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.
Children are apt to live up to what you believe of them.
In teaching, the other main problem related to type is the students’ interest. Intuitives and sensing types differ greatly in what they find interesting in any subject even if they like, that is, are interested in, the same subjects. Intuitives like the principle, the theory, the why. Sensing types like the practical application, the what and the how.
I was a voracious reader and the library fed my curiosity, imagination and my soul. I read by the shelf - biographies, fantasy - all and everything fed my dreams. Then as an adult whenever I would go on location the first thing we would do as a family is sign up at the closest library. Not only would we find books, but what was happening in that town, because the library is the head of the community.
And I’ve said this all across the country when I talk to parents about education, government has to fulfill its obligations to fund education, but parents have to do their job too. We’ve got to turn off the TV set, we’ve got to put away the video game, and we have to tell our children that education is not a passive activity, you have to be actively engaged in it. If we encourage that attitude and our community is enforcing it, I have no doubt we can compete with anybody in the world.
Let us labor for that larger comprehension of truth, and that more thorough repudiation of error, which shall make the history of mankind a series of ascending developments.
When the child begins to think and to make use of the written language to express his rudimentary thinking, he is ready for elementary work; and this fitness is a question not of age or other incidental circumstance but of mental maturity.
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