He was not taught that the lesser of the two numbers was always to be subtracted from the larger; for in order to apply that principle he would have had to decide for himself which was the larger of the two numbers, and the consequent mental effort was one which his teacher could not trust him to make.

It is true that in his desire to save the child from the dire necessity of thinking, the teacher ran the risk of being discomfited by a sudden change of procedure on the part of an inspector.

The inspector, for example, who, having been accustomed to say "From 95 take 57," chose to say, for a change, "Take 57 from 95," would cause widespread havoc in the first two or three schools that were the victims of his unlooked-for experiment.

But the risks which the teacher ran who taught his pupils to rely on trickery rather than thought were worth running; for the inspectors, like the teachers and the children, were ever tending to become creatures of routine, and the vagaries of those who had the reputation of being tiresomely versatile could be provided against--largely, if not wholly--by increased ingenuity on the part of the teacher, and increased attention to tricky by-rules on the part of the child.
The number of schools in which arithmetic is intelligently and even practically taught is undoubtedly much larger than it was in the days of payment by results; but there are still thousands of schools in which obedience to the rule for its own sake is the basis of all instruction in arithmetic.

Now to live habitually by rule instead of by thought is necessarily fatal, in every field of action, to the development of that _sense_ or perceptive faculty, on which right action ultimately depends.