Quotessence
Home / Authors / George Polya
George Polya

George Polya Quotes

Mathematician

Filter quotes by topic

AllMathematicsMathScienceProblemMathematicalIfsFirstsSolveEducationMayStudentsDiscoveryMath And ScienceMathematicianIdeasShouldTeacherTheoremsWayKnowledge

Famous George Polya Quotes

“Even fairly good students, when they have obtained the solution of the problem and written down neatly the argument, shut their books and look for something else. Doing so, they miss an important and instructive phase of the work. ... A good teacher should understand and impress on his students the view that no problem whatever is completely exhausted.”

ShouldLooksImportantBookProblemScienceUnderstandingViewsTeacherWrittenMissingStudentsHard WorkSolutionsArgumentMathematicsMathMathematicalPhasesImpressExhaustedNo ProblemGood TeacherGood StudentsMathematical Problems
Author:George Polya
Create image

“One of the first and foremost duties of the teacher is not to give his students the impression that mathematical problems have little connection with each other, and no connection at all with anything else. We have a natural opportunity to investigate the connections of a problem when looking back at its solution.”

GivingFirstsLittlesProblemScienceOpportunityNaturalTeacherStudentsDutySolutionsConnectionsMathematicsImpressionMathematicalLooking BackMathematical Problems
Book:How to solve it: a new aspect of mathematical method
Create image

“Where should I start? Start from the statement of the problem. ... What can I do? Visualize the problem as a whole as clearly and as vividly as you can. ... What can I gain by doing so? You should understand the problem, familiarize yourself with it, impress its purpose on your mind.”

ShouldMindWholeProblemSciencePurposeUnderstandingGainsExperimentsStatementsShould IImpress
Book:How to solve it: a new aspect of mathematical method
Create image

“A great discovery solves a great problem, but there is a grain of discovery in the solution of any problem. Your problem may be modest, but if it challenges your curiosity and brings into play your inventive faculties, and if you solve it by your own means, you may experience the tension and enjoy the triumph of discovery.”

IfsMayMeanPlayProblemScienceEnjoyChallengesSolutionsDiscoveryCuriositySolveTriumphTensionFacultyGrainProblem SolvingModest
Author:George Polya
Create image

“Solving problems is a practical skill like, let us say, swimming. We acquire any practical skill by imitation and practice. Trying to swim, you imitate what other people do with their hands and feet to keep their heads above water, and, finally, you learn to swim by practicing swimming. Trying to solve problems, you have to observe and to imitate what other people do when solving problems, and, finally, you learn to do problems by doing them.”

PeopleTryingProblemHandsWaterEducationPracticeFeetSkillsMathematicsSolveMathPracticalsAcquireSwimSwimmingProblem SolvingImitationHands And FeetPractical Skills
Author:George Polya
Create image

“The first and foremost duty of the high school in teaching mathematics is to emphasize methodical work in problem solving...The teacher who wishes to serve equally all his students, future users and nonusers of mathematics, should teach problem solving so that it is about one-third mathematics and two-thirds common sense.”

ShouldFirstsTwoProblemSchoolWishCommonEducationTeachTeacherTeachingStudentsDutyHigh SchoolThirdsMathematicsMathCommon SenseUsersProblem SolvingMethodical
Author:George Polya
Create image