“I've always liked trees. And then, growing up, I took an interest in ecology, hedges being destroyed, the landscape being turned into prairies.” InterestGrowing UpGrowingTreeDestroyedLandscapeEcologyPrairie Author:Clive Anderson
“I am going to have to stick to the script. If I muck around with the words it will defeat the object.” IfsObjectsSticksDefeatScripts Author:Clive Anderson
“Doing mathematics should always mean finding patterns and crafting beautiful and meaningful explanations.” ShouldMeanBeautifulFindingsMathematicsPatternsMathMeaningfulExplanation Author:Paul Lockhart
“Mental acuity of any kind comes from solving problems yourself, not from being told how to solve them.” KindProblemSolveMathProblem Solving Author:Paul Lockhart
“A good problem is something you don't know how to solve. That's what makes it a good puzzle and a good opportunity.” KnowsProblemOpportunityKnow HowSolvePuzzlesGood Opportunity Author:Paul Lockhart
“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?” ThinkingWantFeelsChildrenHardSeemsCapableArgumentOur ChildrenMathematicsMathConclusionWhy NotDon't TrustTriangles Author: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?” IfsIdeasWonderTeacherTeachingInformationStudentsMereCreatorDataExcitementPassiveNew IdeasTransmission Author: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.” IfsArtProblemInspirationTogetherOpportunityStudentsActivityDiscoveryMathematicsDenyProofExplanationFrustratedConjecture Author:Paul Lockhart
“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.” HateMemoriesClearWalkingMembersFormulasVagueDiagramsGeometric Author:Paul Lockhart