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    paul lockhart Quotes

    Mathematicians enjoy thinking about the simplest possible things, and the simplest possible things are imaginary.
    — Paul Lockhart
    tags: thinking 
     
    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 Lockhart
    tags: time  world  logic  giving  craft  goal  scientist 
     
    [Math is] not at all like science. There's no experiment I can do with test tubes and equipment and whatnot that will tell me the truth about a figment of my imagination. The only way to get at the truth about our imaginations is to use our imaginations.
    — Paul Lockhart
    tags: truth  imagination 
     
    In any case, do you really think kids even want something that is relevant to their daily lives? You think something practical like compound interest is going to get them excited? People enjoy fantasy, and that is just what mathematics can provide - a relief from daily life, an anodyne to the practical workaday world.
    — Paul Lockhart
    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 Lockhart
    tags: chance  truth  secret  divine  god 
     
    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
    tags: society  memory  vague 
     
    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
    tags: reality  world  questions  craft  book 
     
    [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
    Mathematics is not a language, it's an adventure
    — Paul Lockhart
    Doing mathematics should always mean finding patterns and crafting beautiful and meaningful explanations.
    — Paul Lockhart
    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
    tags: time  help  mathematics 
     
    It is the story that matters, not just the ending.
    — Paul Lockhart
    tags: stories 
     
    Mental acuity of any kind comes from solving problems yourself, not from being told how to solve them.
    — Paul Lockhart
    tags: mental  problem 
     
    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
    tags: world  crying  property 
     
    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
    tags: children  trust  child  learn 
     
    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
    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
    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
    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
    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
    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
    tags: wonder  sharing  teaching  hope  ideas 
     
    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
    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
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