Fables for Children, Stories for Children, Natural Science Stories, Popular Education, Decembrists, Moral Tales by graf Leo Tolstoy

Author:graf Leo Tolstoy [Tolstoy, Leo, graf]
Language: eng
Format: epub
Published: 0101-01-01T00:00:00+00:00

[1] The Russian way of saying "Noah had three sons."

Let anybody understand at once Mr. Evtushévski's problem: "A certain boy had four nuts, another had five. The second boy gave all his nuts to the first, and this one gave three nuts to a third, and the rest he distributed equally to three other friends. How many nuts did each of the last get?" Express the problem as follows: "A boy had four nuts. He was given five more. He gave away three nuts, and the rest he wants to give to three friends. How many can he give to each?" and a child of five years of age will solve it. There is no problem here at all, but the difficulty may arise only from a wrong statement of the problem, or from a weak memory. And it is this syntactical difficulty, which the children overcome by long and difficult exercises, that gives the teacher cause to think that, teaching the children what they know already, he is teaching them anything at all. Just as arbitrarily are the children taught combinations in arithmetic and the decomposition of numbers according to a certain method and order, which have their foundation only in the fancy of the teacher. Mr. Evtushévski says:

"Four. (1) The formation of the number. On the upper border of the board the teacher places three cubes together—I I I. How many cubes are there here? Then a fourth cube is added. And how many are there now? I I I I. How are four cubes formed from three and one? We have to add one cube to the three.

"(2) Decomposition into component parts. How can four cubes be formed? or, How can four cubes be broken up? Four cubes may be broken up into two and two: II + II. Four cubes may be formed from one, and one, and one, and one more, or by taking four times one cube: I + I + I + I. Four cubes may be broken up into three and one: III + I. It may be formed from one, and one, and two: I + I + II. Can four cubes be put together in any other way? The pupils convince themselves that there can be no other decomposition, distinct from those already given. If the pupils begin to break the four cubes in this way: one, two, and one, or, two, one and one; or, one and three, the teacher will easily point out to them that these decompositions are only repetitions of what has been got before, only in a different order.

"Every time, whenever the pupils indicate a new method of decomposition, the teacher places the cubes on a ledge of the blackboard in the manner here indicated. Thus there will be four cubes on the upper ledge; two and two in a second place; in a third place the four cubes will be separated at some distance from each other; in a fourth place, three and one, and in a fifth one, one, and two.

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