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Risky mnemonics

Discussion in 'Mathematics' started by simonc1978, Feb 26, 2011.

  1. Thanks to both Vince for clarifying his position (I understand much better now) and to scentless_apprentice. I don't think you are going against the grain scentless, most posters seemed either neutral or in favour of the 'rock star physicist'. Oddly, Vince has probably gained Professor Cox and extra viewer since I hadn't seen the show but I'm now most intrigued to see what all the fuss is about!

    I would agree with scentless in that there has been a general dumbing down of tv, you only have to watch the BBC News at Six to see that it's of a lower standard than Newround was in the old days!

    In terms of the making of tv programmes, I've no real comment. I certainly don't think many would switch on to see any presenter deliver a monologue on a scientific topic so I suppose it's a question of balance.

    I'm more inclined to side with the people who are saying that anything that gets the public to take an interest in science has to be worth a shot. At a time when several leading universities have lost physics departments, surely the more people who have at least some interest has to be a good thing. I'm sure how Vince can say with such certainty that popular TV like Prof Cox won't spark interest amongst youngsters, it might not be to everyones taste but at least the BBC are having a go.

  2. Apologies for the typo, it's been a long day, what I meant to say was 'I'm not sure how Vince can say...', or 'what it is that leads Vince to be so certain'.
  3. Haha I like that.
  4. Vince_Ulam

    Vince_Ulam Star commenter

    None. Let them read books. Televisions aren’t allowed under exam conditions and pens are filled with ink, not inspiration.
  5. pipipi

    pipipi New commenter

    Thanks Vince! [​IMG]
    I have really enjoyed the discussion but I'm going to leave now.
    I'll try and get that link of yours to work.
  6. bombaysapphire

    bombaysapphire Star commenter

    If you have Autograph there is an excellent Autograph extras page which shows generating the trig graphs from the unit circle.
  7. Surely it's best to use an ASTC mnemonic as this reflects the route they will take around the memory aide and fits with the way angles in general are measured?
  8. Nazard

    Nazard New commenter

    If you are just using ASTC as a mnemonic that the students won't understand then you may as well use SATC as a mnemonic that the students won't understand. Frankly, if you need the mnemonic you are as likely to want to "read" the unit circle left to right at the top and left to right at the bottom.
    I am really not sure this is worth bothering about, though.
    We were taught 'CAST', but I could never see the point of starting bottom right and working round the circle.

  9. I don't mind how they remember it and actually find that they have no trouble remembering the order at all. 'Sex and the City' has become a nickname they use rather than a mnemonic really. I labour the unit circle and try and make sure they understand this and how to use the acute angle to get the related angles.
  10. I do have Autograph but only one license but we have an excellent animated Geometer's Sketchpad file for unit circle. I've had it that long I don't remember where it came from.
  11. pipipi

    pipipi New commenter

    that unit circle method keeps coming round
  12. Do people use unit circle for teaching basic Trig? It's always something pupils seem to find difficult. I'd be interested to hear other peoples views.
  13. pipipi

    pipipi New commenter

    I don't for basic trig. I do for when it's time to look at sine graph so they get an idea of why it continues past 90.
    For basic trig. I introduce names of sides, and ratios. Then give them a sheet with an angle of 20 degrees drawn on A4, with the horizontal and hypotenuse drawn on. The pupls get to draw on the vertical wherever they like, and then do vertical divided by hyptotenuse and hopefully they notice that wherever they draw the vertical (which i change to opposite) they get the same decimal answer. I might put the mean on the board of their attempts. Try and get the idea that this wil always happen when they draw a right angled triangle with an angle of 20.
    Then some more sheets with 30, 40 etc. Pupils are beginning to see that they different values with different angles.
    Then we look at what the calculator 'says' is sin20 and compare with their value.

    And to be old school. I also use 4figure table here as well. Pupils seem to get a better idea of which way to 'travel' when they are trying to find the angle/side.

    Itry and see if they can remember SOHCAHTOA.Then I show them the 3 triangles for sin cos and tan, which look like the Speed Distance Time triangls which eally helps them rearrange and solve.

    For unit circle. I normally introduce by saying that we check their calculators are working. Sin0, sin 10, sin20 etc. Then when we get to sin90 and I ask what happens next? We keep going up in 10 degrees, writing down the answer. Looking back at their list they can see that sin10 matches with sin170, sin20 with sin160 etc! Then it is time to go beyond that and see we get negative values.
    Then I will get them to plot their points and they get to see the shape of the sine wave. And maybe the last bit is to show them the unit circle, to prove it isn't just a calculator making it up! And it's always nice to fool them with a YOU NIT circle!

  14. If you get them to reconstruct the graphs at the beginning of the next lesson, on their own and in silence, you'll clearly see who's got it and who hasn't. So can they.
    I tend to go through it in one way in class then set them the mymaths for homework with the clear expectation that they are to work at it until they do understand it and that they will be contructing the graphs for themselves next lesson.
    For those who clearly haven't bothered, I'd produce a knife (no not a carving knife) and get them to take a quick peek under their desks, with the clear implication (for them to deduce for themselves) that the chuddy needs to be chipped off. If you don't state it as an explicit threat they're too busy puzzling out what you're on about to start arguing that they won't do it.
    I'd breeze straight on with the lesson.
    I have a wide variety of ways of making the point that they need to do the work properly. I don't usually enforce them (better to come up with a new threat) because in the end you can take a horse to water but to fiddle with him is dodgy.
    Clear expectations.
    Clear consequences in terms of the not getting the maths.
    Clear disapproval if they haven't got it (tailor to the level of laziness).
    A lot of humour.
    Some will always be lazy but a lot wont.
    And if they haven't got it the day before the exam we do ASTC.
  15. pipipi

    pipipi New commenter

    you produce a knife and get them to look under their desks?

    this was risky mnenomics, not risky lessons!
    (but I have the feeling this is just to generate a hurricane)
  16. For teaching trig I have a set of several similar right angled triangles each with an angle of 5 degress; another set with 10 degrees and so on. Each pair gets a different set of triangles.

    In their pairs I get them to measure the side lengths and work out O/A. - they quickly notice that all the triangles in their set give the same answer (near enough) irrespective of how big or small their triangle is.

    Together we draw up what is basically a Tan trig table for the multiples of 5 degrees.

    I have a powerpoint that then has loads of triangles with O and A measurements on - I project and ask the students to work out the marked angle .... the first few are ones from their trig table but quickly move to ones where the answer is, for example, "between 50 and 55 degrees".

    Proceed to discussion about whether I have loads of 51 degree triangles, and 52 degrees etc. and, hey presto, Mr Google finds a trig Tan table for us to use.

    Look at sin and cos in a similar way (not as long winded as they have the idea) so we have 3 trig tables each with only integer angles (someone always asks about decimals and I will project something hideous looking from the web).

    For a few lessons we work solely using these trig tables - mixed up questions with various angles marked as 'to find'; different side lengths given; some 'real life' questions.

    At some point after a lesson or 2 somebody asks whether they are given this table in exams or whether they have to learn it all! At that point I introduce the calculator functions as a time saving device (which is all they are afterall!) - by this point the understanding of why trig works is secure and the step to using a calculator is just a small step.
  17. Vince_Ulam

    Vince_Ulam Star commenter

    You threaten your students with a knife?

  18. Nobody else uses scraping the chuddy off with a CUTLERY knife as a punishment?[​IMG]
    I provide rubber gloves... (weebecka wonders what illustrations are coming next[​IMG])
  19. Vince_Ulam

    Vince_Ulam Star commenter

    No. Do you?
  20. Not these days Vince - chuddy on the bottom of desks isn't a huge problem in HE.

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