Why don't we want our children to learn to do mathematics? Is it that we don't trust them, that we think it's too hard? We seem to feel that they are capable of making arguments and coming to their own conclusions about Napoleon. Why not about triangles?
Paul LockhartStichwörter: education learning math mathematics
Mental acuity of any kind comes from solving problems yourself, not from being told how to solve them.
Paul LockhartStichwörter: intelligence education problems
A good problem is something you don't know how to solve. That's what makes it a good puzzle and a good opportunity.
Paul LockhartStichwörter: education problems
Doing mathematics should always mean finding patterns and crafting beautiful and meaningful explanations.
Paul LockhartStichwörter: beauty math mathematics
Be honest: did you actually read [the above geometric proof]? Of course not. Who would want to?
The effect of such a production being made over something so simple is to make people doubt their own intuition. Calling into question the obvious by insisting that it be 'rigorously proved' ... is to say to a student 'Your feelings and ideas are suspect. You need to think and speak our way.
Stichwörter: intuition math mathematics geometry
It is the story that matters not just the ending.
Paul LockhartStichwörter: journey story math mathematics
So how does one go about proving something like this? It's not like being a lawyer, where the goal is to persuade other people; nor is it like a scientist testing a theory. This is a unique art form within the world of rational science. We are trying to craft a "poem of reason" that explains fully and clearly and satisfies the pickiest demands of logic, while at the same time giving us goosebumps.
Paul LockhartStichwörter: reason logic math mathematics
The thing I want you especially to understand is this feeling of divine revelation. I feel that this structure was "out there" all along I just couldn't see it. And now I can! This is really what keeps me in the math game-- the chance that I might glimpse some kind of secret underlying truth, some sort of message from the gods.
Paul LockhartStichwörter: inspiration math mathematics
Mathematics is the music of reason. To do mathematics is to engage in an act of discovery and conjecture, intuition and inspiration; to be in a state of confusion—not because it makes no sense to you, but because you gave it sense and you still don't understand what your creation is up to; to have a break-through idea; to be frustrated as an artist; to be awed and overwhelmed by an almost painful beauty; to be alive, damn it.
Paul LockhartStichwörter: mathematics
Mathematics is the art of explanation.
Paul LockhartStichwörter: mathematics
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