"Before the child has to work at geometry, see that he realizes:-- That there are in nature no lines, except the edges of solids, nor surfaces, except the sides of solids. That natural movements and growths take place usually in curves, not straight lines. That axes, diameters and co-ordinates are not part of any natural figure, but measuring rods introduced for man's convenience. Connect in the pupil's mind these devices with that earlier invention, mentioned in the former paper, of breaking big numbers into tens and hundreds; explain that man extracts no more real instruction out of such devices than a monkey gets by breaking things in bits, unless he completes the cycle of study by the transcendental (or supra-simian) act of synthesis. The parent will translate these words into such as she finds suit the child; the essential thing is for the parent herself to grasp the idea clearly. If she does not, she should get herself taught to do so by some competent person.
"In connection with this idea of synthesis, a child should be taught that if he wants to learn anything about an object by breaking it open, he should not break it till he has taken a good look at it in its original state, so as to be able to reconstruct it in his mind as a whole.' ~~ "Home Algebra and Geometry," by Mary Everest Boole, in The Parents' Review, Volume 3, 1892/93, pgs. 854-857
And check this one out (emphases mine):
"May I make an example of flowers to illustrate the application of the science of appearances? Amongst other sciences applicable to them is horticulture, which treats of their civilization, the robustness of their constitution, their span of life, their propagation, their cultivation, the improvement of their characteristics of form and colour, the soil suitable to them, its texture, and its chemical constituents. There is also botany, a science which deals with their habits, their structure, their organs, their classification and variety. These are all concrete facts, to acquire which we examine the flowers from every point of view. We uproot them, we dissect them, we remove them from their surroundings, and consider them almost without reference to them. The facts of their appearance are different. They depend, not only upon the aspect and condition of the flowers themselves, the relation of the parts to the whole, and of the parts to each other, in different qualities and characteristics, but their aspect also depends upon their relation to surroundings, and to the aspect and condition of surroundings, and to relations, conditions, influences outside themselves and their immediate surroundings.
"We may be able to change their surroundings and the outside influences, but we cannot disassociate them, We may take flowers from the field, or hedgerow, or garden, and bring them indoors, place them in a vase or upon a table or in a box, we may change their conditions in a countless number of different ways, but do what we may, we cannot see them without some surroundings. Any change of surroundings or change of relation of outside influences will cause change of appearance. Their appearance amongst the green grasses in the field will be different from their appearance as they grow in the garden soil against the red-brick wall, or as they lie indoors upon a polished mahogany table. They will appear different under the influence of sunshine, or gray weather or rain, at a distance from us or near at our feet. The appearance of the flowers will in every possible case have certain fixed relations to surroundings and outside conditions and influences. We cannot see or conceive flowers or any other object except under aspects influenced by outside conditions, for that is the way nature conveys to us the impression of them." ~~
"The Fine Arts and Education, Part 1," by Francis Bate, in The Parents' Review,
Volume 7, 1896, pgs. 561-571.
Do you get the feeling we're talking about a lot more than botany here?