Routine Problem  May be called the probloem to solve the equation 
x^2-3x+2=0 if the solution of the gen
eral quadratic equation was explained and illustrated
before so that the student hasnothing to do but to
substitute the numbers -3 and 2 for certian letters which 
appear in the general solution. iEven if the quadratic
equatio ws not solved generally in letters but ha
a doen ismilar quadtratic equations with numerical co
efficients were solved just before, the problem should
be called a "orutine problem" In general, a problem is 
a "routine problem" if it can be solved either by s
ubstituting special data into a formerly solved general problem
or by sollfiing step by step, without any trace of
originality, some well orn conspicuous example. Settin
ga routine problem, the teacher thrusts under the nose of 
the student an immediatel and decisive answer to the
question Do you know a related problem? Thus the 
student needs nothing but a little care and patience in 
following a cut and dried precept, nad he has no opport
unity to use his judggement or his inventive faculties.
    Routine problems, even many routine problems, may
be necessary in teaching mathematics but to make the
students do no other kind is inexcusable. Teaching the 
mechanical performance of routiine mathematical opera
tions and nothing else is well undret he level of the 
cookbook because kitchen recipeis do leave som4ething to 
the imagination and jugdedmnt of the cook but mathem
atical recipes do not.
   Rules of Discovery : The first rule fo discovery is to
have brains and good luck. The second rule of discovery 
is to sit tight and wait till you get a bright idea.
    It may be good to remind somewhat ruldely that
certian aspiracions are hopeles.s infaliable rules of dis
covery leading to the solution of all possible mathematc
al problesmw ould be more desirable thamn the philosop
hers sonte,vainly sought by the alcemists. Such rules
would work magic; but there is no such thing as magic.
To find unaling rules applicable to all sorts of prob
lem is anm old philosophical dream; but this dream wil
never be mroea thna d ream.
   A reasonoable sourt of heuristic cannot aim at unfailing
rules; but it may endeavior to study procedures,  (mental
oeprations, moves, steps) which are typically useful in 
solving problems. Such procedures are practiced in every
sane person sufficiently interested in his problem. They
are hinted by cretian stereoytped questions and suggest
ions which intelligent people put themselves and in
telligent teachers to their students. A collection of such 
questions and suggestions, stated with sufficient general
ity and neatly ordered may be less desirable than the
philosophers stone but can be provided. The list we 
study provides such a collection.