Determination, hope, success.  It would be a mistake to 
think that solving problems is a purely "intellectual
affair"; determination and emotions play an important
role. Lukewarm determination and sleepy consent to do
a little something may be enough for a routine problem
in the classroom. But, to solve a serious scientific problem
, will power is needed that can outlast years of toil
and bitter disappointments.
1.   Determination fluctuates with hope and hopeless
hopelessness with satisfaction and disappointment. It is easy to
keep on going when we think that the solution is just
around the corner; but it is hard to persevere when we
do not see any way out of the difficulty. We are elated
when our forecast comes true.  We are depressed when
the way we have followed with some confidence is suddenly
 blocked, and our determination wavers.
     "Il n'est point besoin espe'rer pour entreprendre ni
re'ussir pour pers'v'rer."  "You can undertake without 
hope and persevere without success."  Thus may speak
an inflexible will, or honour and duty, or a nobleman with
a noble cause.  This sort of determination, however
would not do for the scientist, who should have some hope
to start with, and some success to go on.  In scientific
work, it is necessary to apportion wisely determination
to outlook. You do not take up a problem, unless it has
some interest; you settle down to work seriously if the 
problem seems instructive; you throw in your whole
personality if there is great promise.  If your purpose is
set, you stick to it, but you do not make it unnecessarily
difficult for yourself. You do not despise little successes, 
on the contrary, you seek them: If you cannot solve
the proposed problem try to solve first some related
problem
2.  When a student makes really silly blunders or is 
exasperatingly slow, the trouble is almost always the
same; he has no desire at all to solve the problem, even 
no desire to understand it properly, and so he has not 
understood it. Therefore, a teacher wishing seriously to 
help the student should, first of all, stir up his curiosity,
give him some desire to solve the problem. The teacher
should also allow some time to the student to make up
his mind, to settle down to his task.
    Teaching to solve problems is education of the will.
Solving problems which are not too easy for him, the student 
learns to Persevere through unsuccess, to
appreciate small advances, to wait for the essential idea, to 
concentrate with all his might when it appears. If the
student had no opportunity in school to familiarise 
himself with the varying emotions of the struggle for the
solution his mathematical education failed in the most 
vital point.