AN OUTLINE OF ARITHMETIC LEARNING—(1) ADELIA R. HORNBROOK State Normal Training School, Sar Jose, California T is a fact well-known to those who have studied the development of the mathematical sense of little children that in the case of the ordinary child the desire to count and to deal with numbers in various other ways appears at an early age, usually from four to six, sometimes earlier. When this desire of the child is gratified in a natural way there comes to him many clear perceptions of number relations and much pleasure in them. In this way interest is generated and the child moves on by force of its minor urge. To prevent this early desire for number knowledge from being deadened by unsuitable instruction, and to broaden and deepen the pupil's interest by relating arithmetic to many other interesting things in his life, is one of the aims of the work all through the grades. For instance, in the early years, when play is the child's leading activity, a system of organized number play is used. Again, in the higher grades, when the pupils begin to be alive to the economic side of life, they are set to studying the more obvious phases of the actual business and industrial life of the community and to making their own calculations upon the data which they obtain. All through the grades of the Training School the ideal is that of many groups of interested workers; each group advancing according to the ability of its members all working happily, accurately, without hurry and without worry or humiliation; all the pupils gradually mastering the "minimum essentials" of arithmetic, while many whose tastes incline that way, make extended excursions into the subject. It is evident that the real advancement of each pupil in a class in arithmetic depends upon his power of comprehension of the facts presented to him, and that this involves a series of insights which come to him from time to time. This is purely a personal matter with the child and the ways and the times in which these insights come to different children vary greatly. For instance, after the children in the first grade have played with numbers for several months, using number charts. and various kinds of apparatus in occupations, plays and simple games, but with no direct teaching some of them suddenly show ability to realize many numbers and to discover and report the relations of these numbers to one another. There seems to be a sudden opening of the mind, as it were, "an uprush of the subconsciousness," the number sense of the child becomes active, he thinks about numbers accurately, clearly, eagerly. Montessori refers to the same mental phenomenon when she speaks of her children bursting into writing. Students of child psychology report that the same kind of sudden mental action sometimes appears in children learning to talk. While some children, after a period of number play, in which many subconscious acquisitions of number facts are made, come suddenly into a realization of these facts, others learn them gradually and slowly. These are greatly helped for a time by the activities of those whose minds are more alert. But soon it becomes advisable to place the most successful learners in a group by themselves, and the least successful in a separate group, other groups being between. The working plans of the school facilitate this arrangement. Each grade is divided into groups of from ten to eighteen children, each group reciting in a separate classroom under the tuition of a student teacher who teaches only one subject during a term of twelve weeks. At the beginning of each term the department teacher of the grade, who has general charge of the children and their student teachers, divides the grade into sections on the basis of the children's attainments. Besides her own observation of the pupils' work, she has the reports of the supervisors of the respective subjects taught in her grade and those of the student teachers. This sectioning is not done for promotion purposes. The regular promotions take place at the end of each semester. The sectioning of the grades is done to prevent the quick children from being hindered by the mental action of those of their mates who have slower (but not necessarily inferior) minds and to prevent the slow pupils from being bewildered or discouraged by the mental action of the quick. No hint of inferiority or superiority in the work of any of the groups is given to the children. It is considered that a child who is naturally slow or has inferior brain power ought not to be humiliated, but helped. When a group of such children is placed under the care of an alert and sympathetic teacher, who waits patiently for their development and assists them in many bright and happy ways, it frequently happens that some members of the group get the needed insights and become able to advance at the normal rate. At the end of the term of twelve weeks, these children are quietly transferred to a group working more rapidly. On the other hand transfers are often made in the opposite direction. It would be absurd to expect a child to work upon a subject for several years with an unbroken flow of interest. Illness, absence from any cause, and especially the lagging of the spirit which accompanies rapid physical growth, all interrupt the pupil's work. When a child comes to one of these periods of temporary disability, the situation is frankly met, and he is placed in a slower group without discredit. Under these plans when a pupil fails in arithmetic only, it is not necesasry for him to be left over in his grade. Usually he can be suitably cared for in the least advanced section of his class. If, however, his general work is such that it is best for him to repeat it, he is placed in the most advanced section of the class which has overtaken him. No home work in arithmetic is given. We strongly urge parents not to teach their children nor allow them to be taught out of school and the more judicious of them refrain from this pernicious practice. It often happens, however, that children become so interested in arithmetic that they involuntarily work upon it at home, some of them carrying it so far that the supervisor of arithmetic feels obliged to forbid them to take their books home except by special permission. Our ideal pupil is not a nervous, bespectacled, und-r sized worker, fired with the ambition to excel all others, but a vigorous, happy child developing naturally. 5 15 25 35 45 55 65 75 85 95 color, secured by 6 16 26 36 46 56 66 76 86 96 77 87 8 18 28 38 48 58 68 78 88 the use of colored crayons. A désk chart written on Manila paper is supplied to each 98 pupil. After the 97 first the desk 99 charts are made by the children. 100 This chart is Each student teacher takes up the work at the point at which her predecessor has left it. After reviewing until she has a basis for new work she carries the pupils on in the course laid out by the supervisor of arithmetic. She is judged upon her success in securing clear thinking and accurate work from her pupils, not upon the point of advancement reached by them. One of the pressing facts of addition and subtraction and of the multiplication duties of the supervisor of arithmetic is that of preventing young teachers from going rapid and premature instruction and drill which lead to arrested development on the part of learners. These plans are the outcome of the convictions of the faculty of the mathematics department and that of the Training School, and they embody practical results of long professional experience. They are a step in the solution of that pressing problem, which thoughtful educators all over the country are solving in various ways-the problem of adjusting the instruction to the powers and needs of the pupils. In order to make the adjustment still more complete we use in the written work of the grades the plan of progressive writing with individual advancement. Under this plan, all regular classwork, the explanations, games, drills, reviews, tests, etc., are given to the group as whole; but in the written work from the book, each child advances as far as he can in the time allotted to writing. The subjects of the book are carefully anticipated in the regular classwork. The individual work in the books is an occupation each day and is in the nature of a final review. If however, a pupil finds difficulties in the work when he comes to write it, he has an opportunity to consult the teacher while the other pupils are writing. CHART OF FIVES and division tables of tens and fives. used not only in the number play but later in the memorizing of the Each play or occupation has its specific purpose. The general purpose of the first year activities are to lead the child to know the sequences and values of the first hundred numbers, to give him motive and opportunity to perceive and use many independent number facts, to help him to memorize the combinations whose sum is ten or less, and to enable him to read and write numbers as far as thousands. ac In order to prevent the information of careless habits in dealing with numbers, absolute curacy in all the plays and exercises is insisted upon as an essential part of the play. One way of securing this is by letting the children "count out" the facts upon the chart whenever they are in doubt. Another way is to stop the play whenever a mistake is made and have the pupils get the truth from the chart. The correction is emphasized in these ways and the children are led to consider a mistake as a serious but avoidable evil. Testing games and individual tests are used. Each pupil's acquirements are carefully noted and 'the notes are used as a basis in sectioning the grades. The charts given here are taken from Hornbrook's Primary Arithmetic by permission of the American Book Co. A brief but interesting presentation of certain facts of psychology, the consideration of which led the author to prepare and use these charts, and also comments upon their use is to be found in Dr. G. Stanley Hall's Educational Problems, Vol. 2, pp. 350-356. They are ill advised who put Modern Montessori amcng the significant contributions to educational theory. Stimulating she is; a contributor to our theory, hardly, if at all. -William Heard Kilpatrick, Columbia University. "THE MAN WITH A SPARK” Have you ever seen an automobile standing on the road, apparently spic-and-span and in good condition, yet absolutely powerless? It may have electric lights and self-starter and "one man top" and demountable rims, and twelveinch upholstery-but while it is a thing of beauty it is not a "joy forever"-at least not until the garage man comes along and brings a new set of batteries. For the trouble is, the car has lost its spark. Without that spark all else is useless. Many men there are similarly affected-men who have lost their spark-who possess outward appearance, gentility; who are willing enough to do; who may have had a good education; who show up well enough until action is required! Every business seems to have its quota of these "sparkless" men. In surface analysis their opinion shine like the 1914 car. But when they are needed to put "punch" or "go" into a proposition, they "miss" in every cylinder. The spark of originality-that's the most difficult of all to strike. The spark of energy-just as necessary. The spark of sincerity-how rare, only those experienced in the quest can verify! Some men have energy in static form-as in the car with the batteries. They must be "charged" at regular intervals, or they will run down. Others have a dynamic spark-self-created. Their mental magneto is always on the job. They climb hills of difficulty with ease, go through the rough places of a campaign "sweet running"-and they have plenty of reserve power.-Richard A. Foley in the Advertising Digest. The teacher must never forsake the teaching point of view, in the view that his duty is not to train the boy for business, but to use business as a powerful instrument in training the boy.-J. P. Munroe, Boston. STAR SPANGLED BANNER CENTENNIAL EXERCISE JANE A. STEWART [Decorate the room with flags. Have ready a quantity of tiny flags for distribution. The words of the Star-Spangled banner Anthem may be written upon the blackboard.] Teacher-It is just a hundred years ago since one of our national anthems, called "the Star-Spangled Banner" was written. This song has been sung all through the years by young and old in our country. Whenever its words and notes are heard, true lovers of our country rise to their feet and stand during the music. That is to show respect and honor. And I hope that every child in this school will always thus honor the flag. 2. Flag Salute [as teacher (or pupil) waves a flag and the chorus of the Star Spangled Banner is sung by school: "Tis the star-spiangled banner-O long may it wave O'er the land of the free and the home of the brave!" 3.-EXERCISE. Acrostic (for twenty-one children who come one by one to the front of the platform and then form a line in the rear, remaining there till the close of the exercises. Each carries a gold paper letter.) First-T is for Truth that in God we feel Who on our land has put His seal. Second-H is for Hearts and Homes that stand United in our happy land. Third-E is for Equality For everybody, we agree. Fourth-S is for the Spirit high That lifts us nearer to the sky. Fifth-T is for the Treaties Before which Warfare quickly flees. Sixth-A is for the Accord sweet, With which we other nations meet. Seventh-R is for the Regard we hold For other countries, young and old. Eighth S is for the Service great, Freely given by every state. Ninth-P is for Peace, our conqueror; With us there is no room for war. Tenth-A is for Amity which ends All strife and makes us many friends. Eleventh-N is for our name so great, Many other nations high we rate. Twelfth-G is for Glory which we get; If towards Right our way is set. Thirteenth-L is for love the greatest thing In all the world, its praises ring. Fourteenth-E is for the Example good We'd like to show and surely should. Fifteenth-D is for Duty done, a joy That nothing can ever alloy. Eighteenth-N is for Nobility Of our country's pedigree. Nineteenth-N is for our Nation grand Greater than any other land. Twentieth-E is for Encouragement For our nation's government. Twenty-first-R is for Radiance in the skies When our starry banner flies. [All wave flags previously held behind them.] 4. EXERCISE. Questions and Answers:Teacher-What is the event which we celebrate to day? Pupil-The centennial of our "Star-Spangled Ban ner" song. Teacher-What is the "Star-Spangled Banner" song? Teacher-Who was Francis Scott Key? Pupil-He was born in Maryland. Pupil-He lived in the District of Columbia. Pupil-One night he saw the British bombard Fort McHenry. He was glad that they did not get Fort McHenry and that the flag was still there in the morning. Teacher-Where is Fort McHenry? Pupil-On the Patapsco river not far from Baltimore, Maryland. Teacher-When did Key write the poem? Pupil-That very night and day. Teacher-Did the people like the song? Pupil-Yes. Everybody in Baltimore was singing it after the British went away. Teacher-What was the date on which Key wrote the Nobly our flag flutters o'er us today With our's in beauty no flag can compare Our star-spangled flag loved and honored by all 6. RECITATION-(for three girls.) For God, home and country and good of our race Hail flag of our country, your stripes and bright stars Then pledge we our faith to our nation so strong 7. EXERCISE "The Star-Spangled Banner" by five boys and five girls. First child (Shows facsimile of the original StarSpangled Banner which floated over Fort McHenry (Continued on page 36.) subjects. PRACTICAL ARTS SERIES — (I.) BASKET WORK N. M. PAIRPOINT OR handwork to be done in the schoolroom without special equipment, with either mixed classes or for boys alone while the girls are sewing, basketry is one of the most practical If it is planned out by the pupils, and working drawings made first, there is a good deal of educational value in the subject. Also if it is desirable to make objects that can be sold to help pay the expenses of the manual arts department, the baskets that are artistically planned and care centre until a second row is worked. After this row, always have the connecting stitch pass under the coil below. Make a flat circular mat for the bottom of the basket about seven inches in diameter, then begin to turn the sides up by placing the new coil on the top of the preceding one, and let the basket grow smaller as the sides are made. When about two inches have been worked, mark off six places round the edge and begin to work the design. Have three stitches of colored raphia at each point marked, then lay the colored strand along the foundation and work over it with fully made are very saleable; and as their sale is not intended to pay a profit on the time expended, excellent value can be given the purchaser, and the pupils can gain the knowledge of reckoning cost of materials and time and what a reasonable profit should be. A pretty work basket is always a good subject and is one of the best things to make first, as a little variation in shape will make no difference in the finished project and all the technical difficulties can be mastered in it. The coiled basket is the most practical for schoolroom use and this first effort can be made on jute or hemp twine as a foundation. Twist the end of the twine into a loop and lay an end of the strand of raphia along the end of the twine, then twist two or three times round the two pieces where they cross, and wind over the loop until about half of it is covered with raphia. Take the long end of the twine and pull it until the loop is drawn together as tightly as possible. Now use the lazy squaw stitch, twisting over the twine twice, then taking a stitch through the plain raphia until the place is reached for the next colored square. Work a second row in the same way and allow the third one to be made entirely of the color, then finish with one row above like the first two making squares. Finish the top with the plain color. The cover is made just as is the bottom of the basket. The knob is made from a piece of very fine reed, well soaked in water to make it pliant, and twisted into a tight ball and held in place with a few stitches of raphia. Very attractive holders for flowers, can be made by covering glasses of all kinds with coiled basketry. Secure small bottles, tumblers, finger bowls, or even test tubes, and have the basket coverings planned so these glasses will slip inside easily and stand firmly. An excellent opport:.nity is given in these objects to design attractive shapes that are practical for the pupose for which they are made. Handles can be added that will make the baskets quite elaborate and color schemes planned that will help the color of the flowers and harmonize with the surroundings. |