If you look at a maths question and don't believe you'll do and are depressed: STOP.
No really, we mean that. You'll never do any but the most trivial maths when in that state, subconciously you'll deliberatly write yourself into corners and go down wrong routes, I've been doing it myself recently (and when more cheerful going "Well anyone awake would have done it this way ...").
And algebra errors ... yeah, we had a proof a little while ago, all the hard maths was there but I just made silly algebra error after silly algebra error (When we multiple x by y Neil it does not stay x! And no, when you mutliple a bracket by y you can't just put it it only on those terms where it's convient to do so).
Good algebra is a serious advantage but often entirely capable mathematicians' algebra goes pearshaped.
In such situations the cure I have found is to reach the end of the question, realise that 1 does not 0 or that the expression you have is nothing like what you're supposed to get, and go and do something else for at least 15 minutes (cake and drink and someone to talk to are good options, so's going for a walk). When you come back your mind won't be locked in the cycles it did before and you'll be able to analyse your work properly and find the mistakes you made.
Being able to spot all but the most blatent errors (and often not even them) without a break would mark you down as a mathematician of the highest calibre and I'd have to start working hard to keep up.
Next time give up before you start trying, Often maths is like revision: if you aren't at your best there's no point doing it (this is of course dependant on the maths in question).
As for improving your algebra: lose the calcuator. You'll probably want to check everything using it for reassurance (I did) but make sure you do everything in your head first (well, expect when it's after midnight and they want sin 10.25 degrees, you know what I mean).
And because GCSE makes us stupid (no really, it does) it will be a while before your algebra gets to where it ought to be (or at least it takes everyone else a while (some of my class were still not there a year later but I'm not excusing you for more than a few months!)).
Pling's right for debugging maths (and when you start dealing with matricies) but onyl do this is you have to, the harder you can push your brain the better you'll get (but don't break it cos then you don't get anywhere).
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Defeatist attitudes in maths
Date: 2001-10-04 01:20 am (UTC)From:No really, we mean that. You'll never do any but the most trivial maths when in that state, subconciously you'll deliberatly write yourself into corners and go down wrong routes, I've been doing it myself recently (and when more cheerful going "Well anyone awake would have done it this way ...").
And algebra errors ... yeah, we had a proof a little while ago, all the hard maths was there but I just made silly algebra error after silly algebra error (When we multiple x by y Neil it does not stay x! And no, when you mutliple a bracket by y you can't just put it it only on those terms where it's convient to do so).
Good algebra is a serious advantage but often entirely capable mathematicians' algebra goes pearshaped.
In such situations the cure I have found is to reach the end of the question, realise that 1 does not 0 or that the expression you have is nothing like what you're supposed to get, and go and do something else for at least 15 minutes (cake and drink and someone to talk to are good options, so's going for a walk). When you come back your mind won't be locked in the cycles it did before and you'll be able to analyse your work properly and find the mistakes you made.
Being able to spot all but the most blatent errors (and often not even them) without a break would mark you down as a mathematician of the highest calibre and I'd have to start working hard to keep up.
Next time give up before you start trying, Often maths is like revision: if you aren't at your best there's no point doing it (this is of course dependant on the maths in question).
As for improving your algebra: lose the calcuator. You'll probably want to check everything using it for reassurance (I did) but make sure you do everything in your head first (well, expect when it's after midnight and they want sin 10.25 degrees, you know what I mean).
And because GCSE makes us stupid (no really, it does) it will be a while before your algebra gets to where it ought to be (or at least it takes everyone else a while (some of my class were still not there a year later but I'm not excusing you for more than a few months!)).
Pling's right for debugging maths (and when you start dealing with matricies) but onyl do this is you have to, the harder you can push your brain the better you'll get (but don't break it cos then you don't get anywhere).
Neil