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Never Taught Proof

Discussion in 'Mathematics' started by Piranha, Oct 26, 2011.

  1. Piranha

    Piranha Star commenter

  2. One nice way to start I have found is with odd and even numbers
    Eg three consecutive odds are always divisible by 3 And any three consectutive numbers are divisible by 3
    First experiment with numbers and then use 2n, 2n+1, 2n+2, 2n+3, etc
    They can then pose their own number theories and try to prove they are always true
    It's great fun
    You can throw in if they find a pattern with primes they will win a $1,000,000
     
  3. I think as long as they know that even numbers are 2n, odd numbers are 2n-1, and how to express consecutive numbers and consecutive even and odd numbers, and have the basics of geometric proof (every time you do a calculation, write down what angle fact(s) is/are telling you you can do that sum), you're fine for GCSE?
    Though I am going to look at those resources too!
     
  4. DM

    DM New commenter

    Think you need to add congruency to your list rusty.
     
  5. Thanks folks, just wanted to check that I wasn't missing out on anything. I think I will work on the consecutive number bits and bobs first and leave the Geometry for next year.
     
  6. Oh yes - thanks.
    So is that exhaustive now, then?
    We are with Edexcel, so there's no proof needed at A-Level, but I did a course recently based on the OCR course that I think sees proof as central to one's mathematical understanding. I certainly don't feel as strong on it as I'd need to be if we switched away from Edexcel.
     
  7. Wasn't aware of that - Proof features explicitly in C1 and C3 with MEI, and also in C4 proof is a key feature of many Section B questions. It's something that definitely gets easier with practice, as with anything. If you want to cement your own understanding, I would definitely recommend working through the MEP unit on Proof, and then work through the relevant exercises in C1 and C3 of the MEI A-level books if you have access to them.
     
  8. And how would you prove the triangle POSTULATE?
     
  9. DM

    DM New commenter

    To be fair various National Curriculum documents have made direct reference to students being taught such a "proof".
     
  10. is this a reference to angles of a triangle relying on the dodgy old 5th postulate?
    surely it doesn't make the angles in a triangle a postulate in itself - it's still a derived conclusion
     
  11. sorry - i take that back - i see they're equivalent, not derived. oh it's a long time since i did geometric proof
    am curioous as to why this is so - anyone point mein the direction of something readable on the subject?
     
  12. True.

    The parallel postulate and the triangle postulate are equivalent.
     
  13. er - i just said that
     
  14. I know. I got interrupted in the middle of my post. By the time I finished it.....Sorry about that.
     

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