"I do this," replied Einstein, "only when I speak of the ultimate aims of pure research, that is, of aims that are visible to only a vanishing minority. It would be a complete misconception of life to uphold this point of view and to expect its regulative effectiveness in cases in which we are dealing only with the preliminaries of science. On the contrary, I maintain that science can be taught much more practically at schools than it is at present when bookwork has the upper hand. For example, to return to the question of mathematical teaching: it seems to me to be almost universally at fault, if only for the reason that it is not built up on what is _practically_ interesting, what appeals directly to the senses, and what can be seized intuitively. Child-minds are fed with definitions instead of being presented with what they can grasp, and they are expected to be able to understand purely conceptual things, although they have had no opportunity given them of arriving at the abstract by way of concrete things. It is very easy to do the latter. The first beginnings should not be taught in the schoolroom at all, but in open Nature. A boy should be shown how a meadow is measured and compared with another. His attention must be directed to the height of a tower, to the length of his shadow at various times, to the corresponding altitude of the sun; by this means he will grasp the mathematical relationships much more rapidly, more surely, and with greater zeal, than if words and chalk-marks are used to instil into him the conceptions of dimensions, of angles, or perchance of some trigonometrical function. What is the actual origin of such branches of science? They are derived from practice, as, for example, when Thales first measured the height of the pyramids with the help of a short rod, which he set up at the ultimate point of the pyramid's shadow. Place a stick in the boy's hand and lead him on to make experiments with it by way of a game, and if he is not quite devoid of sense, he will discover the thing for himself. It will please him to have discovered the height of the tower without having climbed it, and this is the first thrill of the pleasure which he feels later when he learns the geometry of similar triangles and the proportionality of their sides."