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Kill off a topic. (1 Viewer)

anomalousdecay

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As a teacher, I've found Conics to be the most pointless topic. It leads nowhere, has little to do with university maths beyond knowing the basic equations, and seems to be used merely to tests students' algebraic skills.
I don''t understand why you said this. Look at every traffic light intersection. There are conics (mainly hyperbolas) for the lines along the road.
Therefore, it is useful for engineering.

In Physics we started throwing boomerangs around (our teacher is rad out of the classroom but doesn't teach in the classroom),
and I realised that the shape of a boomerang is hyperbolic. The Aboriginals were doing 4-unit maths before all of us, and implemented it for hunting :lol:.

In focal lenses and also many mirrors (particularly blind-spot mirrors), you use a conical shape for the lenses and mirrors to refract/reflect light.

In a way, mainly engineers will need Conics, but for pure mathematics it isn't as important as, say Complex Numbers.
 

Carrotsticks

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As a teacher, I've found Conics to be the most pointless topic. It leads nowhere, has little to do with university maths beyond knowing the basic equations, and seems to be used merely to tests students' algebraic skills.
Actually, it has a lot to do with university mathematics and it most certainly does not lead to nowhere, because it introduces students to the concept of 'Projective Geometry'.

http://en.wikipedia.org/wiki/Dandelin_spheres

http://en.wikipedia.org/wiki/Projective_geometry

https://en.wikipedia.org/wiki/Lambert_conformal_conic_projection

I understand what you mean about testing students' algebraic skills (I also find it a bit tedious sometimes too), but I think the 'pointlessness' is moreso brought upon the treatment of it from the Board of Studies. Not many students fully understand what the directrix actually is (and I daresay even teachers too), and what the focus is.

The actual topic in itself, when studied properly (by considering its implications in real life), is absolutely amazing and extremely cool.

Check out these videos:



 
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As a teacher, I've found Conics to be the most pointless topic. It leads nowhere, has little to do with university maths beyond knowing the basic equations, and seems to be used merely to tests students' algebraic skills.
lol
 

TheGreatest99.95

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I don''t understand why you said this. Look at every traffic light intersection. There are conics (mainly hyperbolas) for the lines along the road.
Therefore, it is useful for engineering.

In Physics we started throwing boomerangs around (our teacher is rad out of the classroom but doesn't teach in the classroom),
and I realised that the shape of a boomerang is hyperbolic. The Aboriginals were doing 4-unit maths before all of us, and implemented it for hunting :lol:.

In focal lenses and also many mirrors (particularly blind-spot mirrors), you use a conical shape for the lenses and mirrors to refract/reflect light.

In a way, mainly engineers will need Conics, but for pure mathematics it isn't as important as, say Complex Numbers.
all that stuff is done in 3 unit. conics is useless
 
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all that stuff is done in 3 unit. conics is useless
If by useless you mean it doesn't have applications in real life then it is not useless but I can think of better topics to study instead of it such as topics that prepare students for university maths and have more applications (linear algebra, differential equations, etc.).
 

Makematics

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But keep in mind that the 4 unit course isnt necessarily done to prepare students for uni maths. I'm not entirely sure but i believe they teach it again. By introducing heavy algebra they are able to test students skills in that specific area, while other topics like harder 3 unit will test other mathematical abilities.
 
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But keep in mind that the 4 unit course isnt necessarily done to prepare students for uni maths. I'm not entirely sure but i believe they teach it again. By introducing heavy algebra they are able to test students skills in that specific area, while other topics like harder 3 unit will test other mathematical abilities.
Yeah, it doesn't have to prepare student for undergrad maths but I think there are many topics other than conics that are more interesting and more useful in uni. If students know basic coordinate geometry, calculus, and algebra they can definitely do conics so it isn't really teaching you anything essential.
In my opinion, there is a lot of calculus in 4U maths. I would prefer if there was also some advanced analysis and algebra.
 

Makematics

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Yeah, it doesn't have to prepare student for undergrad maths but I think there are many topics other than conics that are more interesting and more useful in uni. If students know basic coordinate geometry, calculus, and algebra they can definitely do conics so it isn't really teaching you anything essential.
In my opinion, there is a lot of calculus in 4U maths. I would prefer if there was also some advanced analysis and algebra.
Of course, the reality is that there are a select few who will easily be able to handle harder maths like linear algebra and stuff in high school. I too would love it if there was harder content. But the reality is that if the course was harder asian parents would still force their children into tuition and even more people will fail and the scaling will be even more fucked up. I can also see why an extension 3 maths is obviously not possible. From a quick skim through the new national curriculum, it doesnt seemed to have solved anything...
 
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Of course, the reality is that there are a select few who will easily be able to handle harder maths like linear algebra and stuff in high school. I too would love it if there was harder content. But the reality is that if the course was harder asian parents would still force their children into tuition and even more people will fail and the scaling will be even more fucked up. I can also see why an extension 3 maths is obviously not possible. From a quick skim through the new national curriculum, it doesnt seemed to have solved anything...
Yeah, that is why I want to get to uni asap, high school is just fucked up.
 

seanieg89

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Analysis will never happen in high school, it is too sophisticated a topic to be part of MX2 and by a pretty large margin.

Linear algebra makes more sense, at least the basics thereof.

Personally I would remove Graphs and Conics from the course and replace them with two topics out of:

-Elementary Number theory
-Differential equations (could make for some nice joint questions with mechanics)
-Linear algebra (Basic stuff only set in R^n (not abstract vector spaces), solvability of simultaneous equations, some vector geometry, etc.)


I think that graphing is a skill mx2 students should have (to help them understand the behaviour of functions) but not one that should be assessed.

The properties of conics have many applications, but the actual mathematics involved in the current syllabus is just glorified coordinate geometry.
 

jenslekman

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as much as i love mechanics, i don't think the topic "belongs" to high school maths. i think this should be moved to become part of physics while leaving more room in the maths syllabus for more topics.
 
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as much as i love mechanics, i don't think the topic "belongs" to high school maths. i think this should be moved to become part of physics while leaving more room in the maths syllabus for more topics.
I have to agree here...it is a mathematics course after all.
 

Kiraken

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lol why all the harder 3u hate? It's by far the most interesting and awesome of the topics in 4u imo. If i had to get rid of one topic, it would be conics just because i personally found it really bland in comparison to the other topics
 

Kiraken

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as much as i love mechanics, i don't think the topic "belongs" to high school maths. i think this should be moved to become part of physics while leaving more room in the maths syllabus for more topics.
but what about all the general maths and 2u maths people who do physics? it would be difficult for them to cope tbh

mechanics does belong in 4u imo, it's pretty much glorified integration with a bit of practical application
 

BlugyBlug

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lol why all the harder 3u hate? It's by far the most interesting and awesome of the topics in 4u imo. If i had to get rid of one topic, it would be conics just because i personally found it really bland in comparison to the other topics
This, fuck conics. Most annoying and least interesting topic.
 
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Analysis will never happen in high school, it is too sophisticated a topic to be part of MX2 and by a pretty large margin.

Linear algebra makes more sense, at least the basics thereof.

Personally I would remove Graphs and Conics from the course and replace them with two topics out of:

-Elementary Number theory
-Differential equations (could make for some nice joint questions with mechanics)
-Linear algebra (Basic stuff only set in R^n (not abstract vector spaces), solvability of simultaneous equations, some vector geometry, etc.)


I think that graphing is a skill mx2 students should have (to help them understand the behaviour of functions) but not one that should be assessed.

The properties of conics have many applications, but the actual mathematics involved in the current syllabus is just glorified coordinate geometry.
I like your ideas very much, very similar to mine.

I think there is way too much applied maths in HSC maths. This may make it more interesting and 'useful' but I think applied maths belongs to university as it is basically divided into engineering, physics, actuary, stats, computing, etc. which are best studied at university. I think high school maths should be mainly pure maths with an emphasis on understanding and problem solving. This will give student the skills required to do well in courses that involve maths at university.

Pure maths is divided into algebra, calculus, analysis, combinatorics, logic, geometry and topology, and number theory so extension 2 maths should be an introduction to advanced algebra, calculus, combinatorics, geometry, and number theory, the other topics are too advanced I think.
 
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anomalousdecay

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Pure maths is divided into algebra, calculus, analysis, combinatorics, logic, geometry and topology, and number theory so extension 2 maths should be an introduction to advanced algebra, calculus, combinatorics, geometry, and number theory, the other topics are too advanced I think.
Then again, would you include topics like Complex Numbers and Polynomials as a part of advanced pure mathematics? I probably wouldn't know since you are the uni student.
 
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Then again, would you include topics like Complex Numbers and Polynomials as a part of advanced pure mathematics? I probably wouldn't know since you are the uni student.
I think polynomials should be studied in extension 1 and complex numbers should remain.
I'm not a uni student btw.
 

Carrotsticks

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as much as i love mechanics, i don't think the topic "belongs" to high school maths. i think this should be moved to become part of physics while leaving more room in the maths syllabus for more topics.
Although it is a part of Physics, we cannot place it there. The reason is because the Physics course (and all the science courses) are designed such that a person NOT even doing 2 Unit Mathematics can still attempt the course.

I like your ideas very much, very similar to mine.

I think there is way too much applied maths in HSC maths. This may make it more interesting and 'useful' but I think applied maths belongs to university as it is basically divided into engineering, physics, actuary, stats, computing, etc. which are best studied at university. I think high school maths should be mainly pure maths with an emphasis on understanding and problem solving. This will give student the skills required to do well in courses that involve maths at university.

Pure maths is divided into algebra, calculus, analysis, combinatorics, logic, geometry and topology, and number theory so extension 2 maths should be an introduction to advanced algebra, calculus, combinatorics, geometry, and number theory, the other topics are too advanced I think.
I am interested to see what topics you define to be 'Applied', and what is 'Pure'.

And in response to the idea of making HS maths mainly 'Pure'... I don't exactly agree. One of my reasons is because part of the enjoyment of learning a topic (or learning anything for that matter) is being able to 'see where this finally leads to'. If I taught you how to A, B, C topics that are seemingly unrelated to begin with, chances are you will tell me "Cool story bro, what's the point of teaching me this stuff?". But say I tell you that A, B and C allow us to build a bicycle, then you will have motivation because some direction is provided. Many students start losing motivation once they ask the question 'What's the point of this?' and not receiving an adequate answer (if any).

For some seemingly more abstract topics such as Complex Numbers, the 'point of this' is not so clear (which is natural because it is one of the more abstract Extension 2 topics). Most students would not be able to easily identify its use and where it leads to, and this makes it more difficult to grasp the topic holistically. However, topics such as Mechanics offer a very obvious 'point of doing it' for even the average student. We need such topics to keep students motivated and to help them see where their simultaneous equations, trigonometric identities, geometry etc finally lead to (ie: Conical Pendulums needs all of the aforementioned sub-topics).

tl;dr

- Students learn better when they see applications of things.

- Although in 'pure' problems, there are applications, they are not as obvious as 'applied' problems.

- A very small percentage of students are able to appreciate the applications of mathematical tools into 'pure' concepts.

- Making the course mainly 'pure' would be catering to the minority, which would not be ideal.

- However, we still need some 'pure' things to allow students a glimpse into learning more abstract topics.

I think polynomials should be studied in extension 1 and complex numbers should remain.
I'm not a uni student btw.
Polynomials in MX2 is an extension of Polynomials in MX1 with the added tool of Complex Numbers (ie: Conjugate Root Theorem, Roots of Unity).

If we were to move MX2 Polynomials to MX1, it would not be very much different as we are limited by the fact that Complex Numbers is not present in the MX1 course.
 
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Makematics

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Polynomials in MX2 is an extension of Polynomials in MX1 with the added tool of Complex Numbers (ie: Conjugate Root Theorem, Roots of Unity).
If we were to move MX2 Polynomials to MX1, it would not be very much different as we are limited by the fact that Complex Numbers is not present in the MX1 course.
I reckon that they can just chuck the part of polynomials that involves complex numbers straight into complex numbers. There isnt much extra to be learnt anyway.
 

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