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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