Schopenhauer’s essay “On Thinking for Oneself” captures very well the pedagogical spirit on which my calculus book and manifesto are founded.
A textbook should strive not to explain, but to stimulate the reader to explain for himself:
“Even if occasionally we had been able very easily and conveniently to find in a book a truth or view which we very laboriously and slowly discovered through our own thinking and combining, it is nevertheless a hundred times more valuable if we have arrived at it through our own original thinking. Only then does it enter into the whole system of our ideas as an integral part and living member; only then is it completely and firmly connected therewith, is understood in all its grounds and consequents, bears the colour, tone, and stamp of our whole mode of thought, has come at the very time when the need for it was keen, is therefore firmly established and cannot again pass away. ... [Whereas] the truth that has been merely learnt sticks to us like an artificial limb, a false tooth, [or] a nose of wax.” (§260)
The student must resist the temptation to demand that things be explained to him, and to seek out an “answer key” as soon as he is stuck:
“The mind is deprived of all its elasticity by much reading as is a spring when a weight is continually applied to it; and the surest way not to have thoughts of our own is for us at once to take up a book when we have a moment to spare.” (§258) “We should, therefore, read only when the source of our own ideas dries up, which will be the case often enough even with the best minds. On the other hand, to scare away our own original and powerful ideas in order to take up a book, is a sin against the Holy Ghost. We then resemble the man who runs away from free nature in order to look at a herbarium, or to contemplate a beautiful landscape in a copper engraving.” (§260)
The student should be aware that nothing could be easier than spotting one who is speaking thoughts not genuinely his own:
“According to these observations, it will not surprise us to learn that the man who is capable of thinking for himself and the book-philosopher can easily be recognized even by their style of delivery; the former by the stamp of earnestness, directness, and originality, by all his ideas and expressions that spring from his own perception of things; the latter, on the other hand, by the fact that everything is second-hand, consists of traditional notions, trash and rubbish, and is flat and dull, like the impression of an impression.” (§263)
Those who dislike thinking for themselves are those who approach learning with dishonest and ignoble intent:
“Thus we can divide thinkers into those who think primarily for themselves and those who think at once for others. The former ... are the real philosophers. For they alone take the matter seriously; and the pleasure and happiness of their existence consists in just thinking. The others are the sophists; they wish to shine and seek their fortune in what they hope to obtain from others in this way; this is where they are in earnest. We can soon see from his whole style and method to which of the two classes a man belongs.” (§270)