Mathematics is the art of explanation. If you deny students the opportunity to engage in this activity-- to pose their own problems, to make their own conjectures and discoveries, to be wrong, to be creatively frustrated, to have an inspiration, and to cobble together their own explanations and proofs-- you deny them mathematics itself.
Interpretation
The quote emphasizes the importance of active engagement in learning mathematics.
Paul Lockhart's quote illustrates that mathematics is not merely about finding correct answers, but about exploring concepts, posing questions, and discovering personal understandings. He insists that denying students the chance to engage creatively and make mistakes prevents them from truly experiencing the essence of mathematics, which is fundamentally an art form of explanation and reasoning.
In practice
This quote can be used at the beginning of a mathematics workshop to inspire educators.
The first eight years of schooling was with all white people. So that helped me to understand how white people think. I think that transition is what helped me bridge the gap, because that's what my success has really been about: bridging the gap between the black community and the white community.
No religious reading, instruction or exercise, shall be prescribed or practiced [in the elementary schools] inconsistent with the tenets of any religious sect or denomination.
Whatever landscape a child is exposed to early on, that will be the sort of gauze through which he or she will see all the world afterwards.
Across time and generations, books carry the thoughts and feelings, the essence, of the human spirit.
You can never learn less; you can only learn more.
Teaching is a distraction and a burden, but it's also an incredible stimulus. And a reprieve, in a way. When you're trying to work on something and it's not going anywhere, you can go to school and there's a two-and-a-half-hour block of time in which you can accomplish something.
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