What is a good definition? For the philosopher or the scientist, it is a definition which applies to all the objects to be defined, and applies only to them; it is that which satisfies the rules of logic. But in education it is not that; it is one that can be understood by the pupils.
Interpretation
A good definition should be precise and logical for philosophers and scientists, but it must also be comprehensible for students in education.
Henri Poincare emphasizes that while a good definition in scientific or philosophical terms should adhere strictly to logical principles, in the realm of education, the primary focus should be on clarity and understandability for learners. This highlights the importance of tailoring definitions to the audience, ensuring that knowledge is accessible and meaningful for students.
In practice
A teacher might use this quote to highlight the importance of clear definitions in lesson planning.
When the logician has resolved each demonstration into a host of elementary operations, all of them correct, he will not yet be in possession of the whole reality, that indefinable something that constitutes the unity ... Now pure logic cannot give us this view of the whole; it is to intuition that we must look for it.
It is a misfortune for a science to be born too late when the means of observation have become too perfect. That is what is happening at this moment with respect to physical chemistry; the founders are hampered in their general grasp by third and fourth decimal places.
A scientist worthy of his name, about all a mathematician, experiences in his work the same impression as an artist; his pleasure is as great and of the same nature.
. . . by natural selection our mind has adapted itself to the conditions of the external world. It has adopted the geometry most advantageous to the species or, in other words, the most convenient. Geometry is not true, it is advantageous.
The mathematical facts worthy of being studied are those which, by their analogy with other facts, are capable of leading us to the knowledge of a physical law. They reveal the kinship between other facts, long known, but wrongly believed to be strangers to one another.
Most striking at first is the appearance of sudden illumination, a manifest sign of long unconscious prior work.
If my books can help children become readers then I feel I have accomplished something important.
I like that there are young people being given opportunities to explore and learn and grow and become themselves with a path that is associated with my mother. She would have liked that very much.
If I can get a story about a player, I would give you a ship load of numbers, batting averages and all just for that one precious story. That's the kind of thing that I love to do.
Kids all want to look cool, as if knowledge is a great burden, but they're always looking around. They remember.
Nowadays, a 13-year-old would probably know more than Bobby Fischer knew when he retired. They analyse all the moves and prepare themselves on their computers. But that doesn’t mean they are special.
Reading is important. Books are important. Librarians are important. (Also, libraries are not child-care facilities, but sometimes feral children raise themselves among the stacks.)
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