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Developing problem solving skills in the new GCSE

Discussion in 'Mathematics' started by jad518nexus, May 17, 2016.

  1. jad518nexus

    jad518nexus New commenter

    With the introduction of the new GCSE there is an increased emphasis on problem solving. Looking at specimens and practise papers, as well as new textbooks there are plenty of problems where pupils have to choose an appropriate technique to solve the problem.

    The issue I have with teaching Mathematics with an increased amount of problem solving is how to get pupils to actually try to solve difficult problems and improve their skill set in this higher level skill. Generally most pupils can be taught a procedural skill, but for them to solve a problem which isn't explicitly asking for this skill is far more difficult. I am also referring more to a UKMT style of problem, and not simply those worded problems where it is more obvious which maths is required. (Such as written calculation worded problems).

    Are there any hints or tips that you can share? How is your school implementing the new GCSE with an increased emphasis on problem solving?
     
  2. Vince_Ulam

    Vince_Ulam Star commenter

    1. How do get your students to try problems? The same way you get them to try anything: Tell them it's required in examination so they had best get to grips with the idea or have an awful sitting and poor result.
    2. How to improve their problem-solving skills? There is no trick to it. Problems are problems and need to be read, inspected and understood in the light of the syllabus. First thing's first, they need to know the instruments and facts, and then, problems in hand, practise, practise, practise all the way. If your students learn the facts and practise with the instruments then the schema will embed and with that fluency the structure of problems just pop off the page and smack a big wet one right onto their brains.If you want something tangible to guide you then you may wish to consider something like these, published in 2015 for Foundation & Higher and explicitly focussed upon A02 & A03:

    [​IMG] [​IMG]


    Each problem has a direct curriculum reference and are graded either Accessible, Intermediate or Challenging.

    Should you wish something which discusses problem-solving as an abstract skill, then there's old Mr. Polya:


    [​IMG]

    It's a useful little manual but really of more use for KS5 and up than KS4 for whom my earlier advice is sufficient.

    Good luck.
     
  3. Bensusan

    Bensusan New commenter

    Do a google search for Dan Meyer for an interesting approach to engaging pupils in problem solving.
     
  4. Vince_Ulam

    Vince_Ulam Star commenter

    The headache thing? It's awful.
     
  5. Vince_Ulam

    Vince_Ulam Star commenter

    While we're on the subject of problems, I like to have several books knocking around for idle hours and just enjoy them for their own sake or to adapt individual problems for students. The name who appears most frequently among these books is Martin Gardner. Here is one of my favourites:


    [​IMG]

    Always useful during invigilation.
     
  6. Bensusan

    Bensusan New commenter

    No, not the headache thing. The real-world problem solving thing. The "lets get out of the habit of structuring our problem solving in such a way that all the pupils have to do is fill in the blanks" thing. Real problem solving, not problem solving to get marks.
     
  7. Geoff Thomas

    Geoff Thomas Star commenter

  8. Vince_Ulam

    Vince_Ulam Star commenter

    I've seen Meyer's TED example. Students still need to fill in the blanks, he's just pushing for more blanks and promoting frustration as a means of engagement. It won't work on an everyday basis.
     
  9. Vince_Ulam

    Vince_Ulam Star commenter

  10. Geoff Thomas

    Geoff Thomas Star commenter

    I think it was Polya in my day - four decades or so ago.

    But doesn't matter in this case where it originated so much as whether it is useful.
     
  11. Bensusan

    Bensusan New commenter

    Nothing works on an everyday basis. Even he says that he only used this approach once a week, reinforcing with more traditional approaches and other problem solving activities. Worthwhile digging a little deeper rather than dismissing out of hand. TED talks are short and need to catch the audience's imagination. As such, there's only so much depth he can go into. There are other, longer videos with more explanation of how he incorporates this approach into his planning. There are also articles and examples on his blog.
     
  12. Vince_Ulam

    Vince_Ulam Star commenter

    If you can recommend any online materials for my review then please do, thanks, but I am not in favour of anxiety as a teaching strategy, especially in maths.
     
  13. Bensusan

    Bensusan New commenter

    Just Google his name and start reading. There's loads out there. It's not about anxiety as a teaching strategy but about engagement, enjoyment and relevance.
     
  14. Vince_Ulam

    Vince_Ulam Star commenter

    In a lot of his material, Meyer is scornful of chasing engagement, enjoyment and relevance.

    I don't see anything novel in his advice to strip surface detail from problems, this is just mathematics. His general message seems to be 'I did this thing for six years', he doesn't discuss outcomes or evidence at all. The only outcome of which we know is that after six years he stopped teaching. That may be the takeaway message.
     
  15. Bensusan

    Bensusan New commenter

    No, there's nothing novel in this approach to problem solving. But you don't see it being used much in class and as such he does well to draw attention to it.
     
  16. Vince_Ulam

    Vince_Ulam Star commenter

    It's used in classes every day, everywhere. As I said, it's just mathematics.
     
  17. Bensusan

    Bensusan New commenter

    Then it's a useful resource for the OP to check out, as I initially suggested.
     
  18. Vince_Ulam

    Vince_Ulam Star commenter

    What is a useful resource? All you said was:

    Google is the resource? Youtube videos of Dan Meyer?
     
  19. Bensusan

    Bensusan New commenter

    Dan Meyer is the resource. :rolleyes:
     
  20. Vince_Ulam

    Vince_Ulam Star commenter

    He'd take up a lot of space in the cupboard.
     

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