[Maths-Education] The resource for the course
Hugh.Burkhardt@nottingham.ac.uk
Hugh.Burkhardt@nottingham.ac.uk
Wed, 19 Sep 2001 08:14:03 -0700
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I see some key points in this 'conversation':
* Most teachers prefer predictable questions in high-stakes exams,
for understandable reasons.
* Flexibility and adapability are important aspects of doing
mathematics (indeed most things) well -- we need Thinkers not
Automata (which can now be bought cheaply, putting human automata out
of work) Assessing these requires non-routine questions. The
balance of "transfer distances" is a subject for legitimate debate,
but all 'zero-transfer' seems hardly defendable in terms of the
declared goals of education.
* Thus there should be an ongoing tension 'task-designers v
teachers', seeking to 'maintain v minimise' non-routine-ness. This
is healthy. It leads to teaching that pays attention to higher-level
skills and metacognition.
* Non-routine assessment tasks do not have to be more difficult than
routine ones -- the balance of 'load', between strategic and
technical/conceptual aspects is different. Such tasks do demand more
design skill, and time, than simply tweaking questions from the past
few years papers. In particular:
* Getting the level of challenge right requires trialling and
revision of the tasks, sometimes through several iterations. (Hence
the opportunities for KS tests; they are not always taken)
* Trialling is not within the official methodology of GCSE or A
level (though some senior examiners have told me they do it, "of
course") The members of monitoring committees have to 'estimate' how
students will respond to questions; their sense of responsibility
naturally makes them unwilling to 'risk' unfamiliar tasks. Should
such trialling be introduced into these most important examinations?
I think so**.
(It is ironic that the most important exams have the least design
effort. KS test: =A310^6
A level/GCSE: =A310^3)
* If the test is broad and balanced, so will be the "The resource
for the course". WYTIWYG There are excellent materials about that
help teachers prepare their students for tackling non-routine
problems. We believe that it is the responsibility of QCA + OCR/AQA/
=2E.... to ensure that their exams are such that "teaching to the test"
leads teachers to deliver a curriculum that matches the declared
goals for learning (which are usually broad and balanced)
Most recognise that there is still some way to go!
Hugh
MARS: Mathematics Assessment Resource Service
** A few years ago, I suggested to SEAC (was it?) that in each main
subject all exam groups should include about 25% of "common
questions", commissioned and then selected by SEAC on a competitive
basis with criteria of imaginative design and systematic development.
These tasks would serve to provide:
* an "engine for improvement" (in the sense of this discussion)
* evidence on comparability of standards across groups
which would reduce the need for SEAC to micromanage the groups' work.
A fairly positive response did not lead to change.
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--></style><title>Re: [Maths-Education] The resource for the
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<div>I see some key points in this 'conversation':</div>
<div><br></div>
<div>* Most teachers prefer predictable questions in high-stakes
exams, for understandable reasons.</div>
<div><br></div>
<div>* Flexibility and adapability are important aspects of
doing mathematics (indeed most things) well -- we need Thinkers not
Automata (which can now be bought cheaply, putting human automata out
of work) Assessing these requires non-routine questions.
The balance of "transfer distances" is a subject for
legitimate debate, but all 'zero-transfer' seems hardly defendable in
terms of the declared goals of education.</div>
<div><br></div>
<div>* Thus there should be an ongoing tension 'task-designers v
teachers', seeking to 'maintain v minimise' non-routine-ness.
This is healthy. It leads to teaching that pays attention to
higher-level skills and metacognition.</div>
<div><br></div>
<div>* Non-routine assessment tasks do not have to be more
difficult than routine ones -- the balance of 'load', between
strategic and technical/conceptual aspects is different. Such
tasks do demand more design skill, and time, than simply tweaking
questions from the past few years papers. In particular:</div>
<div><br></div>
<div>* Getting the level of challenge right requires trialling
and revision of the tasks, sometimes through several iterations.
(Hence the opportunities for KS tests; they are not always
taken)</div>
<div><br></div>
<div>* Trialling is not within the official methodology of GCSE
or A level (though some senior examiners have told me they do it,
"of course") The members of monitoring committees have
to 'estimate' how students will respond to questions; their sense of
responsibility naturally makes them unwilling to 'risk' unfamiliar
tasks. Should such trialling be introduced into these most
important examinations? I think so**.</div>
<div><br></div>
<div>(It is ironic that the most important exams have the least design
effort. KS test: =A310^6</div>
<div>A level/GCSE: =A310^3)</div>
<div><br></div>
<div>* If the test is broad and balanced, so will be the
"The resource for the course". WYTIWYG There are
excellent materials about that help teachers prepare their students
for tackling non-routine problems. We believe that it is the
responsibility of QCA + OCR/AQA/ ..... to ensure that their
exams are such that "teaching to the test" leads teachers to
deliver a curriculum that matches the declared goals for learning
(which<i> are</i> usually broad and balanced)</div>
<div><br></div>
<div>Most recognise that there is still some way to go!</div>
<div><br></div>
<div>Hugh</div>
<div>MARS: Mathematics Assessment Resource Service</div>
<div><br></div>
<div><br></div>
<div>** A few years ago, I suggested to SEAC (was it?)
that in each main subject all exam groups should include about 25% of
"common questions", commissioned and then selected by SEAC
on a competitive basis with criteria of imaginative design and
systematic development. These tasks would serve to
provide:</div>
<div><x-tab> </x-tab>*
an "engine for improvement" (in the sense of this
discussion)</div>
<div><x-tab> </x-tab>*
evidence on comparability of standards across groups</div>
<div>which would reduce the need for SEAC to micromanage the groups'
work.</div>
<div><br></div>
<div>A fairly positive response did not lead to change.</div>
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