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.
Read a lot. Read broadly... Tell stories to your friends, and pay attention to when they get bored... Write a lot.
From daycare to graduation, our education system stacks the odds against the poor. Predicted grades is just one of many hurdles that are set a little higher for those whose parents do not have the money to smooth their path in life or the inside knowledge of how the system works.
The proper method for hastening the decay of error is by teaching every man to think for himself.
The mission that unites all of the programs of the Teach For All global network is that of cultivating the leadership capacity critical to ultimately ensuring educational opportunity for all.
Most of the people who will walk after me will be children, so make the beat keep time with short steps.
When girls are educated and free to pursue their passions, they contribute more to a thriving society. When women have a voice, they raise it to demand a life that is greater than what they've been told they have a right to expect. And these demands change the future for everyone.
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