a list of topics, they agreed that if they were to write the story of his life they must speak first of his birthplace and parents, then of his boyhood. school, occupation, poems, and death. For a language lesson soon they will write it out. “John said as little as any one, but he listened attentively; and as he passed out I noticed that he stopped at the desk to look more closely at the water-color sketch of a bunch of geutians I had brought in for the afternoon." “John's best is not equal to Marion's or Willie's, and we must not forget that it is unjust to compare child with child, but the work of each pupil with that done before and with what he is capable of doing;" adding, as they took different streets, in that firm, low tone of approval which Miss Barton had rather hear than volumes of praise from a casual visitor, “You have lifted that boy, if but for a moment, to a higher level. Just so you can help to bring out the best in them all, if you can reach each. How you can do that no teacher, no book on pedagogy, can tell you. Ways will come to you through an intelligent, loving, sympathetic study of your children." awkwardness, or confusion, though the usual gymnastic signal of "One, two, three, begin," was wanting. In their places they followed their teacher through a long series of varied movements, gentle, rhythmic, graceful, in harmony with the soft music that accompanied them. Every muscle was stretched and relaxed, yet every movement was easy and natural; every motion showed a gentleness and grace that told of well-trained strength. They ran, they walked, they went to their seats in the hippity hop" fashion that children love. They passed before Dr. Lee in line and gave her easy, courteous greeting. They made gestures of giving, receiving, throwing away; of fear and of gladness; of welcome and repulsion; and these needed no interpreter. In all was plainly seen the fact that somehow their physical selves had been so trained that they rendered willing obedience to the power dwelling within. They had learned to give expression to the higher nature, to do its bidding. "But how?" I asked. "By having every movement taught in harmony with law; by having graceful, rhythmic movements repeated before the pupils till they see the grace; by having these imitated till they feel the grace; by arousing noble feeling and then giving its natural gesture expression; by THE DELSARTE SYSTEM OF GYMNASTICS IN awakening noble feeling and calling for its expression, re THE PUBLIC SCHOOLS. BY SARAH L. ARNOLD. joicing if a dozen different gestures are given, each true to the sentiment; by shaking the stiff and awkward out of the body and substituting the easy and attractive; by E have talked of the broad meaning of the word "Ed-making the body and soul free." ucation," the harmonious development of all the powers of the child, intellectual, moral, and physical, and have agreed that this full development is necessary to complete living. But have we not as teachers tacitly consented to attempt the training of the first two, leaving the physical culture largely to happen as it will? Have we realized that the growing intellect, the developing moral and spiritual natures need for a home a body recognized and cared for as the temple of God? Has the physical training in our schools taught our children to feel this truth? These questions have been clamoring for an answer in my thought since a Friday, not long past, when I had the pleasure of witnessing some of the work done by Dr. Mary V. Lee, who has had charge of the classes in Physical Culture in the Oswego Normal and Training School. I was present at one of the class exercises in the lange, well-fitted gymnasium in the Normal School Building. The sixty young ladies and gentlemen had had forty or fifty lessons during the school year. "But how will you do all this?" I pursued. "I cannot tell you in five minutes. Come to my suinmer classes and I will show you." The primary classes from the Training School, directed by a pupil of Dr. Lee's, showed me that this system proves as great a success with the children as with the older pupils. They walked with ease and grace. They were proud of their growing chests and obedient muscles. They gathered for Dr. Lee imaginary flowers, growing on the gymnasium floor, with such truthfulness that the room seemed a real wood, and they among the flowers and ferns. Then with glad, graceful gestures of giving, and faces that spoke their feeling, they brought them to her. They held up their hands to catch imaginary apples which she tossed them; and they caught them, too. They lived the thing they acted, and their souls shone through their faces and spoke in every attitude. Is not such physical training what our schools need? It will do away with the narrow chests, stooping shoulders, and awkward movements too common in our schoolrooms, and at the same time teach the children how their bodies may express, rather than stifle, the soul within them. And with such training the mind and soul will grow in harmony with their dwelling-place. NUMBERS AT SIGHT. the desk, ready for use. A piece of paper, 4x6 inehes, is given each child, and is placed on the desk thus: UPT. MORROW, of Allegheny, handled a class in the lowest grade of the primary school admirably in testing their knowledge of numbers at sight. There were little sticks upon the table, and he arranged them in vari-gether with the left hand, ous ways, thus : The pupils take the edge of the paper nearest them and turn it toward the teacher till it touches the edge nearest her. The edges are held to while the right presses the paper school. Is there a story in your book? No? I have a story in my book of a little boy and girl who went up the hill. Up came the hands, and,-" I know that story, Miss Tell me the name of the boy and girl; what they were carrying. and where going. Can we make a bucket out of clay? To. morrow we will try. There is now no lack of original composition, and our drawing lesson has now become one of language. He multiplied these tests to make sure that they knew them at sight. He would have the class close their eyes every time while he arranged them, and then as they opened their eyes they would tell as nearly instantly as we could determine just the number. The phases of the exercise were the closing of the eyes, and the arrange morning we found the hen-coop blown ment of the sticks, blocks, etc. LESSONS IN CUTTING. BY ABBIE M. WHITE, Providence, R. I. HE scissors asked for a month ago are now properly marked and ready for use. How did we get them ? In various ways. In the first place asked the children if they wanted to cut,-of course they did,then we would furnish paper if they would bring scissors; this seemed a very satisfactory arrangement to both parties, till word came from mamma that she was afraid the little five-year-old would get injured carrying the scissors to school. We were on hand with paper, and armed against objections: Tell mamma to put a cork on the end of the scissors, or give you five cents and we will furnish you with a pair. Some principals levied a tax of five cents on each child in the building (4, 6, or 8 rooms); they then invested the amount in fifteencent scissors (a little lower rate at wholesale), enough to supply th largest room. These are the property of the school, and do not require tagging. The class entering school next fall will be taxed at the same rate, which sum will defray the expense of sharpening. By this method no time is wasted in getting the scissors from home, none in reading the names for distribution, and no one is working with poor tools. O her teachers had the children bring five cents,-the price of iron scissors; each room acts independently, and the scissors are the property of the pupils, but are not tagged. When the children bring scissors from home, all shapes and kinds may be expected. The best way to tag these is to write the name in ink on light colored leather, three inches long. Cut a slit in one end, put the tag through the handle, and draw the end of the leather through the slit. Time, an important facter in school work, is gained if the scissors belonging to each row are kept by themselves, either in boxes, on cardboard, or in bundles fastened with rubber 44444 bands. When distrib uted, they are kept We will now turn our book over on the desk, thus, and think about the stories. We now have a tent, the roof of a house, a hen-coop, etc. We all heard the wind last night. This down. We will some day make a new one, Children flower, etc. We can see the shadow of the ship in the water. the pupil is folded over to the center and very interesting one. The Mayflower is going to China, we will say, and we must send off the goods we make,-those that the people of China will want to buy. As the Mayflower is towed down the harbor by a tug, the house is one in which the goods were stored, and the letter is from the captain describing the passage to China, the delight of his children seeing the “ships of the Desert," flying-fish, sharks, junks, sampans, customs and costumes of different nationalities, and ends by asking us to telegraph him (can we ?) what to bring back. If the children do not seem familiar with all the passengers of the Mayflower have seen, suggest books of travel for home reading. How can mucilage be used? and don't the children daub themselves and everything they touch? To the last question, No. We will take the paper remaining on the desk and fold the short edges together and cut in two as before. We make a square from each piece, and put them together to make a star. The pupils then watch the teacher while she puts a little mucilage in the middle of one square, places the other square upon it, and holds till dry. They wish to do the same, so they hold one of the squares on the desk while the teacher passes up the aisles with bottle and brush, giving to each square a little mucilage, when the children proceed to place the second square on the first and hold them in place till dry, as they have seen the teacher do. in my practice as a teacher that pupils taught by this method acquire skill in working with numbers far superior to that gained by pupils taught in the old way." (The old way he refers to here is the one in use now, which, however, was, at the time, taught in that purely mechanical way that is best characterized by the following little anecdote: A teacher who asked one of his pupils: Why did you do it this way? received this reply: Because it gives the answer!) As to the use of the lines and spaces Risen explains: "The first and lowest line means units; the one above it, tens: the next, hundreds; the next, thousands, etc.; the one above always having ten times the value of the one directly below. And every space equals one half the value of the line directly above that space." etc. 1000000 500000 100000 50000 10000 5000 1000 500 100 50 Tens. Fives. Units. Thus: THE FOUR FUNDAMENTAL RULES IN THE 16TH CENTURY. BY FRANK KARBAUM. P to the sixteenth century the Roman Notation was used in European countries almost exclusively. Then a change took place in Germany. The man that brought about this change was Adam Risen. Adam Risen, generally called Risen von Staffelstein, on the supposition that he was born at Staffelstein, was born at Zwoenitz, Saxony. This place being in a mining district, his first vocation was that of a miner. Afterward, however, he took to mathematics, in the history of which his name has found a most honorable place. For it was he that introduced the Arabic Notation, as we have it to-day, based on the two principles that: 1. Ten units of any order in a number make one unit of the next higher order; and that, 2. When any order of units in a number is vacant, the place is filled with a cipher. This alone would suffice to secure Risen a place in history; but he has done considerably more. He has written books on mathematics which were quite a means of diffusing mathematical knowledge. Among these, the one Risen published in the year 1525 at Erfurt, Germany, is of most interest to teachers, as it contains instructions pertaining to the teaching and learning of the four fundamental rules of arithmetic, by which he tries to do away with an "old way" of teaching these operations, and which are so original and unique, that they are well worth the time devoted to their study. Before explaining his "method" let me state that Risen distinguished not four but six fundamental rules of arithmetic. Besides addition, subtraction, multiplication, and division he has what he terms "mediation and duplication," the former of these meaning multiplication by 2, the latter division by 2. The following is what might be called "Risen's method": Risen uses lines and spaces in teaching the four fundamental rules, partly as a means of demonstration, partly as an aid to the memory and partly as a means of performing the operations. Regarding the merits of his "method" he says: "I have found Instead of slate and pencil, the pupil required what was called a counting-board and a number of counting-pennies or buttons. After finishing numeration the pupil had to learn that a button or penny on the lowest line stands for one; in the lowest space, for 5; on the second line, for 10; in the second space, for 50); on the third line, for 100; in the third space, for 500; on the fourth line, for 1000; in the fourth space, for 5000; etc. Then practice in representing numbers on the counting-board set in, and finally the four rules were taught. The rule Risen gives for addition is: "And note, that when on any line you get five buttons, pick them up and put one in the next space above; but when in any space you get two buttons, pick them up and put one on the next line above." Fig. 2 illustrates an example in addition. Example: What is the sum of 761 +8135 + 408 ? FIGURE 1. 761 + 8135 + 408 These numbers, expressed in figures, were not on the countingboard. Pupils knew nothing of figures at that stage of school life. Explanation: The parts were reduced to counting-buttons and arranged in columns, so that no line contained more than four and no space more than one. (See Fig. I., II., III.) Then the child found how many units there were by counting them. In this case 3 in III, 1 in I. = 4, to be put down on first line of IV. Next, = = 8 100 s 5's. 1 in III., 1 in II. = 2 5's=110. To be put down on 10's line of IV. 10's. 1 in IV., 3 in 1I., 1 in l. = 5 10's = 1 50. Take of the 1 10 and put 1 in 50s space of IV. 50's. in IV., 1 in I. = 2 50's. 1 100. To be put down in IV. 100's. 1 in IV, 4 in III., 1 in II, 2 in I.. 1 500 (to be put in 500's space of IV.) and 3 100s (to be put in 100's line of IV). 500's. 1 in IV., 1 in I. = 2 500's 1 1000. To be put on 1000 s line in IV. 1,000's. 1 in IV, 3 in II. = 4 1,000's. To be put on 1,000's line in IV. 5,000's. 1 in II. = = 15,000. Put down in IV. The 5 in the minuend was reduced. To get 5's, reduce a 10 =25s. Less 15 = 15. One 10 was reduced, leaves 3 10s. Less 2 10's=1 10. 2 100's from 3 100s = 1 100's. Remainder: 1 100, 1 10, 1 5, and 2 1's =117, which is gallons. Risen also tells his pupils how to prove their work. He says: 'If you would prove the correctness of your work, add the subtra hend to the remainder. If the amount is equal to the minuend, 66 It is yet to be mentioned that the pennies or buttons were picked your work is correct." up as they were counted. From the preceding it will be readily seen how subtraction was done. Risen's rule is: "Put the number from which you mean to subtract on the board. and the other number some distance from it. If you cannot subtract, reduce one, the upper buttons, to lower terms. Fig. 3 illustrates multiplication : 24 X 386. I. 10000 If it 5000 is on a line, take it up and put one in the next space below and five on the next line below. (One on a line two in the space below; reducing one of these still further 5 on the next line below.) But if it is in a space, pick it up and put five on the next lower line. And note, if it should happen that you are to subtract quarts and pin's where you have none, you reduce gallons to quarts and in the same way quarts to pints, and then take away what is to be subtracted." (Risen does not name gallons, quarts, and pints, but floren. groschen, and pfenning, which means money used in those days. In giving the rule in English, I have chosen the terms gallons, quarts, and pints, that American readers nught the better understand the rule.) After the rule Risen gives an example: "Some one owes me 396 fl ren, 8 groschen, and 7 pfenning; has 279 floren, 16 groschen, and 9 pfenning. How much is due to me yet?" Fig. 2 shows the solution of a similar example. 396 gallons, 3 quarts, 1 pint, less 279 gallons, 2 quarts. FIGURE 2. 7,720=1 5,000, 2 1 000's B. 386 X 4. = 200= 1 500, 2 100's, 2 10's ible by 12, hence 50's space remains vacant. 5 50s = 25 10 s, plus 2 10's = 27 10's, divided by 12 2 10's, with a remainder of 3 10's. 310's reduced = 6 5 s, plus 1 5 7 5's; no divisible by 12. Reduced 35 1's, plus 11 = 36 1's, divided by 12 3 1's. = Maine. 1. Lay off the width of Maine on the 45th parallel (4 times the measure). 2. Connect with the southern angle of New Hampshire. 3. From the middle of the 45th parallel in Maine raise a line equal to the longest line of New Hampshire. 4. Connect with the 45th parallel where New Hampshire is separated from Vermont ( measure from the eastern boundary of New Hampshire). 5. Bisect this line. 6. Draw the eastern boundary line of Maine. (An indefinite line opposite the centre of the most eastern division of the 45th parallel in Maine) Quotient: 1 100, 2 10's, 3 1's €123. Considering the merits of Risen's method, I think that though it is for the greater part purely mechanical, yet it must be conceded that the analyzing and synthetizing of the numbers, which were required of the pupils, afforded a valuable means of mental training, and were, for the time, a very good pr paratory course for the work with written numbers (which in Risen's book follows the work before described), teaching (1) Arabic Notation; (2) the four [six[setts, (1 measure on the 73d meridian south from Vermont repre1. Complete a rectangle, which is the general shape of Massachufundamental rules with numbers expressed by figures. Risen's method was used till about the year 1700, when it was crowded out of the schools by a book published by Peschek, who was born 1676. Peschek's is the doubtful honor of reviving, by means of his book. that " go-as-you-are-started " way of teaching numbers which, for a number of years, was the only one used; which was almost the only one used even in Germany as late as 1800; and which is not quite obsolete yet. Massachusetts, Rhode Island, and Connecticut. sents the width of the western part of Massachusetts, 50 miles). measure). 3. Place a point for Cape Ann, (measure east of 2. Extend the southern boundary of Massachusetts to the west (% the northeastern angle of Massachusetts). 4. Place a point for Boston Harbor. (Bisect the eastern side of the rectangle.) 5. Place a point for Cape Cod, (1 measure east of the southeastern angle of Massachusetts). 6. Place a point for the southeastern part of Rhode Island, (34 measure south of the southern angle of Massachusetts). 7. Place a point for the southwestern corner of To illustrate Peschek's "go-as-you-are-started" way, I now give Connecticut. (Place point on the 73d meridian, 14 measures below an extract from his book. "Example.-If a man gets $25 on Monday and $35 on Tuesday; how many dollars does he get both days? Put it down like this: 25 35 60 dollars. Explanation: Say: 5 and 5 are 10. Put down the O below the 5, and keep the 1. Then say, The 1 that was kept and 3 and 2 = = 6. Put down below 3." Happily, this dead weight of mechanism has been lifted off by Pestalozzi's imperative Base all your instruction on intuition!" For, ever since the time of Pestalozzi good methods for teaching Arithmetic bave been issued in Germany, among which the one of Grübe, published 1842, has found its way to American teachers. And the last ten years especially have brought out most valuable handbooks for "Teaching Arithmetic." But, on studying all or more than one of them, one finds: 1. That " Imany ways lead to Rome"; and 2, That it is yet to be decided which is the best! MAP DRAWING. BY L. DE SENANCOUR. NEW ENGLAND STATES. Construction Lines. Vermont and New Hampshire. 1. Draw a line to represent the 45th parallel of north latitude. 2. Lay off a portion of this line to represent the northern boundary of Vermont, plus the width of the northern part of New Hampshire. 3. Bisect this line, and one division will be the unit of measure for the rest of the map It represents the width of the rectangle of Massachusetts, 50 miles. 4. From the end of the northern boundary of Vermont draw a line that will pass through the western part of Vermont, Massachusetts, and Connecticut. This line repres nts the 73d meridian. 5. Lay off the length of Vermont on this line (3 times the measure). 6. Complete a rectangle, which is the general shape of Vermont and New Hampshire. 7. Place a point for the head of Lake Champlain ( measure opposite the second point from the north, on the 73d meridian). 8. Extend the southern boundary of Vermont to the west (measure). 9. Extend the eastern boundary of New Hampshire to the north ( measure. Massachusetts, and a point 1 measure west of it, which will be the one required.) Partly erase for drawing map. II. Outline of States. Vermont and New Hampshire. 1. Draw Lake Champlain and describe it. 2. Draw the Richelieu River and describe it. 3. Complete the western boundary of Vermont. 4. Draw the boundary line between Vermont, New eighteen miles of sea-coast for New Hamp-hire. 6. Draw the Hampshire, and Massachusetts. 5. Draw a line representing Salmon Falls River, and descr.be it. 7. Complete the eastern boundary of New Hampshire. 8. Draw the northern boundary of New Hampshire, to the 45th parallel. 9. Draw the 45th parallel and describe it. Maine. 1. Draw the northwestern boundary of Maine, which partly separates it from Canada. 2. Draw the St. John River, which forms the northern boundary of Maine, etc. 3. Draw the northeastern boundary of Maine, which separates it from New Brunswick. 4 Complete tl e eastern boundary of Maine to the Atlantic coast. 5. Draw Passamaquoddy Bay, Machias Bay, Frenchman's Bay, Penobscot Bay, mouth of Kennebec River, Casco Bay to coast of New Hampshire. Massachusetts, Rhode Island, and Connecti ut. 1. Passing the coast of New Hampshire draw Cape Ann, mouth of Merrimac River, Massachusetts Bay, Boston Harbor, Cape Cod Bay, Buzzard's Bay, Narragansett Bay, southern coast of Rhode Island, month of Connecticut River, mouth of Housatonic River, to southwestern corner of Connecticut, and continue the coast-line of Long Island Sound westward. 2. Complete the western boundary of Connecticut and Massachusetts. 3 Draw the boundary between Connecticut, Rhode Island, and Massachusetts. boundary between Rhode Island, and Connecticut. III. Surface. 4. Draw the 1. Rivers belonging to St. Lawrence System. |