ONE day, when Lucy was about five years old, her mother came home from the city. Lucy’s brother Royal had been to the city with his mother; but Lucy had remained at home. Royal went to drive the chaise in which his mother rode.
When Lucy’s mother had got out of the chaise, Royal handed her some parcels, which were in the back part of the seat. There was one thin, flat parcel, which was partly behind the cushion. Royal held this up to Lucy, saying,—
“Lucy! Lucy!—something for you.”
Lucy took it, and ran into the house. She asked her mother if she might open it.
“Yes,” said her mother, “but be careful.”
So Lucy ran to the sofa, and sat down to open her parcel. Royal came up to her, and said,—
“Let me open it for you, Lucy. I know how to open it.”
“No,” said Lucy, “I want to open it myself.”
“You can’t open it,” said Royal; and, as he spoke, he took hold of the parcel, and attempted gently to take it away from Lucy. “You can’t open it. You can’t untie the string; it is in a hard knot. I saw the man tie it myself.”
“Royal! Royal!” said Lucy, in a tone of displeasure, “let my book alone.”
“It isn’t a book,” said Royal; “and you can’t open it, to see what it is.”
Royal did wrong. He ought to have reflected that it would have given Lucy great pleasure to open the parcel, and he ought to have been willing that she should open it, and to have been contented with giving her such assistance as she needed. However, he knew that it would be wrong for him to take the parcel away by force, and so he let go of it, and sat by, to see Lucy open it.
Lucy found that she could not untie the knot. Then she looked about to find her scissors, to cut it; for she had a pair of scissors, which her mother had bought for her, some time before; but, then, as she was accustomed to leave them any where about the house, wherever she had been using them, they were continually getting lost; and she could not find them now. Royal, instead of helping her, seemed rather inclined to tease and trouble her.
While Lucy was thus walking about the room, sometimes looking for her scissors, and sometimes stopping to make one more attempt to untie the knot without them, Miss Anne came into the room. Miss Anne was a young lady about seventeen years of age. Miss Anne was always very kind to Lucy.
“Miss Anne,” said Lucy, “do you know where my scissors are?”
“No,” said Miss Anne; “can’t you get your parcel open?”
“No,” said Lucy; “I can’t untie the knot; and I can’t find my scissors to cut it.”
Miss Anne sat down in a little rocking-chair, and asked Lucy to come to her, and let her look at it.
“See what a hard knot,” said she.
“I should have been willing to have untied it for her,” said Royal, “but she would not let me.”
Miss Anne did not reply to this remark, for she supposed that probably Royal had offered his help to Lucy in some way which was not pleasant to her.
“Should you like to have me loosen the knot a little?” she said to Lucy; “and then perhaps you can untie it.”
“O yes,” answered Lucy; and she put the parcel into Miss Anne’s hands.
Miss Anne, who understood the convolutions of a knot better than Lucy, and who consequently knew just where to attempt to open it, soon got it loosened. Lucy watched her, afraid that she would open it too much.
“There,” said she, “Miss Anne, there, that will do. I can open it now.”
So Miss Anne put the parcel into her hands, and Lucy now succeeded in untying the knot. After taking off the string, she opened the paper, and there came out a handsome slate, of a beautiful purple color, and a red morocco frame.
“O, what a pretty slate!” said Lucy.
Near one corner of the slate was a sort of socket, made by a duplicature of the morocco, and Lucy observed a slate pencil sticking into it. She pulled it out, and said,—
“O, here is a pencil; I mean to mark on my slate.”
“I expect you are going to study arithmetic,” said Miss Anne.
“Yes,” said Royal, “she is, and I am going to teach her.”
“No,” said Lucy, “I would rather have Miss Anne to teach me.”
“No, Lucy,” replied Royal; “mother said, if I would teach you to add little sums in arithmetic, without any carrying, she would give us a paint-box.”
“Give who a paint-box?” said Lucy.
“Why, you and me,” replied Royal.
“Well,” said Lucy, “then you may teach me.”
Accordingly Lucy went and sat down by Royal upon the sofa, to take her first lesson then, as they were both in haste to get the paint-box. Royal set Lucy a sum; but, on looking at it after he had set it, he rubbed it out, and set another. This also he rubbed out. At length Lucy said,—
“Why, Royal, what makes you rub them all out?”
“Because,” said Royal, “there’s carrying in them.”
“I don’t know what you mean by carrying,” said Lucy.
Royal attempted to explain it to her, but she could not understand. He told her that, when she added up a column, and the amount was in two figures, she must carry one of them. But Lucy could not understand at all. She did not know what he meant by a “column,” or an “amount,” or by any thing being “in two figures.” In the mean time, Miss Anne, who had seated herself at the window, with her sewing, went on quietly attending to her work, until at length the conversation between Royal and Lucy came to be almost a dispute; and she said,—
“Royal, I thought you were not going to teach Lucy carrying; but only sums that had no carrying in them.”
“So I was,” said Royal; “but then she asked me herself what carrying was, and so I had to tell her.”
“No,” replied Miss Anne, “you need not have attempted to explain it to her fully. It would have been enough to have told her, that it was a difficult process in addition, which she would understand by and by.”
“Why, Miss Anne,” replied Royal, “I think it is very easy.”
“It may be easy to you, now you understand it, but difficult to her,” replied Miss Anne.
“Well,” said Royal, “then I won’t explain that to you now, Lucy. I’ll teach you what carrying is when we come to it.”
So he went to work, to set Lucy a sum, trying to make the figures of so small a value, that there should be no carrying in any column. But he did not succeed very well. He made the sums so large that, although he made all the figures ones, twos, threes, and fours, yet, in some of the columns, the amount, on adding them, would come more than ten; and of course there would be something to carry. At last, however, he succeeded; and then he began to teach Lucy how to add up.
But the work was altogether too difficult for Lucy’s powers. In the first place, she did not know the figures, and she could not remember which was two, and which was three. Lucy tried to follow him in his explanation and calculation, but she soon became hopelessly perplexed and discouraged.
“Two and two,” said Royal, “are how many?”
“Three,” said Lucy.
“No,” said Royal; “four; and one are how many?”
“One is one,” said Lucy.
“No,” said Royal; “one makes five.”
“One makes five?” repeated Lucy, in a tone of surprise.
“Yes,” said Royal, “one and four make five.”
“O, you did not say one and four,” replied Lucy; “you said one.”
“No,” replied Royal, “one and four; you see we got four by adding two and two. Here they are.”
So saying, Royal pointed to the figures which he had been adding.
Lucy did not know a two from a three very well; so she put her head down close to the slate, and said, in a gentle, timid voice,—
“Is that a two?”
“Yes,” said Royal. “Let us see; where were we? We added up to three, didn’t we? and it made six, didn’t it?”
“I don’t know,” said Lucy, shaking her head.
“Yes, it was six; and two more make how many?”
“Five?” asked Lucy, timidly.
“No indeed,” said Royal; “why, Lucy, you don’t know how to count.”
“Yes I do,” said Lucy.
“No you don’t,” said Royal; “you don’t know how to count, I verily believe.”
“Well, let’s hear you count: come, begin.”
“One, two, three, four,” said Lucy, and so far she went on very well; but then she began to hesitate,—“four—five—nine—seven.”
Royal burst into a fit of laughter. “You don’t how to count, Lucy,” said he; “and how do you think I can teach arithmetic to a girl that don’t know how to count?”
“Well, then, give me my slate,” said Lucy, “and I’ll go away.” So she took her slate, and went away out of the room, disappointed, discouraged, and sad.
As soon as she had gone, Royal’s feelings began to change from those of ridicule to a sentiment of pity. He sat upon the sofa silently musing, when Miss Anne terminated the pause by saying,—
“I was surprised at such ignorance.”
“So was I,” said Royal. “I should have thought any body would have known that.”
“I should have thought so, certainly,” said Miss Anne.
“Any body five years old,” added Royal.
“Yes,” said Miss Anne, “and yet you are ten.”
“I?” said Royal; “yes, I am ten, but Lucy is only five.”
“Yes,” replied Miss Anne, “but I was not speaking of Lucy; I was speaking of you.”
“I thought,” rejoined Royal, “that you were speaking of the ignorance Lucy showed, in not knowing how to count.”
“O no,” said Miss Anne, “I was speaking of the ignorance you showed.”
“My ignorance,” said Royal, surprised. “I am sure I added it right.”
“I think it very likely you added it right,” said Miss Anne; “it was your ignorance of human nature, I was speaking of, not your ignorance of arithmetic.”
“Of human nature?” repeated Royal.
“Yes; to think that you could teach Lucy arithmetic in that way.”
“Why, I thought that that was the way,” said Royal.
“No,” said Miss Anne, “you began at the end, instead of at the beginning.”
“How?” said Royal.
“Why, you undertook to teach her to add certain sums, and you took such sums, as difficult as it was possible to make, and got out of humor with her because she could not do them at once.”
“O Miss Anne, they were not as difficult as could be made.”
“Yes,” replied Miss Anne, “they were, I presume, as difficult sums as you could make, without having any carrying. In fact, the first attempts which you made to set sums, you got the figures so many, and of so high value, that you couldn’t add them without carrying; so you reduced them by little and little, until you just got the figures barely small enough to make the amount less than ten; and thus you made the sums as difficult as they could be made, without carrying; and this you gave her for her first lesson. The thing which you were to come to in the end, you took as the beginning.
“Then, besides this, I think you were unreasonable in being dissatisfied with her. When your mother promised you a paint-box, if you would teach her to add such sums, was it reasonable to expect that she could know how to do it already?”
“Why—no,” said Royal, hesitatingly.
“And yet you did expect it. You were employed to go over a process with her, which would end in her knowing how to do a certain thing; and then you were vexed and out of humor with her, for not knowing how to do the thing at the outset, before you had gone over the process at all.”
“Why, I wasn’t out of humor, Miss Anne,” said Royal.
“I thought you were,” replied Miss Anne; “at any rate, you spoke unkindly to her, and wounded her feelings.”
Here there was a pause. Royal was really sorry for what he had done. He saw very clearly the unreasonableness and folly of it. But he did not know exactly what to do.
“Well, Miss Anne,” said he at length, “how should you have managed it?”
“I,” replied Miss Anne, “should have begun at the beginning, instead of at the end.”
“And how would you have begun at the beginning?”
“Why, I should have first ascertained exactly where Lucy was, in her knowledge of figures, and then I should have gone to her there, and led her along by plain and easy steps to where I wanted her to go. You must know that teaching is a kind of ladder-making.”
“Ladder-making?” repeated Royal.
“Yes,” replied Miss Anne; “that is, it consists in preparing a succession of steps for the pupil to mount by, and the success of it depends upon beginning upon the ground, or wherever the pupil is, and then having the steps so near together, that she can ascend from one to the other, and so get up. Now, you did not even stop to inquire where Lucy was in her knowledge, much less to make any ladder for her; but you remained upon the top of the house, and tried to drag her up by main force.”
Royal laughed at Miss Anne’s singular metaphor.
“Now, I should have thought,” continued Miss Anne, “that the first thing would have been, to teach Lucy the figures, at least as many of them as you are going to use in the sums. This alone will take several lessons. Then I should set her some very small sums, with only ones in them, and let her add those. Then I should set some more sums, and put in a two here and there, and let her practise a day or two upon those. Then I should put one or two threes into her sums, and have the rest ones. After that I should put threes and twos both in; and thus, after a time, she would get so as to add such sums as you set her just now.”
“All that would take a great while,” said Royal.
“Yes,” replied Miss Anne; “teaching is slow work; but then it would not take so long as it would to make a paint-box.”
“No,” replied Royal, “it would not.”
“I suppose you expected that you could sit down and earn your paint-box in half an hour, and by one single lesson.”
“Why not exactly in one lesson,” said Royal.
“In one or two then,” said Miss Anne; “whereas you ought to calculate that it will take twenty.”
Royal said no more upon the subject at this time; but he determined to try the plan which Miss Anne had recommended.