perplexity vanishes, and he knows that he has mastered the problem.
It is true that the pupil, while doing his sum incorrectly, may (and frequently does) think he has done it correctly, but he is not sure; his perplexity is still there, and if he is an earnest and apt pupil, he will recognize his own error when it is pointed out by the teacher. So in life, men may think they are living rightly while they are continuing, through ignorance, to live wrongly; but the presence of doubt, perplexity, and unhappiness are sure indications that the right way has not yet been found.
There are foolish and careless pupils who would like to pass a sum as correct before they have acquired a true knowledge of figures, but the eye and skill of the teacher quickly detect and expose the fallacy. So in life there can be no
