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Best way to teach differentiation at A-level?

Discussion in 'Mathematics' started by cjwray, Jan 12, 2011.

  1. Not having much experience of teaching A-level I was just wondering what approach people would advise? Is it best to teach from first principals or will that be too difficult for the pupils? Does anybody have any different approaches to beginning the topic of differentiation?
  2. Me 4.
    I didn't understand what the heck was going on when I was a student but it sure made me wake up, pay attention and realise I was going to have to up my game.
    It's much for students to explore now with spreadsheets and other ICT.
  3. I agree. You have to teach differentiation properly so that they understand the concept of what is going on, else what is the point? It is such a vital topic that underpins so much pure mathematics (differentiation, rates of change, optimisation problems, integration, differential equations, parametric equations to name a few) that to not do it properly wouldn't be fair on students capable of understanding it.
    IF once you have discovered differentiation properly, some students just can't understand it and want to just apply the rote-learning method, then fine, but these are the students who will struggle with A2 level maths.
  4. No, in the same way exam boards dont state "This year we are going to make the exam paper easier than last" yet it happens.
    I would love to teach from first principles but some pupils accepted onto A level courses with B grade GCSEs have no idea of anything beyond the first two basic rules of indices. Negatives, fractional and even zero powers seem to be s struggle let alone dropping or increasing by a power. The idea of a tangent only sparks basic memories of algorithms used in 'dat so car towa thinngy, innit'
    So, as stated, first principles would be lovely, looking at SOME classes and the current edexcel C1 paper........I think the last one I found on a C1 paper was WJEC about 3-4 years ago but thats a guess
  5. I remember about 8 years ago helping a student with her GCSE coursework, which involved finding the gradient of y = x^2 and y= x^3 at various points, by increasing x a tiny bit, working out the corresponding change in y etc etc....
  6. Absolutely. At A-level we should be abstracting from concrete investigations done earlier.
    One of the hardest topics for students to understand is the practical application of calculus to solve maximum/minimum problems in real life. I've developed a really lovely way of doing with A-level students (with play dough). Anyone on LinkedIn can find it written up in the Math, Math Education, Math Culture Forum there on the 'what is a function thread'.
    Alternatively I'm doing it with the ATM North Cumbria group next Friday evening if anyone wants to come along. (Details through the ATM site).
  7. DM

    DM New commenter

    Nice. I've got a nice activity on solving second order non-linear homogeneous differential equations involving pasta shapes, a coat hanger and a generous dollop of ear wax. I might show you sometime if you behave yourself.

  8. Really ... yet I have often had KS3 students solving Sheep Pen problems and drawing the graph and discussing the turning point ... and talking about the change in the graphs steepness

    All quite intuitively

    So what do you think creates the problem at sixth form level
  9. I work with trainee teachers. When we give them these problems they notoriously don't have a clue how to start them (even though they've all done A-level of course).
    It stands out how poorly this topic is retained in comparison with other topics.
  10. Nazard

    Nazard New commenter

    Cough. Really? Did that sort of thing happen ... one person helping another with their coursework? Gosh - seems unlikely to me.
  11. It is still on the WJEC C1 paper and the Chief Examiner has made it clear that it stay. Pupils I teach see this, and all of the proof questions in fact, as an easy marks since they can memorise the required solutions.
  12. Superb, I think thats a nice inclusion. I shall contact edexcel and see if they are up for having it in their exams. I doubt it but I am really for moving away from the 'plug and chug' culture which supports pupils who are not really suited to A level maths.
    Afterall you dont have to answer a question on algebra or number work of any note to get a B at GCSE.

    Do you put that down to their past exposure to the subject or their present exposure?
    I can imagine a big circle of 23-50 year olds sitting round on the carpet being taught how to cut and stick boxes made of card being given instructions in words with 8 syllables an acronymns galore

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