visit to the school in question, but he has seen it before, he will not only have acquired some knowledge of the capacity and industry of this particular teacher, in a previous part of his course of apprenticeship, but will also have some notion whether the school is one in which the training of pupil-teachers is so intelligently and carefully superintended, that he may feel justified in giving such a special recommendation. But if this is his first visit to the school he will remember that there is no part of his work as an inspector which is more important than this duty of thoroughly testing the fifth-year pupil-teacher. He will grudge no sacrifice of time for the purpose of doing this properly. And whatever other part of the inspection he finds it requisite to cut short for want of time, he will not hurry over this. He may learn much of the capacity and qualifications of such a teacher, by requiring him to assist him in the examination of some of the classes in geography, grammar, and history, or in any other subjects besides the elements which are taught in the school, and looking carefully over his note-book of the lessons which he has given in the course of the year. If the pupil-teacher has not been properly trained to give collective lessons on such subjects, carefully to prepare such lessons beforehand, and to make notes of such preparation with the help and under the superintendence of the principal teacher, or if he displays, in giving his lesson, any of those gross faults of which I have spoken, in treating of the teaching of the younger pupil-teachers, and thus shows that he has not been properly trained even in the rudiments of his profession, it is scarcely necessary to say that the inspector will absolutely

refuse to give such special recommendation, and will speak very seriously to the principal teacher on the subject at the end of the day.

32. Teaching of Arithmetic. Importance of Discipline. Having heard the teaching of the fifthyear pupil-teacher, and either satisfied himself as to his fitness for being recommended for a provisional certificate, or made due preparation for so satisfying himself at a later period of his inspection or examination of the school, the inspector will proceed to take the arithmetic lesson of the fourth-year pupilteacher (see § 20). And there are a few observations and suggestions which I desire to make in this place, before proceeding to treat of the course taken by the inspector in his inspection of this lesson, upon the general question of the teaching of arithmetic in elementary schools.

The successful teaching of arithmetic in a public elementary school for boys is eminently a question of order and discipline. In girls' schools the unsatisfactory results in arithmetic are probably due as much to defects of knowledge of the subject_on the part of the teacher, as to defects of order. But in boys' schools this is not the case. Our certificated masters have always been, within their range, good arithmeticians, and well qualified as a class both to teach the subject to their scholars, and to train their pupil-teachers to teach it. And if the results of their teaching have been in many schools unsatisfactory, the fault has been due as much to want of discipline as to anything else. And the discipline, it must be remembered, which is sufficient for teaching reading or writing, or any other subject, is not sufficient for the teaching of arithmetic. No serious mischief is done in a writing lesson by one

of the scholars overlooking the work of another. And the evil produced by undetected prompting in a reading or geography lesson, though it is, of course, real and serious, is trifling by comparison with the harm produced by undetected copying and prompting in arithmetic. It happens also unfortunately that copying and prompting are particularly easy, and therefore specially difficult to detect, in arithmetic. One glance, or one whispered word, will often do the mischief. And teachers and examiners are always apt to underrate the powers of children in carrying on these practices so as to avoid detection. In testing how far a class has mastered the instruction which it has received in a new rule of arithmetic, or in reviewing a class in back-work, or in conducting any examination in arithmetic, it is not sufficient to place the children a few yards apart from one another, or to give different sums to alternate children, or (unless there is ample space for spreading the children out so as to leave every alternate row of desks vacant) even to give different sums to every third child. Children who are lazy, and anxious to avoid the trouble of thinking, or who have been inattentive during a lesson, and are anxious to avoid being detected and blamed for such inattention, or who have been accustomed to copy, and are therefore not self-reliant, can exercise an ingenuity which is perfectly marvellous in obtaining help at such a pinch from their fellow scholars. No one who has not experience of schools would believe how far they can see, and how rapidly take in, the mode of working a sum pursued, or the result obtained, by their more clever or diligent class-fellows.

33. Effects of Want of Discipline in Teaching

Arithmetic. And the effects of this copying are as disastrous in arithmetic as its practice is easy. The way in which the evil works is this. A new process in arithmetic is taught to a class of children. The diligent and clever members of the class have taken it in quickly, while the slower or less attentive members have obtained a less thorough, or perhaps a very slight grasp of the subject. The teacher proceeds, by setting examples to be worked, to test how far his instruction has taken hold of the class. At once the temptation presents itself to those slower or careless members of the class to copy from their quicker class-fellows. And, unless the teacher detects the attempt, he may be so far deceived as to think that the whole, or almost all, of the class have mastered what he has been endeavouring to teach them, and may therefore conclude that it is safe for him to pass on to the next stage in his instruction. The further he proceeds in this course, the more helpless and dependent become the children who have taken to copying, and the more necessary is it for them to persevere and become adepts in that deceptive practice, until at last the school is visited by an examiner, who takes such precautions as make it impossible for the children to copy, and then there comes a break-down which astonishes the teacher as much as the examiner and the managers. The reason why, after the introduction of the Revised Code, so many boys' schools failed in arithmetic, was, mainly, that copying had been much more general than was suspected. The schools do much better in this subject now than they did on the first introduction of the Revised Code. Yet the teachers are no better trained in it,

the same.

and their methods of teaching are very much But the payment by results, and those results being tested by inspectors, who adopt measures which render copying impossible, have forced the teachers to adopt similar measures; and the effect has been a general improvement in the arithmetical acquirements of the scholars.

It is

34. How to Stop Copying in Teaching Arithmetic. There is only one way of making sure that copying in arithmetic is not practised in a school, and that is to make it impossible. absurd to talk as if copying could be stopped by appeals to the children's honour, or by punishment of those who are detected in the practice. The sense of honour in children, in an elementary school, cannot be expected to be greater than that of Eton boys, or undergraduates, or candidates for the Civil and Military Services, and for Holy Orders. The code of honour of the examinee is naturally a different one from that of the examiner ; and what examinees at the public schools and universities will freely do, unless prevented, children in elementary schools will do. As for punishment, idle or slow boys will run the risk of it. Detection is not certain, but the trouble of having to apply the mind to a difficult question is most certain. So that the only real way to stop copying in a school is to make it impossible. Pupil-teachers who have charge of the lower classes should always be trained in simple mechanical methods of giving from three to six different examples at once, so as to make it impossible for their scholars to copy; and they should be required to use such mechanical methods with their classes whenever they are