Our present methods of teaching originate from a time when the accomplishments required from an educated person were extremely limited; and they have been maintained, notwithstanding the immense increase of knowledge which must be conveyed…
Petr Alekseevich Kropotkin
The Public Record
Hence the over-pressure in schools, and hence, also, the urgent necessity of totally revising both the subjects and the methods of teaching, according to the new wants and to the examples already given here and there, by separate schools…
German teachers have shown how the very plays of children can be made instrumental in conveying to the childish mind some concrete knowledge in both geometry and mathematics.
The children who have made the squares of the theorem of Pythagoras out of pieces of coloured cardboard, will not look at the theorem, when it comes in geometry, as on a mere instrument of torture devised by the teachers; and the less so…
Complicated problems of arithmetic, which so much harassed us in our boyhood, are easily solved by children seven and eight years old if they are put in the shape of interesting puzzles.
On the other side, we all know how children like to make toys themselves, how they gladly imitate the work of full-grown people if they see them at work in the workshop or the building-yard.
But the parents either stupidly paralyse that passion, or do not know how to utilise it.
Most of them despise manual work and prefer sending their children to the study of Roman history, or of Franklin’s teachings about saving money, to seeing them at a work which is good for the “lower classes only.” They thus do their best…
Take, for instance, mathematics, which every one ought to know, because it is the basis of all subsequent education, and which so few really learn in our schools.
In geometry, time is foolishly wasted by using a method which merely consists in committing geometry to memory.
Therefore, nine boys out of ten, if asked to prove an elementary theorem two years after having left the school, will be unable to do it, unless mathematics is their speciality.
They will forget which auxiliary lines to draw, and they never have been taught to discover the proofs by themselves.