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.
If you have any young friends who aspire to become writers, the second-greatest favor you can do them is to present them with copies of The Elements of Style. The first-greatest, of course, is to shoot them now, while they're happy.
The makers of dictionaries are dependent upon specialists for their definitions. A specialist's definition may be true or it may be erroneous. But its truth cannot be increased or its error diminished by its acceptance by the lexicographer. Each definition must stand on its own merits.
Reading a book is like re-writing it for yourself.
Even today, when an Aboriginal mother notices the first stirrings of speech in her child, she lets it handle the "things" of that particular country: leaves, fruit, insects and so forth. "We give our children guns and computer games," Wendy said. "They gave their children the land."
Throughout elementary and middle school, I was used to hearing other words: Smart. Studious. Well-spoken. Well-read. They became pillars of my self-confidence, enabling me to build myself up on what I contributed rather than what I looked like.
But once we realize that people have very different kinds of minds, different kinds of strengths -- some people are good in thinking spatially, some in thinking language, others are very logical, other people need to be hands on and explore actively and try things out -- then education, which treats everybody the same way, is actually the most unfair education.
Subscribe for the occasional hand-picked quote. No noise.