In the International Baccalaureate system, in which there are external
exams, the use of graphing calculators (and QWERTY keyboard
calculators) is not allowed in the science exams. At the time I was Chief
Examiner, I did not agree with this, but the chemists (especially) had
grave reservations about graphing calculators because (apparently)
students could store chemical formulas in them.
It wouldn't really help all that much in physics. During my tenure as
Chief Examiner most of the questions were of the conceptual type, and
there were even some questions that asked studenst to explain formulas
that they had already been given on an accompanying (clean) formula
booklet (that also contained some physical data). Our objectives were to
assess conceptual understanding, and we had a range of difficulty embedded
in each question - simple knowledge recall all the way to synthesis and
evaluation. Of course, there was also a calculation or two at one stage
or another, because that _is_ a part of physics (and we did take into
account significant figures, and units were required or the answer was
incorrect). Very few points were allocated to the use of the calculator,
as compared with equation manipulation and conceptual reasoning.
One other section that we had on the exam was a compulsory data-based
question, in which some physical situation was described, such as an
experiment, data were given, an expected relationship between some
variables was described, and then some tasks were given. This included
completing a data table, including some transformations (such as doing a
square, or inverse), and including uncertainties (just for end-points
usually, to check that students could do it, but not to overly burden
their time with these detailed calculations), plotting a graph (linear,
semi-log, and even log-log. Then students were asked to estimate various
parameters from the expected relationship (they were not told how) and
even to make judgements about data points (are they outliers, or not).
Often, at the end of the question there was a little zinger that might ask
them to explain some feature or quirk in the data (such as a non-zero
intercept) from a physical perspective.
A reason for including this on the examination was to ensure that such
skills were, in fact, being covered in the curriculum.
Now, calculators were allowed, but any student that did a quick regression
without thinking would have included an outlier that was a bad data point,
and their fit and parameters would be wrong. Graphing calculators may
have helped as a check on a mis-plot. In fact, I don't have a huge problem
with the use of calculators. It's easy to create questions that
don't require them, and others, in which skills with these tools may be
assessed. After all, more and more in the practice of science today data
are recorded by logging software and manipulated by software anyway. Our
task, as educators, is to create learning experiences in which we give
students exposure to the merits of efficient, appropriate, meaningful,
exploratory and directed analytical, and (finally) critical uses of these
technologies.
Having said all this, the IB is having some difficulty coming to grips
with the issues, not so much of whether or not calculators should be used,
but of how to specify generic machines that would not give any group of
students who have a "cadillac" version a special advantage. Remember that
the exams are taken by students all around the world. The mathematicians
have declard that graphing calculators _must_ be used in their exams and
they have had to create "calculator neutral" questions.
I'm hoping that the IB can manage to come up with something that _will_
allow the use of graphing calcualtors in sciences, maybe even require
them. One option that we considered for the new syllabus (but which did
not squeeze through because teachers voted for more popular options) was
one on "numerical physics", in which numerical methods themselves could be
used to investigate not only the physics that the students learned in the
core materials, but go on to explore things quantitatively that are
mathematically intractable for students at that level (or just plain hard
for anyone). In that case, some very interesting things could be done,
and the more capable programmable/graphing calculators would be a
necessity.