Mm okay now I feel obliged to respond to that point, given so much dissent. Hard work, to me, does not mean completing 100 trial papers. Doing so is an incredibly inefficient way of 'learning', unless one approaches said papers with the correct mindset. I will focus on maths here, but the same principle applies to all subjects worth studying for.
Firstly, I will pose a very broad question: what exactly is maths? Most students, mainly on account of indifference, do not spare a thought for questions of this kind. Feel free to disagree with my definition of maths, but to me, maths is simply an exercise in deduction. Indeed, the entire discipline is grounded on a set of fundamental axioms (which incidently, derive not from 'reason', whatever you may consider that as being, but experience, by which I mean raw empirical data). The concept of 'one', for instance, originates from what I like to call the world of experience. Unless we experience 'oneness' in some way, we would not have any conception of it. But I will make a giant leap of faith and claim that it so happens that most, if not all, humans have experienced 'oneness' before, ensuring mutual understanding of this mystical concept called 'integers' (obviously in order to properly conceive of integers, one would require experience of more things than 'oneness', but I will terminate my admittedly rather crude example here, mainly because I cbs delving into this too deeply). ALL mathematical results (encompassing everything from theorems to solutions to a random maths problem from IMO or whatever) stem from these fundamental axioms. Let's denote the set of axioms of which I speak by the letter A, and a particular mathematical result by the letter B. To get from A to B, all that is required deduction, by which I mean the application of logical relationships between concepts gained from experience (i.e. the relationship that sort of guarantees the 'truth' - coincidence of concept with world of experience - of B given the two premises (1) If A then B, and (2) A.)
I say all this because I want people to realise that competence in maths does not come from blindly doing questions and memorising a lot of formulae/pre-existing results and techniques. Succinctly, a person who is good at maths is (a) familiar with at least most of the fundamental axioms upon which mathematical premises are grounded and b) good at deduction. (a) is easy to accomplish. Most people have an intuitive understanding of 'oneness', and 'addition', etc., gleaning all of that from 'unconscious' experience (e.g. most people aren't aware that when they accompany their parents to buy fruit, or when they are literally just staring at an object like a table, they are already being acquainted with a good deal of mathematical axioms). (b) is infinitely harder to accomplish, mostly because maths is rarely taught 'properly' at a high school level (probably even at a tertiary level but not sure due to lack of experience). You learn a lot of mathematical methods in say VCE mathematical methods, but you are not told that these methods are in fact forms of deduction. Learning individual methods without an understanding of what they actually are in themselves is dangerous and horribly inefficient because you begin to build isolated techniques (e.g. Markov chain technique, etc.) without really knowing the bigger picture and how they relate to each other. 'Hard work' in maths means literally working to fully understand the 'bigger picture' of deduction, which, I confess, is really, really, really hard to do without instruction. Once you have understood the 'bigger picture', the raw substance of deduction, you should theoretically be able to derive ALL theorems, etc. BY YOURSELF without references to pre-existing proofs. By 'dedication', I literally just mean dedication to the journey one must inevitably take towards an understanding of the 'raw deduction'.
EDIT: If you buy into my theory of maths and to a certain extent my theory of the mind, then you would realise how bogus is the suggestion that mathematical ability is in part a result of natural talent. Indeed, the very concept of natural talent is farcical, unless you can come up with legitimate (aka not simply scientific) justification for the claim that some babies are touched by the maths god on birth, or that some babies have deduction in built into them when they come out of their mother's womb.
Hope that clears things up a bit.
Addendum: Also, assuming that people are pushing for a change in the 'rules of VCE' and not merely questioning the moral status, whatever that may mean to them, of choosing Spesh and Further concurrently, this debate can basically be reduced to consideration of one single question: Is the difference between Further and say Spesh as great as, say, the difference between Classics and English? I've already stated explicitly my stance on this matter, and I guess an objective answer can never really be established unless one actually undertakes to do both courses. I think that maths is broad enough a discipline to warrant 'divisions'. As far as I'm concerned, a great deal of the Further Maths course is entirely unique to that particular course, and is not learned in either Spesh or Methods. Of course, students can circumvent this issue by simply focussing on becoming really good at deduction.
Home
Help
Search
Login
