The intelligent reader  of a mathematical book desires
two things: 
     First, to see that the present step of the argument is 
correct.
     Second, to see the purpose of the present step.
     The intelligent listeners to a mathematical lecture has
the same wishes. If he cannot see the present step
of the argument is correct and even suspects that it is
possibly, incorrect, he may protest and ask a question. If
he cannot see any purpose in the present step, nor suspect
any reason for it, he usually cannot even formulate
a clear objection, he does not protest, he is just dismayed
and bored, and loses the thread of the argument.
     The intelligent teacher and the intelligent author of 
textbook should bear these points in mind. To write
and speak correctly is certainly necessary; but it is not
sufficient. A derivation correctly presented in the book
or on the blackboard may be inaccessible and uninstructive,
if the purpose of the successive steps is incomprehsensible,
if the reader or listener cannot understand how
it was humanly possible to find such an argument, if he
is not able to derive any suggestion form the
presentation as to how he could find such an argument by
himself.
    The question and suggestions of our list may be 
useful to the author and to the teacher in emphasising the 
purpose and the motives of his argument.  Particularly
useful in this respect is the question: 
DID YOU USE ALL THE DATA? 
The author or the teacher may show by this question a good reason for
considering the datum that has not been used heretofore.  The
reader or the listener can use the same question in order to
understand the  author's or the teacher's reason fro considering such 
and such an element, and he may feel that, asking this question,
he could have discovered this step of the argument by himself.