On Popular Education Page #5

"On Popular Education" is a thought-provoking essay by Leo Tolstoy in which the renowned Russian author explores the role of education in shaping individuals and society. Written in 1862, Tolstoy critiques the existing educational systems of his time, advocating for a more accessible, practical, and moral approach to learning. He emphasizes the importance of fostering critical thinking and moral values over rote memorization, urging educators to nurture the innate curiosity of learners. Tolstoy's reflections serve as a powerful call for a more humane and equitable educational framework that empowers individuals to contribute meaningfully to society.

• Essay

								

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.

"(3) Decomposition in order. It may easily happen that the children will
at once point out the decomposition of the number into component parts
in order; even then the third exercise cannot be regarded as
superfluous: Here we have formed four cubes of twos, of separate cubes,
and of threes,--in what order had we best place the cubes on the board?
With what shall the decomposition of the four cubes begin? With the
decomposition into separate cubes. How are four cubes to be formed from
separate cubes? We must take four times one cube. How are four cubes to
be formed from twos, from a pair? We must take two twos,--twice two
cubes, two pairs of cubes. How shall we afterward break up the four
cubes? They can be formed of threes: for this purpose we take three and
one, or one and three. The teacher explains to the pupils that the last
decomposition, that is, 1 1 2, does not come under the accepted order,
and is a modification of one of the first three."

Why does Mr. Evtushévski not admit this last decomposition? Why must
there be the order indicated by him? All that is a matter of mere
arbitrariness and fancy. In reality, it is apparent to every thinking
man that there is only one foundation for any composition and
decomposition, and for the whole of mathematics. Here is the
foundation: 1 + 1 = 2, 2 + 1 = 3, 3 + 1 = 4, and so forth,--precisely
what the children learn at home, and what in common parlance is called
counting to ten, to twenty, and so forth. This process is known to every
pupil, and no matter what decomposition Mr. Evtushévski may make, it is
to be explained from this one. A boy that can count to four, considers
four as a whole, and so also three, and two, and one. Consequently, he
knows that four was produced from the consecutive addition of one.
Similarly he knows that four is produced by adding twice one to two,
just as he knows twice one is two. What, then, are the children taught
here? That which they know, or that process of counting which they must
learn according to the teacher's fancy.

The other day I happened to witness a lesson in mathematics according to
Grube's method. The pupil was asked: "How much is 8 and 7?" He hastened
to answer and said 16. His neighbour, too, was in a hurry and, without
raising his left hand, said: "8 and 8 is 16, and one less is 15." The
teacher sternly stopped him, and compelled the first boy to add one
after one to 8, until he came to 15, though the boy knew long ago that
he had made a blunder. In that school they had reached the number 15,
but 16 was supposed to be unknown yet.

I am afraid that many people, reading all these long refutals of the
methods of object instruction and counting according to Grube, which I
am making, will say: "What is there here to talk about? Is it not
evident that it is all mere nonsense which it is not worth while to
criticize? Why pick out the errors and blunders of a Bunákov and
Evtushévski, and criticize what is beneath all criticism?"

That was the way I myself thought before I was led to see what was going
on in the pedagogical world, when I convinced myself that Messrs.
Bunákov and Evtushévski were not mere individuals, but authorities in
our pedagogics, and that what they prescribe is actually carried out in
our schools. In the backwoods we may find teachers, especially women,
who spread Evtushévski's and Bunákov's manuals out before them and ask
according to their prescription how much one feather and one feather is,
and what a hen is covered with. All that would be funny if it were only
an invention of the theorist, and not a guide in practical work, a guide
that some follow already, and if it did not concern one of the most
important affairs of life,--the education of the children. I was amused
at it when I read it as theoretical fancies; but when I learned and saw
that that was being practised on children, I felt pity for them and
ashamed.

From a theoretical standpoint, not to mention the fact that they
faultily define the aim of education, the pedagogues of this school make
this essential error, that they depart from the conditions of all
instruction, whether this instruction be on the highest or lowest stage
of the science, in a university or in a popular school. The essential
conditions of all instruction consist in selecting the homogeneous
phenomena from an endless number of heterogeneous phenomena, and in
imparting the laws of these phenomena to the students. Thus, in the
study of language, the pupils are taught the laws of the word, and in
mathematics, the laws of the numbers. The study of language consists in
imparting the laws of the decomposition and of the reverse composition
of sentences, words, syllables, sounds,--and these laws form the subject
of instruction. The instruction of mathematics consists in imparting the
laws of the composition and decomposition of the numbers (but I beg to
observe,--not in the process of the composition and the decomposition of
the numbers, but in imparting the laws of that composition and
decomposition). Thus, the first law consists in the ability of regarding

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