title: The philosophy of education; or, The principles and practice of teaching,
text: 12 113 - •jaqDTS8x JO 9UI13^ < o ' ' ' llll '•w^w 41 g il.a §• oS Los «b I X. I P._^| I. It -^ ^llol 1 ^ (3 fc -m 4 1:111 ^O 2- 52 S' a ToS S3 ■COS 5« o bos 'S — S§8 -1 .^,"Ss. 5Sao.d ..X! fl fe 0) ^ .§ c S 1 «B -^-g-a 0^.25 g ^S 5|c£-2.coj^ a fl <D - s ■Wa; S a „ j3 oj ^ >-i °>Ha'*5 a c m oj *3 a Cti-ht;. aj'oi a o SS2 v.B^i^zi ®g??£2ii.&' •2S S-a ft^S a) tja «t-i 2 (p ® S lu. 2|a ^.§^.2 l^-H"! ft( 41 o a^ i^<^ ^'B^. 288 PHILOSOPHY OS" EDUCATION. Part IV, ON THE APPLICATION OF DIFFERENT SYS- TEMS AND METHODS TO THE VARIOUS BRANCHES OF ELEMENTARY EDUCA- TION. The Scriptures, History, etc. — Bible lessons should always be given, in an elementary school, on the collective system of teaching. The following rules may be advantageously observed in giving these lessons : 1 . The passage on which the lesson is given should be read by the class. In the course of the reading, the meaning of the words should be familiarly explained to the children, and the general purport of the lesson should be constantly kept before them. 3. The teacher should picture out the subject-matter of the lesson, after the manner described in connection with the cul- tivation of memory (see p. 202). This will, generally, be best done by the method of ellipses, occasionally varied by individ- ual or collective interrogation. 3. The subject should be elucidated by the method of con- trasts and resemblances (explained in connection with the cul- tivation of the memory, see p. 192). 4. The progress of the class should be tested by the individ- ual method of examination. 5. The duties to be learned from the lesson should be fully explained. This will generally be most efficiently carried out by the method of suggestive interrogation, or by the method of ellipses. 6. Notes of the lesson should be written, with conciseness and distinctness, upon the black-board. Sketch of a Bible Zess6>?z.— Subject : Trial of Abraham's faith. Genesis, chap. 22, verses 1 to 13. Mixed method : interroga- tive, elliptical, illustrative, etc. 1. TJie reading lesson. — Words and phrases to be explained in the course of the reading : The land of Moriah, burnt offer- ing, worship, etc. APPLICATION OF SYSTEMS AND METHODS. 289 2. The picture.— \The words to be supplied by the pupils are printed in italics.] Abraham was a very good man, and had great faith or trust in his Ood : Abraham had one son called Isaac, one darling boy, that he loved more than anything in the icorld : Abraliam was very happy with his son Isaac : * God was about to put Abra- ham's faith and obedience to a very great trial: Let us see how God tried Abraham's faith and obedience. God told Abraham to take his son Isaac to a mountain a great way off, and offer him there for a hurnt-offering. Oh ! what a trial for Abraham's obedience this was, to slay his only son, as he did lambs and calves and rams, upon the altar as a hurnt-offering. But Abra- ham loved and feared Ood so much, that he never doubted for one moment that whatever God commanded him to do would be for his good — he did not even ask why he was to slay his son, because he was sure that God had a good reason for what He required him to do. Abraham then got up early in the morning, and saddled his ass, and took two of the young men with him, and Isaac his son, and cut some wood for a burnt- offering, and started off towards the place where God had told him to go. After they had travelled for three days and three nights, they at last came in siglit of the mountain : Abraham lifted up his eyes and saw the place afar off. And he told his young tnen to stop and take care of the ass, while he and his son w^ent up the monntain. Behold Abraham and his son, as they climb the mountain ! — Isaac carries the heavy burthen of wood for the hurnt-offering, and Abraham carries the fire to kindle the wood, and in his hand is the terrible knife with which he is to slay his only son as an offering to the Lord. How sorrowful Abraham looks !— God has commanded him to offer his son as a burnt-offering. • Isaac seems at a loss to know what h\^ father is about to do with him. When they came to the i)lctA:e which God had told Abraham of, Abraham laid the wood in order, and bound his son and laid him upon the altar. His hand is stretched forth, and he is about to plunge the knife into his son, but the angel of the Lord, arrested the stroke, saying to Abraham out of heaven, " Kow I know that thou fearest God, seeing that thou hast not withheld thy son, thine only son, from Me." 3. Contrasts and Resemhlances. — Contrast Abraham's charac- ter with that of Balaam's or with that of Jonah's. Compare * If the pupils do not fill in the ellipses, the teacher should ask the question, " What was the name o^ Abraham's son?" 19 280 PHILOSOPHY OF EDUCATION. Abraham's readiness to sacrifice his only sou at the command of God, with the great sacrifice which Christ offered up upon the cross for the sins of the world, 4. Examination. — To what land did God command Abraham to go to offer up his son ? Hoav was Isaac to be offered ? For how many days did they travel before they came in sight of the mountain ? Who went with Abraham to the place of sac- rifice ? What did he say to the young men before be left them ? etc., etc. 5. Duties to be learned from the lesson. — When we are sore beset with trials, what should we always do ? However hard our lot in this world may be, our duty is simply to obey God, who always knows what is best for us. If we simply follow the commands of God, however strange they may appear to our corrupt nature. He will find a way of escape for us. God often tries our faith as He did Abraham's of old, by requiring us to perform painful duties ; but we, like Mm, should obey God and leave the results in His hands, knowing that all things will at last work out for the good of them that fear Him. 6. Notes written on the black-board.— God's command to Abraham — given to try his faith ; his journey to Moriah ; Abraham and his son went alone to the place of sacrifice ; the angel of the Lord prevented Abraham from slaying his son ; etc. History and Subjects of General Reading. — History and other subjects of general reading should be taught by the same method as that which we have just described in relation to the teaching of the Scriptures, Reading and Spelling ; Etymology ; Grammar. — These subjects should be taught in our elementary schools upon the collective system of instruction. While one boy reads or spells, the other boys must listen. Important passages should be read simultaneously by the class, and sometimes words should be spelled, letter after letter, in the same manner. In the course of the reading the master will frequently have occasion to correct the pronunciation, indistinct utterance, the accent, and the in- tonations of the pupils. Whenever he does so, he should always endeavor to put his reasons into the form of a general rule. Above all things, the pupils should be taught to read with intelligence. Very young children should be taught to read from large class-cards, having pictures of the leading subjects of each les- son. The look and say plan of teaching to read is certainly the best, especially when it is combined with some of the most striking principles of the phonic method. In like manner the best plan for teaching children to spell is to get them to write APPLICATION OF SYSTEMS AND MICTHODS. 09 ^ out the lessons which they have read : the eye, hi my opinion, is a better guide to correct spelling than the ear. The lessons for teaching little children to read should contain frequent repe- titions of the same word in each lesson. Let us take an ex- ample : S/pecimen of a Reading lesson for little children Tom is a good boy. A good boy does what he is told. I told Tom to be good, John is a bad boy. A bad boy does not do what he is told. And so on. When the child is able to read words of three letters, he should then be taught to read words of four or more letters ; and after words of one syllable he should be taught to read words of two syllables ; and so on. In the course of these reading lessons the intelligent teacher will not fail occasionally to avail himself of some of the most prominent principles of the phonic system of reading. Certain combinations of letters almost invariably represent certain ele- mentary sounds ; as, for example, the sound of ad in bad, lad, sad, mad, etc.; the sound of ay in bay, lay, say, may, etc.; the sound of un in bun, sun, etc. ; the sound of sh in shut, shark, shave, shall, etc.; the sound of cli in child, chide, chick, etc. ; and so on. The ordinary box of reading letters should be used in show- ing the child how the elementary sounds go to form the sound of the word. Thus in showing the sound of the word sha'i^e, the teacher first gives the sound of the letters sh, next that of am, and then putting the letters together he gives the com- pound sound shave. To follow out the phonic system of reading in all its details is neither practicable nor desirable. The fact is this system re- quires the pupils to make analyses of sounds, which we our- selves never do in the practice of reading, The rules of pronun- ciation in our language are so very complicated, that it seems to be almost ridiculous to attempt to teach reading on a strictly phonic plan. By the practice of reading on the look and say system (aided by occasional hints relative to the elementary sounds of the most common combinations of letters), the child gradually and insensibly acquires the pronunciation of words. On the teaching of the alphabet, see page 194. The etymology of technical words and philosophical terms (particularly those that are derived from the Greek and Latin) should be given in connection with reading lessons. But the teacher should Ijenr in mind that the derivation of a technical 29^ PHILOSOPHY OF EDVCATIOK. term does not supersede the necessity of giving the full mean^ ing of the term as it is used in our language ; the chief pur- pose which etymology serves in the elementary school is to aid the pupils in remembering the signification of technical terms. Important words and phrases which occur in the lesson should be written in large characters upon the black-boaid, with their meanings and derivations. Grammar should also be taught in connection with the read- ing lessons. But besides such desultory exercises on Grammar, the definitions and principles should be systematically taught by collective lessons, and by simple text-books upon the subject. Grammar more fully considered. — Grammar may be taught by a constructive method, or by a method of progressive development. A first course of instruction should comprehend all the simple parts of speech without their inflections, etc. ; the particular and most familiar form of each definition should be explained before the general or most abstract form ; and where the definition contains a comprehensive statement, it should be broken down into its component parts, and after each part has been successively explained, their relative connection or dependence should be distinctly pointed out. A second course of grammar should comprehend the inflections of words ; and'a third course that of the analysis of sentences and the rules of syntax and composition. These rules should be based on the analysis of sentences ; for by so doing we follow one of our most certain general prir;ciples of method, viz., that of teaching the concrete before the abstract. We have too much parsing in our schools, and too little of the practice of composi- tion. Teachers should get their pupils to construct sentences as early as possible ; for it should be borne in mind that pars- ing is only a means for the attainment of an end — that is, to enable the pupils to write and speak with accuracy and facility. All our exercises in composition should have some actual ob- ject ; they should express familiar ideas, or describe things and events which actually exist (see page 1 59). The old plan of teaching syntax (that is, by giving bad English to correct under each rule) has not yet been superseded. In grammar, as in many things else, we seem to know what is right by seeing what is wrong ; and we are the better able to follow what is right by constantly endeavoring to avoid what is wrong. A lesson on Orammar. Subject— The noun. Mixed method, interrogation, ellipses, etc. Now, my children, I am going to show you what a noun is. Listen ! A NOUN is the name of an object or thing ; as book, apple, table, etc. ENGLISH GRAMMAR. 203 Hat IS the name of a thing — what kind of word is hat ? Write the following- sentence on your slates : " Pears and ap- ples grow on trees." Now" put a line below all those words which are nouns. A NOUN is the name of an animal ; as dog, cat, horse, etc. Cow is the name of an animal ; therefore the word cow is a noun. And so on to other examples. A NOUN is the name of a person ; as John, Thomas, Milton, etc. Andrew is the name of a 'person ; therefore the word Andrew is a noun. And so on to other examples. A NOUN is the name" of a place ; as London, York, Leeds, etc, Hounslow is the name of a place ; therefore the word Houns- low is a noun. A NOUN is the name of anything which we can speak of as existing ; as chair, whiteness, darkness, etc. I can speak of table as a thing which exists ; therefore^ the word table is a noun. I can speak of the soul as existing ; therefore the word soul is a noun. And so on. Now let us collect together all that has been said about a noun. A NOUN IS THE NAME OF AN OBJECT, AN ANIMAL, A PER- SON, A PLACE, OR ANYTHING W^E CAN SPEAK OF AS EXISTING. Give me as many words as you can think of which are nouns. AVhy is the word book a noun ? Why is the word heaven a noun ? And so on. Put a mark beneath all the nouns in the following sentences : Thomas has got a dog. London is a large city ; etc. A lesson on Grammar. Subject— The adjective. Mixed method. An adjective is a word which points out the quality of a noun ; as large, good, black, etc. I have a sharp knife. Now what word here points out the quality of the knife ? Sharp, then, is an adjective, for it points out or expresses the quality of the knife. He gave me some ' apples. Now a:l the words which I put before the word apples to make sense are adjectives ; find out as many of these as you can. Small, large, round, ripe, unripe, sour, red. siceet, etc. An adjective limits the meaning of a noun ; this, many, fourth, etc. And so on. Now let us collect together all that has been said about an adjective. An adjective is a word v-rich points out the qual- ity OF A NOUN OR LIMITS ITS MEANING. 3§4 PHiLosoriiY Of education. Put a mark beneath all the adjectives in the following sen- tences : A horse is a noble animal. The cow gives fine milk. Why is the word the an adjective ? Why is the word noble an adjective ? And so on to other examples. Lessons on composition and tlw analysis of sentences. 1. To enlarge the subject. Simple sentence— " The dog is ill."* What is the subject of this sentence ? What is the predicate ? Now I shall enlarge the subject of this sentence, that is to say, I shall add something v/hich shall tell us all about the dog. "The dog is ill." 1. The large dog is ill. 2. The dog Pompey is ill, 3. The carrier's dog is ill. 4. The dog of four years old is ill. 0. The dog, b^ing very fat, is ill. And putting all these enlargements of the subject in one sen- tence, we have — The carrier's large dog Pompey, of four years old, heing very fat, is ill. What purpose is served by these enlargements of the sub- ject ? What do they tell us ? First, that the dog is large ; sec- ond, that his name is Pompey ; third, toat he belongs to the carrier ; fourth, that he is four years old ; and fifth, that he is very fat. What kind of word have 1 used to enlarge the sub- ject in No. 1 ? The adjective large. And so on to the others. Enlarge the subject of the following sentence ; first by an ad- jective, second by a noun in apposition ; and so on : " The boy reads." 2. To extend the predicate. Simple sentence—" The bcj reads." The predicate may be extended in the following different ways : ' ' The boy reads. " 1. The boy reads /^/i'rt^. 2. The boy reads /I??' information. (b) The boy reads at home. 3. The boy reads every day. - 4. Tiie boy reads standing. * Here we suppose this to be reallj' a fact. ARITHMETIC. 095 111 (1) tbc predicate is extended by an adcerh ; iu (2) by a pre- position or by a prepositional phrase ; in (3) by a noun in the objective case ; in (4) by a participle used adverbially. if n (1) and (4) we use an adjunct of manner ; in (2) an adjunct of cause ; in (b) an adjunct of place ; in (3) an adjunct of time. Show the different ways in which the predicate in the fol- lowing sentence may be extended : " The boy runs," Point out the subject, predicate, and object of the following sentence : * ' A had boy called Thomson hurt little William very severely." What words enlarge the subject ? What word qualifies the object ? What words extend the predicate ? Obser mt ion. -—FrocQe(\mg in this wa}^ the pupil will be taught the art of composition. But in all this there is compar- atively little knowledge of parsing required. Arithmstic. — All the junior classes in an elementary school should be taught arithmetic on the collective system. The syn- thetic method of demonstration — first explained, at least in this country, in the writer's treatise on the Principles of Arithmetic — is certainly the best adapted for elementary instruction. The suggestive method of interrogation is most generally applicable to the teaching of demonstrative arithmetic. In teaching common or slate arithmetic the following general rules should be observed : 1. All the demonstrations should be given distinctly upon the black-board. 2. The essential data of the question (not the whole question) should be written, in a proper order, on the black-board, es- pecially when the question contains three or more data. 3. The teacher should fully explain every step of the process as he v.-rites it down. It is a bad plan to work out the whole question, and then to proceed with the explanation. 4. The pupils should take ai part in the investigation. The master should require them, time after tim.e, to tell him what quantities he must write down, at the different steps of the in- vestigation. Let us take a few examples of this method of teaching arith- metic. 1, Lesson on the Addition of Fractions. Let it be required to add one half and three fourths together. Here, before we can add these fractions together, we must bring them to the same part of unity, or, to speak more simply, we must bring them to bits of the same size. Let us suppose that we have to find how much the half of a loaf added to the three quarters of a loaf will make, What do I take as the ujiit 296 PHILOSOPHY OF EDUCATION. here ? (Ans, A loaf.) Now, how do we get the half of a loaf ? (Ans. By cutting it into two equal parts.) How do we get the three fourths of the loaf ? (Ans. By cutting the loaf into four equal parts, and taking three of them.) Now, how should you put the half bits into quarter bits ? (Ans. By cutting each half into two equal bits, for then w^e should haAC the whole loaf cut into four equal bits.) Very well. Now, how many fourths will there be in one half ? (Ans. Two fourths.) So that you have to put together, or add, two fourths and three fourths. What will they make ? (Ans. Fivx^ fourths.) But I want you to gire me the sum in mixed numbers. How many w^hole loaves would you have in five quarter loaves ? (Ans. One and a quarter more.) That is to say, the sum of one half and three quarters will be equal to one and a quarter. I am going to show 3 on how to do this question in another way. A, , . 1 J or 1. Let a stick or a line (A B) be divided on the upper side into two equal parts, and the bottom side into four equal parts. What will each of the upper parts be called ? What will eacli of the bottom parts be called V Look at the figure, and tell me how many fourths there are in each half. And so on, as before. The teacher should also do the same thing by the division of a space. 2. A Lesson on Rule of Three. Let it be required to find the cost of 9 books when the cost of a dozen is 8«. \d. Let us first write the essential data of the question on the black-board. DATA. Cost of 12 is 8s. 1 J.— the cost of 9 is required. SOLUTION TO BE WRITTEN ON THE BLACK-BOABD. Cost 12 books = 8s. Id. .-. Cost 36 books - 3 times 8s. Id. = 24s. Sd. 24s. Sd. .•. Cost 9 books = one fourth part of 24s. 3d. — = 6s. 0|cZ. After the teacher has written down the language, "Cost 12 books =" he asks the class, " What shall I put this equal to?" After he has received the answer he fills it in, and then asks, GEOGRAPHY. 297 " Why is it equal to 86'. Id. ?" " How many books have we to find the cost of ?" " Now if we can get the cost of 36 books we may readily get the cost of 9, as you will see when we pro- ceed with the solution." After writing down " Cost 36 books =" he asks, 'Will the cost of 36 books be more or less than the cost of 12 books ?" " Why ?" " You are quite right : three times the number of books will cost three times as much." " Now, having got tlie cost of 36 books, how are we to get the cost of 9 ?" " Exactly so: one fourth the number will of course cost one fourth the price." And so on. The more advanced boys should be sometimes called upon to give a demonstration on the black-board. Mental Arithmetic. — Tiiis subject should be taught on the collective system in connection with the method of interroga- tion. The boys prepared with an answer to the question pro- posed by the master should hold up their hands, and the mas- ter must then cull upon some boy to give the answer ; and so on to the other artifices described in connection with the subject of collective teaching. Young children should be practised for some time in mental calculation before they are taught anything relative to the symbols and notation of numbers. Strokes, counters, balls, etc., should be taken as the representatives of numbers, and all the leading properties and operations of arithmetic should be demoustrated by the use of these objects before any technical modes of calculation are attempted. All the processes should be thoroughly demonstrative, and no rules should be laid down independently of the inv^estigations. All tricks and clap-traps of mental calculation sliould be conscien- tiously avoided. The boy called upon to give the answer should give the process of investigation. Geography. — Geography may be thoroughly taught to large classes on the collective system. The method of suggestive in- terrogation, followed by or accompanied with catechetical ex- amination, seems well adapted for teaching this subject to all classes in an elementary school. No branch of geography should be taught without the aid of a map. Every collective lesson on geography should be given in connection with a large map, which should be suspended directly before the class. When any country, or city, or river, or mountain is spoken of, its place upon the map should be pointed out, and its relative bearings, boundaries, or extent should be fully explained. Physical geography and history should always be taught in connection with descriptive geography. (See p. 201.) If a teacher can sketch well he should draw his own maps upon the black-board. First, tracing the outline of the country, 298 PHILOSOPHY OF EDUCATION. he mentions the various kingdoms or seas wLose boundaries his chalk is tracing ; second, with a few jottings of his chalk he marks out the principal mountain-ranges forming the great ridges or apexes of the water-sheds ; third, he traces the rivers winding their way from their mountain source or sources to the great reservoirs of the waters of the globe. He pauses for a moment to review his work. He has sketched out the works of nature as the hand of the Creator has left them ; now he has to begin to sketch the works of art and civilization — he has to people the wilderness and to trace the progi-essive steps of civi- lization ; upon the banks of the tidal rivers he marks the site of the great mercantile cities; on the shores of the mountain streams he plants the names of the oldest industrial cities ; on the coal-fields he places those mighty manufacturing cities which have almost sprung into existence since the discovery of the steam-engine— that mightiest monarch of civilization and power, which seems to control the destinies of the w^orld ; last of all, he marks the sites of those large towns which form the market-places of the rural population. We said that the work was progressive : exQvy fi-esh touch of the chalk is associated with some new idea, and every fresh idea has its appropriate association with some line or mark upon the board. The sketch goes on ; it becomes more and more finished ; the skeleton be- comes lined with sinews, then clothed Avith flesh and blood ; every fresh step towards completion excites new interest in the minds of the boj^s ; they wonder how a few jottings can call up the idea of a mountain-range, or how a winding line can call up the idea of the course of a spai'kling river, or hoAV the little mark put for the mountain city should av/aken in their imagina- tions the sound of the flip-flap, flap-flip of water-mills and the busy hum of industry ; they wonder, but they know not, that the visible picture which their master has drawn with his chalk would be dull and lifeless without the living moral picture with which it is associated. Such a lesson is complete in its parts and perfect as a whole. Map-drawing is an excellent means of teaching geography. This exercise, as we l)efo)'e obser\ed, should be set^ apart for home lessons. Drawing.— Collective teaching, combined Avith the system of home studies, is best adapted for giving lessons on this impor- tant branch of school education. As this truly useful branch of knoAvledge does not appear to have received that amount of attention in cur schools generally which its utility demands, DRAWING. 299 we shall enter more fully into the details of the method by which it should be taught in our elementary schools. 1. T/ie teaclier should first explain the elements of form. — Draw- ing, like all other branches of instruction, has its simple ele- mentary principles ; these principles should be learned by the pupil before he can be expected to make any satisfactory prog- ress. All drawing must be "based upon a knowledge of the elements of form. Before a boy can draw a line correctly he should know something about the nature of that line. All forms, whether in nature or art, may be reduced to a few geometrical elements. Straight lines should be copied of various lengths and positions, and next in order should follow the various geometri- cal iigurcs formed b}' straight lines. The CIRCLE is the simplest and most perfect of all curved LINES ; it, in fact, forms the standard by which we judge of the relative degree of curvature of the various portions of any other curved line. To draw a circle by the hand requires some skill ; and the acquisition is well deserving the trouble. Curves of contrary flexure, that is, curves whicli arc convex at one part and concave at another, have been called the lines of beauty. Ex- amples relating to the circle, with various curved figures more or less depending upon it, should be given to the pupils. These elements of form constitute the alphabet op draw ING. No satisfactory progress can be made in drawing until the pupil has become thoroughly acquainted with these forms. You may as well attempt to teach a boy to read before he is ac- quainted with his alphabet, as give him an axe, or any such object, to draw before he is made acquainted with the different kinds of lines found in its outline. In this way drawing is made a useful instrument of a higher kind of instruction ; for the pupil is insensibly, and at the same time pleasantly, made acquainted with the names and properties of geometrical figures. Why should the boy, who is supposed to be skilful enough to draw a chair or a looking-glass, remain ignorant of the names of the geometrical elements of form ? A child of five years of age readily learns the names and under- stands the construction of the most useful geometrical figures ; and not only so, but he reallj^ feels a pleasure in learning them. JTow the best way of learning the names and definitions of geometrical figures is actually to draw them. Children fe^l as much pleasure in drawing beautiful geometrical forms as they do in imitating the drawings of natural objects, more especially if they are taught to draw these geometrical forms by method. 300 PHILOSOPHY OF EDUCATION. The teaching of the first facts of geometry ought to be con- sidered as one of the most important ends which is to be attained by an elementary course of drawing lessons. It is not prac- ticable, and indeed it is not desirable if it were practicable, to teach drawing without embracing a certain amount of geomet- rical knowledge. The pleasure of success is the best incentive to the pupil in learning to draw ; but if the exercises are too difficult for him he will give up in despair, believing that he has no genius for drawing. A teacher gives a boy, as a first lesson, a drawing of an Ass to copy: the boy labors earnestly at his task, for he really would like to draw a donkey ; but notwithstanding his repeated efforts, he cannot decidedly say whether his drawing is more like a horse than it is like a donke3^ That boy should first learn the alphabet of drawing— the 'leading elements of forms— before he attempts to copy such difficult pictures. 2. The teacher' should explain the various lines of construction necessary for drawing a figure. — In these lines of construction we bring principles to aid the eye and the hand. The facility and accuracy with which an artist, will copy any drawing de- pends not more upon his skilful command of the pencil, than upon the method which he adopts, unconsciously it may be, in determining the leading points of the outline of the drawing. The figure or model to be drawn should be first examined as a whole, and then the leading points as well as the general out- line of the drawing should be laid down, before any of the mi- nute or subordinate parts are attempted. All beautiful figures have symmetry ; and therefore, in constructing such figures, there may always be found some geometrical forms which will aid us in the construction. The habit of constracting figures in this way, besides serving the end for which it is directly in- tended, tends very much to improve the observing and reason- ing powers of the pupil, ; it insensibly and gradually instils into the young mind a knowledge of geometrical principles, and lays the "foundation of a more demonstrative course of geometry. Let us take a few illustrations. A pupil having to draw an octagon for the first time would scarcely know how to begin it ; but a glance at the teacher's lines of construction should give him the idea of a method which will enable him to draw the figure with facility and precision. Few persons, even amongst artists, can draw a perfect ellipse by the hand ; but by attending to a few simple principles of construction it becomes easy even to a pupil. All points and lines of construction should be drawn faintly DRAWING. 301 in order that they may be readily erased, and that they may be easily distinguished from the real lines of the drawmg. For various illustrations of the methods of construction, the reader may consult the writer's work on Drawing. 3. The teacJier sliould explain tlie manner of using iJis pencil or crayo?i.— The drawing-pencil, or crayon, as the case may be, should be held in the same manner as the common w^'itrng-pcn. In order to give freedom of motion to the hand, the pupil should be accustomed to hold the pencil loosely, with the first two fingers and the thumb at some distance from the point. Every line should be seen as it is being drawn, and, in order to secure this, all lines should be drawn from left to right, and from the top to the bottom of the paper. As a general rule, lines should be first sketched out faintly, and then any inaccuracies can be corrected as the line is being finished off. The beginning and the end of a line should be fixed before the pupil commences to draw it. Certain intermediate points should also be fixed before the whole line is attempted to be drawn. Great precision cannot be expected from young persons at first, nor should they be required to dwell too long upon any particular drawing at this early stage of their instruction ; the patience of a child should never be wwn out by a fastidious regard to what is called accuracy of finish. The fact is, there is a want of flexibility m the muscles of the hand of young children which time and na- ture only can fully remedy. 4 Proper drawing instruments and materials should be provided for the pupils.— "Tha pupils should be provided vdth slates, drawing books or drawing-paper. If slates are used, the ,_ pointed, _ freedom. If crayons are adopted, they should be of different degrees of hardness, and fixed in a port-crayon, one at each end. Some teachers may prefer pen-and-ink drawings ; this mode of drawing is exceedingly useful and convenient for schools; in this case the drawings may be first traced with black-lead pencil, and then afterwards completed with the pen and ink. Each pupil should be provided with a copy of some drawing exercises, so that he may at certain periods go on with his work without the constant supervision of the master. 5. The pupils should then dra w the outlines of familiar objects. - After the pupil has been made acquainted with the leading ele- ments of form, he will find much interest in tracing the outlines of familiar objects. Outline drawings, it will be observed, are not really representations of the objects, for they want the 302 PHILOSOPHY OF EDUCATION. touches of light and shade, as well as some other artistic arti- fices, requisite for forming a true picture. Notwithstanding this, the drawings are sufticiently like the objects which they are intended to represent, so as to interest the child in the resem- blance. The pupil should first copy from the drawing of the object, and then he should have the object itself plticed directly before him to be drawn in outline. The master should carefully explain to his pupils the different geometrical forms to which the various parts of the outline (U'awing may be referred. 6. T/ie teacher should explain tlie method of drawing a fgure on the'blackboard. — The teacher should construct the figure (which his pupils are about to draw) on the black-board, "on an en- larged SCALE. All the lines of construction should be ex- plained by him as he draws them, and all the pupils should go along with him, drawing line after line as their master pro- ceeds with his exposition. After such explanations, the master may leave his pupils for a time to copy the drawing from their sheets with more care and exactness. The impetus which the master thus gives to his class will be sufficient to render it self- acting for the time which he may require to bestow to the other classes in the school. When a model is to be drawn, it should be placed before the pupils in a position similar to that in which it is given in the drawing copy; the master should then show the pupils hoio and why he draws the different lines in his I'cpresentation. There are a few important points upon which children require to be especially guided. In drawing vertical lines, they are ver}^ liable to make the lines lean in the same direction as the lines of ordinary writing. Children should constantly have their at- tention directed to the pi'oportion of the parts of a figure ; as, for example, a line in a drawing may be exactly the same length as another line, or it may be twice or thiice the length. The jTOsition of lines should be carefully noted : as, for example, one line may be perpendicular to another line ; or a line may be drawn exactly between the vertical and the horizontal ; or a line may rise to the left of the horizontal ; and so on. They are very apt to draw a line before its exact position has been realized in their own minds. Children, if left to themsclvec-, will often begin with some unimportant detail, and thus go on drawing without method ; here the master should show the child what lines to begin with, how to get a good general outline, and then how the minute parts should be finished off. 7. The teacher should carefully inspect the work done by the pupils.— Wh\\Q the pupils are at work, the master should move rapidly amongst them, giving hints to some, correcting the DRAUIXG. 308 errors of others, and in all cases showing them how they should do it, rather than actually doing it for them. A few minutes at the close of each lesson should be devoted to the examina- tion of the slates or books of the pupils. The drawings done at home should also be carefully examined by the master. 8. The nmsier should give his pupils drawing copies for home exercises. — Our present systems of elementary education seem to make too little provision for home instruction. Drawing at home is admirably adapted for supplying the place of evening- tasks, Avhich were once given in the form of columns of spell- ings or paragraphs of geography. Drawing is rather an amuse- ment than a task, and children need very little persuasion to induce them to devote some portion of their leisure time to this delightful study. In home studies esi^ecially, children like to show^ some evidence of their application, with the \iew of com- paring the work of one week with that of another. Exercises on drawing, as we have already observed, are well calculated to eifect this end. 9. The more admnced pupils should draw the figures upon an enlarged scale. — Young persons can draw small tigures much more easily than they can draw large ones. Their eye more readily catches the proportions of small figures than of large ones ; and their hand is better able to draw short lines than long ones. Children have a more perfect perception of an object of moderate size than they have of a large object ; the eye takes in all the parts of the object more readily in the former case than in the latter case, and thus a more perfect picture is formed upon the retina. Hence it is in accordance with nature that a young person should first copy moderate-sized drawings, such as those given at page 308 of this book, before he at- tempts to draw upon a large scale. But after he has drawn the figures upon a small scale, he should then draw^ them upon a scale of twice, thrice, or even four times the size. The draw- ing of figures on a large scale gives freedom and power to the hand and precision to the judgment. But, besides this, the drawing of figures on different scales forms one of the most useful lessons in practical mathematics. If a child is required to draw a figure on double the scale of any given figiu-e, he sees that if he takes the base of his drawing double the length of the base of the original figure, then all ti^ parts of his figure will be respectively double the corresponding parts of the ori- ginal figure; and so on to other cases: in this way he will draw a figure of the same form as the original, the only difference between the two figures being that one is drawn upon a larger scale than the other. 