This is a timely thread for me since I have been thinking of this issue
lately.
My solution is to give an exam which does not ask for numerical
solutions. Calculators which can't do algebra are of no value.
E.g., a recent test question was: A flea can jump vertically to a
height h. (a) What is the initial velocity of the flea? (b) Now assume
the same flea jumps at an angle <theta> w.r.t. the horizontal. What is
the maximum range the flea can jump?
Another question was: A ball can be thrown to a height h. What is the
speed of the ball when it is at a height h/2?
Sometimes I will pose questions in the "Show that" format: Show that the
speed of the ball at h/2 is v0/sqrt2.
Such questions require an algebraic solution and calculators don't
help. I tell my students that they may bring a calculator, but it
cannot be programmable, and even if it were programmable it probably
won't help them since I will be asking for symbolic answers. I have a
small class (<20) students, so policing a calculator rule would probably
not be a problem. If I saw a student peering at his calculator a lot, I
suppose I would wander over to see what's up.
I also pose "semi-quantitative" conceptual questions. E.g., a ball
starting from rest rolls down an incline plane a distance D in the first
second. How far does it roll in the next second? (Ans. 3D)
I tell my students that I'm not particularly interested in whether they
can "plug and chug." And that even if plug and chug were important, the
student needs to learn how to algegraically derive the equation to be
chugged. Some students respond that they don't know when the symbolic
equation is correct. I reply that that's why I use "Show that"
problems.
I also point out that symbolic equation can be quickly and easily
tested. E.g., a falling mass (m1) is connected by a string to another
mass (m2) resting on a frictionless horizontal surface. What is the
tension (T) in the string? The answer is T=m1*m2*g/(m1+m2). Does this
answer make sense? Well, if m1=0 kg, then T=0 N. That makes sense. If
m2=0 kg, then T=0 N. That makes sense, too. The arithmetic can be done
quickly and in my head. My answer might yet be wrong, but for m1=m2=0
kg it makes sense, so I have confidence in my solution. Now, if m1=1.5
kg and m2=2.7 kg, then it's very simple though more time consuming to
show from the symbolic solution that T=9.46 N, but does that answer make
sense? I think it's much harder to tell.
I'd appreciate hearing from others, especially your opinions regarding
symbolic answers.
Thanks.
Glenn A. Carlson, P.E.
St. Charles County CC
St. Peters, MO