[Maths-Education] References on "problem solving"

[John Bibby]

References on "problem solving"Dear Hugh

I agree that 'problem-solving' is much misused (over-used?).

There seem to be three contiguous terms:
* problems
* puzzles
*investigations.

Do we need to distinguish between them?

Your description seems to cover all three (tho' maybe 'puzzle' is somewhat
more recreational and non-pedagogic than the others?
>In this context, at least, "problem solving" (a much abused term) means
tackling tasks in mathematics or in practical contexts that:
        are significantly different from those the solver has been taught to
solve, so that
        recall of learnt procedures is not enough, with
        a substantial part of the demand in understanding the problem,
formulating a mathematical approach/model, interpreting and evaluating
solutions, and communicating the results  (and the other things that
investigation involves)
     Season's Greetings, and Best Wishes for '007!

     JOHN BIBBY  aa42/MatheMagic
                   1 Straylands Grove, York YO31 1EB  (01904-330-334)

All statements are on behalf of aa42.com Limited, a company wholly owned by
John Bibby and Shirley Bibby. See www.aa42.com/mathemagic and
www.mathemagic.org

  -----Original Message-----
  From: maths-education-bounces at lists.nottingham.ac.uk
[mailto:maths-education-bounces at lists.nottingham.ac.uk]On Behalf Of
Hugh.Burkhardt at nottingham.ac.uk
  Sent: 24 December 2006 13:06
  To: maths-education at lists.nottingham.ac.uk
  Subject: [Maths-Education] References on "problem solving"


  ZDM are producing a special issue on:
          Problem Solving Around the World - Summing up the State of the Art
  focussing particularly on what has happened since about 1970


  I have agreed to write the piece on work in the UK.
  (I shall include an outline of some earlier work too).


  I would be grateful for references to:
    *  insight-focused research, particularly at school level, on
          the processes of PS
          the teaching and learning of PS skills
    *  PS materials of any kind developed with research-based methods
  Those that arrive soon and/or with the references attached will be
particularly welcome.  Don't be coyabout your own stuff (but show some
restraint!).


  In this context, at least, "problem solving" (a much abused term) means
tackling tasks in mathematics or in practical contexts that:
          are significantly different from those the solver has been taught
to solve, so that
          recall of learnt procedures is not enough, with
          a substantial part of the demand in understanding the problem,
formulating a mathematical approach/model, interpreting and evaluating
solutions, and communicating the results  (and the other things that
investigation involves)


  Your comments are, of course, also welcome.


  As usual, please just reply to me:
          Hugh.Burkhardt at nottingham.ac.uk
  unless you think the whole maillist would thus feel deprived.


  While, in the current UK context, this may seem a nostalgic enterprise, I
hope it will be a useful reminder of what is missing in school maths.


  All the best for '07


  Hugh
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