Consider the notions of "show your work" and "check your work"
and the intersection between them.
It is important to design the work to make it easy to check.
For example, in the introductory class, all-too-often students
will write down unlabeled numbers
2
3
4
24
when they really should be writing sentences or equations:
L = length = 2 m
W = width = 3 m
H = height = 4 m
V = volume = L W H
= 24 m^3
I tell students:
Rationale for labeling the numbers: This is partly so that you can go
back and check your work ... and partly so that other folks can check
your work.
Rationale for making the work checkable: Some day you won’t be doing
trivial busywork calculations. Some day you will be doing something
important, where a mistake could cost millions of dollars and/or put
people’s lives at risk. Important work obviously needs to be checked.
Therefore you should get in the habit of making your work easy to check.
To put it bluntly, if you cannot be trusted to check your work and to
make it easily checkable by others, you won’t get hired to do anything
important.
This is one of the reasons why standardized multiple-guess tests and
clickers are the enemy of critical thinking: Only the final answer
is scored, so there is no incentive for making the intermediate steps
checkable. (Arguably there is an /indirect/ incentive for double-
checking the result, because it improves the odds of getting the right
answer ... but one major reason for grades in the first place is that
students at this level do not respond well to indirect incentives.
They need more direct, immediate feedback.)
Also note that the architecture of a multiple-guess test rewards
taking a slap-dash approach to many problems. IMHO we urgently need
a different approach, something that rewards taking a meticulous
approach to important problems.
One small step in the right direction is to arrange the scoring
scheme on every quiz such that if the problem is worth ten points,
six points are for getting the numerically-correct answer, two
points are for showing the work leading up to the answer, and two
points are for double-checking the answer and showing that work as
well.
I assume lots of people on this list already do this.
Comments? Refinements? Caveats????