solving problems relating to eccentricity, size of fociis and curve
sketching rather than the Ext 2 way of rigorously proving that tangent ... intersects the point on this curve.

Having said this, I would like the new syllabus to have conics touched very briefly in the Functions and Graphs
topic and at the definition/surface level rather than the existing way it is taught. Also, what are people's
thoughts on teaching basic hyperbolic trig functions at an Ext 2 level?

 

[Paradoxica]

I'd say conics is useful for studies of satellite orbits and astrodynamics, but even when those subjects cover conics, its only
at the definition level (x^2/a^2 + y^2/b^2 = 1) and solving problems relating to eccentricity, size of fociis and curve
sketching rather than the Ext 2 way of rigorously proving that tangent ... intersects the point on this curve.

Having said this, I would like the new syllabus to have conics touched very briefly in the Functions and Graphs
topic and at the definition/surface level rather than the existing way it is taught. Also, what are people's
thoughts on teaching basic hyperbolic trig functions at an Ext 2 level?

I want Hyperbolic Functions, at a level enough for it to be used in Integration.

 

[eyeseeyou]

I really wouldn't be judging the usefulness of topics at this level too critically. I always tell my students that it's akin to analysing the usefulness of a hammer by itself, or a staple by itself, or a piece of wood by itself, or some rope by itself.

Individually, you can achieve little with these components. But when you start mixing them up together, these tools start being useful and you can construct complex things. Just because you are ignorant of their uses (and I admit I too am sometimes ignorant of the uses of various methods/techniques) it doesn't mean it is useless. Chances are, there exists some use of it out there.

For example, last night in actual fact, I found a solution to a nice probability question using Extension 2 volumes techniques. Volumes by slicing to be specific, though I had to generalise to R^n instead of working in the usual R^3.



The parametrisation of the conics is a very tiny part of the course and can be taught in quite literally 1 minute or less. I would not link it very closely with 'parametrics' (though despite the name, the focus really on parametrisations of curves). And I wouldn't label parametrics anywhere near useless. In actual fact not too long ago I was teaching vector calculus and introducing line integrals. A lot of the teaching was slowed down due to a lack of knowledge of how parametrisations really work and how to construct a convenient one.

Lastly yes strictly speaking it is outside the scope of the course. But if you want to stick strictly to a syllabus course, then don't expect interesting/useful things to be introduced into the course. These two things are almost mutually exclusive at this level.



Yes.

Would it be possible to use a matrices method for a conics question? I know someone who did it and apparently they told me they got it right in the HSC (or school exam)

hmmm...interesting...

You didn't answe my question properly carrotsticks lol, I asked how long will schools focus on statistics (given that statstics is a very broad topic)?

 

[leehuan]

Would it be possible to use a matrices method for a conics question? I know someone who did it and apparently they told me they got it right in the HSC (or school exam)

hmmm...interesting...

You didn't answe my question properly carrotsticks lol, I asked how long will schools focus on statistics (given that statstics is a very broad topic)?

Look at the new syllabus.

Look at how many dot points fall under stats.

Compare it to how many dot points in total.

Interpolate.