I have seen the method, attributed to Alan Schoenfeld (below), being
used as a matter of routine for classes equivalent to key stage 4 and
upwards, in a selective school in Leipzig. German black(or white)boards
have vertically hinged, double-sided side boards. Everyone had to try to
start a problem, most on paper, but with two students working on the
backs of the flaps. They then had to turn them and discuss with the
class.
It seemed valuable so I decided to try it out with my next new intake of
GCSE Maths students - repeat GCSE at an FE college. I had two students
working on acetate that they then put on the OHP.
It was too late. They did not like performing in public, especially as
they were in a new class of strangers. Perhaps it would be different if
these techniques were introduced gradually from the age of 13 of 14 in
classes that had been together for some time.
More worrying was that, although they had failed to achieve the grade
they wanted at school, they just wanted to go over everything again in
exactly the same way as the school had done it. At school most had tried
to learn stock solutions for every type of problem rather than seeing
how simple principles could be applied to a variety of problems.
As a marker of A/AS physics papers I found that many schools and
colleges seemed to be adopting the stock answer approach with A level
too. Schools where it appeared that students had been taught to reason,
stood out above the others. Unfortunately the mark schemes often favour
incoherent assemblies of textbook keywords to sound reasoning.

Steve Bolter sbolter@...

-----Original Message-----
From: Andrew Raw [mailto:andrew.raw@...]
Sent: Tuesday 09 December 2003 21:08
To: learning-science-concepts@...
Subject: Re: LSC: All quiet on the learning science front?

I have done quite a bit of work in this area. In one study I observed
some A
level students solving a mechanics problem and classified their problem
solving difficulties using some of the ideas of Reyven Feuerstein. You
can
probably guess the sort of difficulties I found- for example, they did
not
draw diagrams or note down information given, they did not read the
question
carefully, they did not take a planned approach to solving the problem.

I then used some algorithms to help them solve certain types of problem
such
as those involving resolution of forces, or the use of moments or
projectile
problems. The idea is to show them the steps that an expert takes when
solving such problems and so give them a structure (scaffold?) to help
them.
I had some success and think that this approach has some uses, but also
has
problems with it.

Later, I tried to use De Corte's model of a powerful learning
environment to
help students improve their general problem solving. This involved,
amongst
other things, my careful modelling of solutions, stressing various
heuristics such as "read and re- read the question" and "draw a
diagram",
getting students to present solutions and discussing their approaches
and
giving students hints to solving problems.

My students were positive about many of my "techniques" but I found it
difficult to get other solid evidence that the techniques had improved
their
problem solving.

I feel that there are things that a teacher can do to help students'
problem
solving, but that it is difficult to change student behaviour in a short
time.

Eileen Scanlon wrote a paper on A level physicists problem solving and
there
was a lot of work done in the seventies on physics problem solving in
America. where it is still an area of interest . I think that lessons
can
also be learned from the CASE project and from Instrumental Enrichment-
the
programme devised by Feuerstein.

The guru, though, is **Alan Schoenfeld**- who has done a lot of work
about
mathematical problem solving- he really does seem to have improved
problem
solving in his students. His techniques, which involve university maths
students doing work up at the board and having detailed discussions
about
their thinking when solving a problem simply did not work in a sixth
form
college where I found students to be very unhappy about standing up in
front
of a class and not really interested in discussing problem solving
techniques.

If anyone would like to know more, or just would like some references,
or if
they have done any work that they woud like to share, then please get in
contact- "off list" if appropriate.

Best wishes to you all out there- have a good rest over Christmas,

Andy Raw
Holy Cross College,
Bury




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