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“Tell it, then,” I said. He told it in such a racy and realistic way that the class applauded. I had found something that the child liked. The second day I told the story of “ Hiawatha's Fasting,” then “ Hiawatha's Friends,” and so on, two stories a week, until we had told the whole story of Hiawatha.
But you ask, “What did that have to do with grammar?' From the story we got the nouns and verbs we studied, and the sentences that the advanced classes analyzed and studied. (The whole school heard the story, it being an ungraded school, with classes ranging from primary to high school.)
What else did we do with the story? Let us see. When the children told the story orally or on paper it was creative work, and better for expression than memorizing, “ Mary had a little lamb." The child received a mental picture. He heard the story, and re-telling it in his own words he created afresh the picture, thereby becoming a creator and an artist himself. In reciting “ Mary had a little lamb” he was dealing with words only. In telling the story he was dealing with a mental picture.
One day I saw the children playing out on the lawn, and on making inquiries they said, “We are playing Hiawatha and Old Nokomis.” They were dramatizing the story. taking effect. Had I been a trained teacher I would have let them do it in class as a part of their work. Twice a week we got the words for our spelling lesson from the story. The children were so much interested in Hiawatha that they wanted to make pictures of Hiawatha. Then I let them illustrate the story, writing it in their composition books, and illustrating it. As we studied geography, the upper Mississippi Valley and the Lake Regions all took on new meaning, because Hiawatha had once lived, toiled and suffered there.
But most of all, what had I done for those children? I had fed their souls-given them a masterpiece of literature. Starting with the childhood of Hiawatha, they had followed him and admired him. They had seen him when he caught the King of Fishes, “ Slew the Pearl Feather,” prayed and fasted for his people, punished “Pau-puk-kee-wis,” wooed and won Minnehaha, and when his task was done, sailed away into the fiery sunset.
That something inexpressibly sweet and beautiful that I felt in the vision hour, and longed to impart to the children, and heretofore had not been able to, I had at last found incarnate in a hero; while the music, meter and imagery of poetry had awakened the sense of the beautiful, and revealed a new world to them. New life had come into the school. It had been born again, and born from above.
Two months passed. I had tried an experiment; it had succeeded. Grammar, language, composition, drawing, spelling, story telling, had been taught by that method. Formal language had become linked to literature, and thereby to life. The formal had become an expression of the spiritual.
Where could I find another such story. I had recently studied in the university the Idylls of the King. Could the children appreciate the story of King Arthur and the Knights of the Round Table? I feared they could not; but then, I would try them. I must have another story. It was more profound, more complex and more difficult in every way to tell than Hiawatha. I began with the finding of a naked baby on the beach, the childhood of Arthur, Merlin's work, the sword Excalibur, and Arthur's coronation.
At first King Arthur was not so popular as Hiawatha, but as we got more into the meaning of the story the interest deepened, and at times became intense, especially among the older boys and girls, as we gave Gareth and Lynette, Geraint and Enid, the Holy Grail, Elaine, Guinevere and the Passing of Arthur. As with Hiawatha the story was reproduced, illustrated, correlated with English history and geography; at the same time it furnished the most excellent material for ethical and æsthetic culture. After the last story was told, the Passing of Arthur, and the children saw with Sir Bedevere their king pass with the three tall queens in a barge over the sea, they stood in wonder gazing on the splendor of his passing. Defeated in the last weird battle in the West he was victorious in his ideal. “From the great deep to the great deep he goes." The children heard, but did not quite understand. It was the better for that because it awakened in the child something of the mystery of life and death. In that, it served the highest purpose. It helped the child to realize that there are things in life that "eye hath not seen, nor ear heard.” Let it not be forgotten that while we use these great stories for formal work, the formal was always the result of the creative. “The letter killeth ; the spirit giveth life.” Thus it was that children and teacher left the low planes of the “ lesson hearer," and hand in hand walked the upland pastures of the soul.
HELEN CARY CHADWICK
The woe of earth can sadden me no more.
ARTHUR LATHAM BAKER, PH.D., MANUAL TRAINING HIGH SCHOOL,
BROOKLYN, N. Y.
HE word limit is used here in the sense illustrated by the series
x=1+1+4++... fn=2-1where 2 in the value toward which x tends as n is increased, approaching indefinitely near thereto, but never quite reaching ; x always falling short of the limit by Jn. This is the kind of a limit
found in the text-books on elementary geometry, and used in the proofs and processes. This form of limit is used because in the endeavor to measure certain forms we have hitched our form to a numerical series, which has a limit beyond which its value does not pass. To prove that the variable form and the series which measures it does not pass beyond the limit, the custom is to prove that it does not quite reach the limit, by a deficiency less than any assignable quantity.
Then having established the proposition that general theorems concerning variables are true of their limits, we proceed to discuss incommensurable forms, the limits of commensurable forms. This is all right as far as it goes; but uncoupled with the caution that geometric forms may pass beyond the limits which they have when hitched to the numerical series, it leads to many unfortunate conceptions: as that a circle and a straight line are essentially and radically different lines, in that the one can never merge into the other. Similarly with the circle and polygon.
I propose to show that the occurrence of such a limit in geometric forms is the result of the selection of a process which shall produce it, where the selection of some other process would have avoided the limit. The simplest illustration is the generation of an angle, X. If generated by the movement of the intersection A, X has an inaccessible limit, N, a value toward which it tends indefinitely near, but
If the reader objects to the word limit, let him substitute the phrase unattainable value.”
which it never quite reaches. If, however, it be generated by the movement of the intersection B, there is no evasive limit; the value of X reaches N and passes beyond.
As a second illustration, take the case of the hound A pursuing the hare B, and finding that when he has reached the former position of the hare, the hare has jumped } as far ahead. Now suppose a third point C to move ahead continuously at a
finite speed, but so regulated that it will arrive at the jumping points, the former positions of the hare, at the same time as the hound. For convenience, suppose we call these points where the hound A, and C are together contact points. If this process of pursuit is regulated by the finiteness of time interval between the jumps, the points A and C will never overtake the point B, for the very simple reason that the point B is always the half of some distance ahead; and since the contact points (events) are separated by finite intervals of time, the recurrence of events stretches out forever, and is never ended. The recurrence of events, the breasting of A and C, is finitely time spaced, and the speed of C is decreasing to infinite slowness.
On the other hand, if the pursuit is regulated by the finite speed of C, the recurrence of events increases to infinite rapidity, and the point C catches up with B, passes it, and the pursuit is changed into flight. An illustration of this is the pursuit of the hour hand by the minute hand. When the minute hand C has arrived at any previous position of the hour hand B, the hour hand has jumped ahead its of the previous distance, so that the hour hand is always and at the recurrence of every contact event the of some distance ahead. But the contact events occur finally with infinite rapidity, and do not stretch out forever, but are condensed into a limited time, and thus some time run out, and C catches B. Should we undertake to picture the contact points we would get a diagram such as the following, the contact points crowding closer and A
X ' closer together as we approach X, the point of overtaking, and at X crowding together with infinite closeness. It is impos