Mathematicians enjoy thinking about the simplest possible things, and the simplest possible things are imaginary. Paul Lockhart More Quotes by Paul Lockhart More Quotes From Paul Lockhart If I had to design a mechanism for the express purpose of destroying a child's natural curiosity and love of pattern-making, I couldn't possibly do as good a job as is currently being done-I simply wouldn't have the imagination to come up with the kind of senseless, soul-crushing ideas that constitute contemporary mathematics education. Paul Lockhart crushjobschildren There is nothing as dreamy and poetic, nothing as radical, subversive, and psychedelic, as mathematics. It is every bit as mind blowing as cosmology or physics (mathematicians conceived of black holes long before astronomers actually found any), and allows more freedom of expression than poetry, art, or music (which depends heavily on properties of the physical universe). Mathematics is the purest of the arts, as well as the most misunderstood. Paul Lockhart expressionlongart 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? Paul Lockhart datateachingteacher 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. Paul Lockhart inspirationmathdiscovery 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. Paul Lockhart inspirationopportunityart Mathematics is about problems, and problems must be made the focus of a student's mathematical life. Painful and creatively frustrating as it may be, students and their teachers should at all times be engaged in the process - having ideas, not having ideas, discovering patterns, making conjectures, constructing examples and counterexamples, devising arguments, and critiquing each other's work. Paul Lockhart mathteacherideas Teaching is not about information. It's about having an honest intellectual relationship with your students. It requires no method, no tools, and no training. Just the ability to be real. And if you can't be real, then you have no right to inflict yourself upon innocent children. Paul Lockhart realteachingchildren 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 Lockhart solveproblemopportunity 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 Lockhart mathchildrenthinking No mathematician in the world would bother making these senseless distinctions: 2 1/2 is a "mixed number " while 5/2 is an "improper fraction." They're EQUAL for crying out loud. They are the exact same numbers and have the exact same properties. Who uses such words outside of fourth grade? Paul Lockhart usemathnumbers Mental acuity of any kind comes from solving problems yourself, not from being told how to solve them. Paul Lockhart kindproblemmath It is the story that matters, not just the ending. Paul Lockhart journeystoriesmath The only thing I am interested in using mathematics for is to have a good time and to help others do the same. Paul Lockhart good-timeshelping-othersmath Doing mathematics should always mean finding patterns and crafting beautiful and meaningful explanations. Paul Lockhart mathbeautifulmeaningful Mathematics is not a language, it's an adventure Paul Lockhart mathematicslanguageadventure There is nothing as dreamy and poetic, nothing as radical, subversive, and psychedelic, as mathematics. Paul Lockhart poeticpsychedelicmathematics [Math] curriculum is obsessed with jargon and nomenclature seemingly for no other purpose than to provide teachers with something to test the students on. Paul Lockhart nomenclaturemathteacher The mathematical question is "Why?" It's always why. And the only way we know how to answer such questions is to come up, from scratch, with these narrative arguments that explain it. So what I want to do with this book is open up this world of mathematical reality, the creatures that we build there, the questions that we ask there, the ways in which we poke and prod (known as problems), and how we can possibly craft these elegant reason-poems. Paul Lockhart educationmathbook I don't see how it's doing society any good to have so many members walking around with vague memories of algebraic formulas and geometric diagrams and clear memories of hating them. Paul Lockhart diagramshatememories 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. 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