DEVELOPING QUANTITATIVE SKILLS
Professor Raymond Hoobler
Developing quantitative skills in a physics course is surprisingly similar
to developing quantitative skills in a psychology course; only the level
is different. The key, just as with writing, is practice, practice, and
more practice, then, just as with writing, evaluating the ideas. In quantitative
terms, this means drill and estimation.
What can we do in the classroom? Drill may have acquired some negative
overtones, but in my experience nothing beats doing relevant and interesting
quantitative problems for improving quantitative skills. Start early in
the course if you need some quantitative skills for, say, a discussion of
statistical tests. Plan for some "reminders" about basic arithmetic
skills. This does not mean spending thirty minutes a class period for a
month, but it might mean:
- bringing in a calculator to do some problems, carefully writing down
each step (student notes are notoriously unreliable), and then assigning
similar problems that you check for a week or two beforehand
- making up a few simple quantitative problems relevant to your subject
and having students work them in groups as you go around to help and
observe them; having several students work them on the blackboard is
an alternative.
It is important that you see individual students' work, since that is the
only way you can accurately judge the level of their skills and what kinds
of errors they make. You should remember that human beings seem automatically
to desire order and so often will "learn" a quantitative procedure
which is incorrect. Do not automatically do the problem for the student
- ask them to do it for you instead and you may find a procedural error.
For instance, we read from left to right but 5-3(7+4) is -28, not 22!
I think the single most important quantitative skill is estimation. Is
an answer reasonable? Does the answer, whatever it is, have to be positive?
Or less than 100? These are questions that you should always raise when
doing an example. The point, after all, is not the number at the end of
the process, but rather what that number tells you. Students are
usually just happy to get an answer, any answer, to a quantitative problem
and so rarely develop the habit of trying that answer out in the real world.
Of course, part of the problem is that they don't get problems that model
actual events, but since calculators are now ubiquitous, that should change.
Note that skill in estimating is particularly important with calculators
since one of the numbers might have been entered incorrectly by accident
or the calculator mode might have been incorrect.
Finally, there are some psychological observations worth making. Do not
judge quantitative skill by language skill. An ESL student may be quite
competent quantitatively and do well in sophisticated quantitative courses
long before they can succeed in World Humanities. Students should not do
quantitative work without using pencil and paper. If they come for help,
get them to start by writing down and doing some part of the problem.
If we show fear of quantitative work, students will learn fear of quantitative
work. Teach the hard part of quantitative material, don't leave it as an
assignment for the student to do.
Professor Raymond Hoobler
Department of Mathematics
NAC Building, Room R6/203B
(212) 650-5155