In case anyone is interested, I placed the description of an exam
question on my web space that deals with space-time diagrams. The
question allows me to see in a hurry if the students understand what
they're doing or not.
The question asks them to complete a space-time diagram with two events,
A and B, such that A occurs before B for one observer, but after B for
the other observer.
Although I have gone over this in class, I am sad to report that I
generally find only 30% to 50% of my students can do this correctly on
the final exam. They either never caught on in the first place, or they
forgot. Either of these depresses me because generally I make a big
deal out of reading times and positions correctly from a space-time
diagram.
I thank John Denker for pointing out the wording "contours of constant
value" and also pointing out that this problem is not confined to
space-time diagrams. Indeed, most of my students in this class have
already taken thermodynamics and are familiar with isothermal lines and
adiabatic lines on PV diagrams. The next time I teach this course I
will put more emphasis on "contours of constant value," and I will point
out other types of graphs or diagrams where this sort of thing happens.
Hopefully I will have better success.
Here is the link to what I typically get from students compared to what
I expected to get when I ask the space-time diagram question mentioned
above...