Diagnosis is used here as a technical term in education 
meaning "closer characterisation of the student's work."
A great characterises the student's work but somewhat
crudely.  The teacher, wishing to improve the student's 
work, needs a closer characterisation of good and bad
points as the physician, wishing to improve the patient's
health, needs a diagnosis.
    We are here particularity concerned with the student
efficiency in solving problems. How can we characterise
it?  We may derive some profit from the distinction of the 
four phases of the solution. In fact, the behaviour of the 
students in the various phases is quite characteristic.
    Incomplete understanding of the problem owing to 
lack of concentration, is perhaps the most widespread
deficiency in solving problems.  With respect to devising a
plan and obtaining a general idea of the solution two 
opposite faults are frequent. Some students rush into
calculations and constructions without any plan or general
idea; others wait clumsily for some idea to come and 
cannot do anything that would accelerate its coming. In
Carrying out the plan the most frequent fault is
carelessness, the lack of patience in checking each step. Failure to 
check the result a at all is very frequent; the student is
glad to get an answer, throws down his pencil, and is not
shocked by the most unlikely results.
     The teacher, having made a careful diagnosis of a fault
of this kind, has some chance to cure it by insisting on 
certain questions of the list.