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The largest website for English phrases and quotes

Category: Paul Lockhart

And I’ll go even further and say that mathematics, this art of abstract pattern-making — even more than storytelling, painting, or music – is our most quintessentially human art form. This is what our brains do, whether we like it or not. We are biochemical pattern-recognition machines and mathematics is nothing less than the distilled essence of who we are.

Mathematics is the art of explanation.

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.

geometry, intuition, math, mathematics

I don’t see how it’s doing society any good to have it’s members walking around with vague memories of algebraic formulas and geometric diagrams, and clear memories of hating them.

humor, math, teaching

… That little narrative is an example of the mathematician’s art: asking simple and elegant questions about our imaginary creations, and crafting satisfying and beautiful explanations. There is really nothing else quite like this realm of pure idea; it’s fascinating, it’s fun, and it’s free!

art, elegant, explanations, idea, imaginary, imagination, mathematician, mathematics, questions, simple

Mathematicians enjoy thinking about the simplest possible things, and the simplestpossible things are imaginary.

imagination, math

So [in mathematics] we get to play and imagine whatever we want and make patterns and ask questions about them. But how do we answer these questions? It’s not at all like science. There’s no experiment I can do … The only way to get at the truth about our imaginations is to use our imaginations, and that is hard work.

answer, ask, experiment, hard-work, imagination, imagine, mathematics, patterns, play, questions, truth

If there is anything like a unifying aesthetic principle in mathematics, it is this: simple is beautiful. Mathematicians enjoy thinking about the simplest possible things, and the simplest possible things are imaginary.

aesthetic, beautiful, beauty, imaginary, mathematician, mathematics, principle, simple, simplest, simplicity, thinking, unifying

Doing mathematics should always mean finding patterns and crafting beautiful and meaningful explanations.

beauty, math, mathematics

SIMPLICIO: … You have to [learn to] walk before you can run.SALVIATI: No, you have to have something you want to run toward.

inspiration, learning-process, motivation, philosophy-of-education

If teaching is reduced to mere data transmission, if there is no sharing or excitement and wonder, if teachers themselves are passive recipients of information and not creators of new ideas, what hope is there for their students?

creativity, student, teach, teaching

[Math] curriculum is obsessed with jargon and nomenclature seemingly for no other purpose than to provide teachers with something to test the students on.

education, math, mathematics