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alike difficult, the conclusion is evident, the difficulties must be resolved and thus brought within the reach of their powers of comprehension. This is done by analysis, when skilfully applied.
The Practice of the Method of Analysis is of two kinds: Analysis in preparation, and Analysis in teaching.
1. Analysis in preparation. Complete branches of instruction are mostly analysed ready to the Teacher's hand, such for instance are Arithmetic, Language, Writing, Vocal Music, and Model Drawing. In these and other subjects the Analysis is more or less complete, still there are few examples of an analysis so complete, as to leave nothing for the Teacher to do. In fact, it is hardly possible to do so, as the extent of the decomposition must depend on the grade of children under instruction. The subjects of Vocal Music and Model Drawing are said to be among the best examples of analysis we have for teaching purposes in elementary schools.
The introduction, within these last few years, of what are technically known as Gallery or Collective Lessons, has thrown on the Teacher a necessity for cultivating considerable skill in the preparatory analysis of the subjects to be taught. A few such lessons have been published, but not in sufficient number to offer anything like an opportunity of selection, and if it were so, perhaps it would be a loss rather than a gain, as a Teacher will in every case be better prepared to give a lesson after having provided his own matter, and made his own analytic arrangement. In making a preparatory analysis the Teacher should be careful to arrange the matter logically, that it may not be defaced with “cross divisons.” The more natural the divisions are, the more easily and effectively will the work of teaching be done. Perhaps one of the greatest faults in preparing notes for Collective Teaching is the extreme analysis of the subject, the result of which is the introduction of a number of minute particulars, which tend to embarrass the Teacher, confuse the children, and thoroughly obscure the main points of the lesson. Regard should be had to the time to be devoted to the lesson and the analysis in reference thereto. It will be sufficient barely to mention here that the matter thus analysed and arranged, is given synthetically; how, belongs to the subject of another paper.
2. Analysis in teaching. It would far exceed the limits of these few paragraphs to enter upon the various applications of this method in the practice of teaching. It must suffice, therefore, to give a few remarks to the analysis of a Reading Lesson, preferring to notice this application of it, as being more extensively useful in that form, than in any other.
The necessity for analysis in connexion with the Reading Lesson arises out of the circumstance, that the matter for teaching is a
given subject, presented as a whole, and in a determinate form; hence to get children to have an intelligence of its meaning, it must be decomposed, carrying out the analytic process till the elements are reached, and fairly within the children's comprehension. The value to be attached to the analysis of a reading lesson is of the highest kind; as after school-days are over, the main, almost the only means of further instruction with the majority, will be the book.
How valuable then to have formed in the child the habit of analysing sentences, and looking beyond the symbols for the ideas they profess to convey.
A complete analysis of a Reading Lesson consists of two perfectly distinct courses; the subject-matter of the lesson, and the language in which it is couched.
1. The analysis of the subject-matter. This embraces (a) Interrogation, to learn the condition of the child's mind, as to his knowledge of the subject; to break down difficult ideas, that in their elements they may find a ready entrance; and to ascertain that the idea is really received. (b) Mental composition, the knowledge of the power of individual words; and (c. The substance of the passage re-produced in the children's own words, as a test of the correctness of their conceptions of entire sentences, and to train to facility in expressing their own conceptions.
2. The analysis of the language in which the lesson is couched. This part includes, (a) The grammar; obtaining by analysis, the classification of words with the principal laws which regulate their modifications and their relations. (b) The etymology in which a few of the more important derivatives are taken up individually and decomposed so as to show their roots, prefixes and affixes, their relations to others of the same class, and their exact meaning in the connexion in which they are found in the lesson.
It may be profitable to observe here, that a mere analysis of a reading lesson is but a part of a Teacher's duty; the purpose being to reduce to elements, that in their simplicity they may be readily received. To leave a lesson merely analysed is to leave a subject in fragments, for a knowledge of the meaning of words and sentences does not in any way necessitate a knowledge of the subject as a whole; hence, after an analysis, the whole of the elements require a synthetical reconstruction, a method to be treated of in a separate form.
It may hardly be necessary to say, that the analytic process in ordinary cases is carried on by putting such a series of questions as shall, by carefully graduated steps, break down the whole into its elements, and that in doing so very considerable skill is necessary that the questions may be put in a logical order, otherwise the mind
of the child becomes confused, the link is broken which should connect the steps together, and the farther the process is carried the more confusion ensues, till at last there exists in the child's mind no connexion between the first and last steps in the series. Hence, when an analysis is extensive, care should be taken by brief recapitulations, to keep the successive steps clearly and visibly in the child's understanding in an unbroken connexion.
ON TEACHING TO SPELL. The words of the English language are seldom spelt according to their sounds, and hence arises the apparent necessity of teaching to spell. But whether this necessity be not more apparent than real may admit of question; although the fact that many persons, in other respects well instructed, do not spell correctly may be urged to shew that teaching to spell is essential. Yet this is rather an evidence of the inefficiency of existing modes, than of their necessity. Correct spelling ought to be obtained rather as the result of other studies, than of the dull, irksome, unintellectual custom of committing to memory mere lists of words.
The art of correct spelling is to be attained in just the same way as the art of fluent reading; this is the result of making the child's eye familiar with the words, and the more familiar words are to the eye, the greater, except in cases of physical defect, is the fluency of the reading. If it were necessary to prove this, we might refer to the pause which even the best readers make, when they meet with a word to which their eye has not been accustomed.
Correct spelling is chiefly of value in writing, and its attainment can only be secured by making words as they are written, familiar to the eye; familiarity with written words being as essential to correct spelling, as familiarity with printed words is to fluent reading. Hence to secure it, there should be much practice in writing so that the eye may become familiar with written composition. This, we believe, joined with extensive reading, is the only means of insuring a correct orthography.
Correct orthography may very easily be obtained incidentally, as the result of written abstracts of lessons, or composition on familiar objects; or by directing the attention of the children during the reading lesson to words peculiar in their structure or differing in sound and spelling, and requiring them to be produced, written on their slates, at the close of the lesson.
But the methods adopted must vary with the status of the child.
In the lowest section it is a good plan to take each word of the Reading Lesson, and, as the children spell it, for the Teacher to write it on the black-board, and let them copy it on their slates.
In the middle section, the Reading lesson should be dictated to the children. But instead of submitting the slates to the inspection either of the Teacher or of a Monitor, which is a sacrifice of time as useless as it is unnecessary, we would recommend that after each sentence is written, the children should exchange slates, and proceed to spell each word as it has been written by his neighbour; the mistakes to be indicated by holding out the hand, and the mis-spelt word written on the black-board and copied on the other side of the slate by all the children ; this column of corrected words to be submitted for inspection at the close of the lesson.
In addition to this mode, we find good results in this section from permitting the children to copy from their Reading lesson, thus familiarizing the eye at once with the printed as well as the written form. In the highest section we recommend the pen to be substituted for the pencil, and the book for the slate, as a somewhat extended experience has convinced us that slate-writing, valuable as an introduction, is not sufficient to ensure perfect correctness. In this section abstracts of every lesson should be required.
But while we recommend these methods during the ordinary working of the School, we place more reliance on the Composition exercise developed in the “Suggestive Hints for Secular Instruction," by the Dean of Hereford. The home exercises on this plan when produced each morning in the different classes, are to be submitted to the inspection of the Teachers, and the errors are made the subject of conversation between the Teacher and his children, and subsequently re-produced in their correct form.
ON TEACHING ARITHMETIC.
No. V. In the eighth number we laid down the principle which forms the foundation of almost every rule in fractions—that every fraction is not altered in value when its numerator and denominator are either multiplied or divided by the same quantity. If this principle is understood, the rule of addition and subtraction will be seen to be nothing more than a simple application of it.
I am required to add 5 and together. To do this, I must first ascertain how many fourths are contained in 5, that I may then add them to the 3 fourths expressed by the symbol. Now
5 5 X 4 5
1 x 4 4 by the principle first laid down. Our sum therefore stood thus
23 5 +
The same method must be followed, however many fractions there may be. I must in no case add the numerators (or numberers) together until I have by some means made the denominators (i. e. the fractional parts which require to be numbered) alike.
5 The first being of the same value as ', the sum may be represented 1+1+1. The first object must be to make them all of the same denominator, without, of course, altering their real values. Looking now only at the first two fractions, if I multiply the 3 by the 4 and the 4 by the 3 we shall in each case have 12, and the fractions will stand
3 x 4 4 X 3 but in order to prevent the alteration of the value of the whole fraction in each case, we must multiply the numerator by the same quantity by which we multiplied the denominator and the fractions become
11 (x4) 2 x 2
3 (X 4) 4 x 3 and the original sum stands thus11 (x4) 2 (x 3)
1 44 6
+ + 3 (x4) 4 (x 3) 5 12 12 5 Now before we can add all three fractions together, we must by the same method reduce them all to the same denominator. In other words, we must multiply the denominators of the first two fractions, which are now alike, by the 5, and the 5 by the common denominator of the first two, viz., 3X4. And since we must always multiply the numerator by the same quantity with which we multiply the denominator, the sum stands thus11 (X 4 X 5) 2 (x 3 x 5) 1 (x 3 X4)
60 60 60 60 30 Hence the rule-For the addition of two or more fractions, reduce them first to the same denominators. This may be always done by the above method, though by inspection we may discover a shorter way.
Thus1 1 (x 3)
6 3 The rule for subtraction is precisely the same, the nature of the case requiring us to subtract the numerator of the subtrahend from