The Challenge of Developing Statistical Literacy, Reasoning and Thinking PDF
Preview The Challenge of Developing Statistical Literacy, Reasoning and Thinking
THE CHALLENGE OF DEVELOPING STATISTICAL LITERACY, REASONING AND THINKING This page intentionally left blank The Challenge of Developing Statistical Literacy, Reasoning and Thinking Edited by Dani Ben-Zvi University of Haifa, Haifa, Israel and Joan Garfield University of Minnesota, Minneapolis, U.S.A. KLUWER ACADEMIC PUBLISHERS NEW YORK,BOSTON, DORDRECHT, LONDON, MOSCOW eBookISBN: 1-4020-2278-6 Print ISBN: 1-4020-2277-8 ©2005 Springer Science + Business Media, Inc. Print ©2004 Kluwer Academic Publishers Dordrecht All rights reserved No part of this eBook maybe reproducedor transmitted inanyform or byanymeans,electronic, mechanical, recording, or otherwise, without written consent from the Publisher Created in the United States of America Visit Springer's eBookstore at: http://ebooks.springerlink.com and the Springer Global Website Online at: http://www.springeronline.com Contents ListofAuthors vii Foreword ix DavidS.Moore Preface xi DaniBen-ZviandJoanGarfield PARTI: INTRODUCTIONTOSTATISTICALLITERACY, 1 REASONING,ANDTHINKING 1. StatisticalLiteracy,Reasoning,andThinking: 3 Goals,Definitions,andChallenges DaniBen-ZviandJoanGarfield 2. TowardsanUnderstandingofStatisticalThinking 17 MaxinePfannkuchandChrisWild 3. StatisticalLiteracy:Meanings,Components,Responsibilities(cid:3) 47 IddoGal 4. AComparisonofMathematicalandStatisticalReasoning 79 RobertC.delMas 5. ModelsofDevelopmentinStatisticalReasoning 97 GrahamA.Jones,CynthiaW.Langrall,EdwardS. Mooney,andCarolA.Thornton v vi TABLEOFCONTENTS PARTII: STUDIESOFSTATISTICALREASONING 119 6. ReasoningaboutDataAnalysis 121 DaniBen-Zvi 7. LearningtoReasonaboutDistribution 147 ArthurBakkerandKoenoP.E.Gravemeijer 8. ConceptualizinganAverageasaStableFeatureofaNoisyProcess 169 CliffordKonoldandAlexanderPollatsek 9. ReasoningaboutVariation 201 ChrisReadingandJ.MichaelShaughnessy 10. ReasoningaboutCovariation 227 JonathanMoritz 11. Students’ReasoningabouttheNormalDistribution 257 CarmenBatanero,LilianaMabelTauber, andVictoriaSánchez 12. DevelopingReasoningaboutSamples 277 JaneM.Watson 13. ReasoningaboutSamplingDistributions 295 BethChance,RobertdelMas,andJoanGarfield PARTIII: INSTRUCTIONAL,CURRICULARANDRESEARCH 325 ISSUES 14. PrimaryTeachers’StatisticalReasoningaboutData 327 WilliamT.MickelsonandRuthM.Heaton 15. SecondaryTeachers’StatisticalReasoninginComparingTwo 353 Groups(cid:3) KatieMakarandJereConfrey 16. PrinciplesofInstructionalDesignforSupportingtheDevelopment 375 ofStudents’StatisticalReasoning PaulCobbandKayMcClain 17. ResearchonStatisticalLiteracy,Reasoning,andThinking: 397 Issues,Challenges,andImplications JoanGarfieldandDaniBen-Zvi AuthorIndex 411 SubjectIndex 419 List of Authors Bakker,Arthur Gal,Iddo FreudenthalInstitute,UtrechtUniversity, UniversityofHaifa,Israel theNetherlands [email protected] [email protected] Batanero,Carmen Garfield,Joan UniversidaddeGranada,Spain UniversityofMinnesota,USA [email protected] [email protected] Ben-Zvi,Dani Gravemeijer,KoenoP.E. UniversityofHaifa,Israel FreudenthalInstitute,UtrechtUniversity, [email protected] theNetherlands [email protected] Chance,Beth Heaton,RuthM. CaliforniaPolytechnicStateUniversity, UniversityofNebraska-Lincoln,USA USA [email protected] [email protected] Cobb,Paul Jones,GrahamA. VanderbiltUniversity,USA GriffithUniversity,GoldCoastCampus, [email protected] Australia [email protected] Confrey,Jere Konold,Clifford WashingtonUniversityatSt.Louis,USA UniversityofMassachusetts,Amherst,USA [email protected] [email protected] delMas,RobertC. Langrall,CynthiaW. UniversityofMinnesota,USA IllinoisStateUniversity,USA [email protected] [email protected] vii viii LISTOFAUTHORS Makar,Katie Reading,Chris UniversityofTexasatAustin,USA UniversityofNewEngland,Australia [email protected] [email protected] McClain,Kay Sánchez,Victoria VanderbiltUniversity,USA UniversidaddeSevilla,Spain [email protected] [email protected] Mickelson,WilliamT. Shaughnessy,J.Michael UniversityofNebraska-Lincoln,USA PortlandStateUniversity,USA [email protected] [email protected] Mooney,EdwardS. Tauber,LilianaMabel IllinoisStateUniversity,USA UniversidadNacionaldelLitoral,SantaFe, [email protected] Argentina [email protected] Moore,DavidS. Thornton,CarolA. PurdueUniversity,USA IllinoisStateUniversity,USA [email protected] [email protected] Moritz,Jonathan Watson,JaneM. UniversityofTasmania,Australia UniversityofTasmania,Australia [email protected] [email protected] Pfannkuch,Maxine Wild,Chris TheUniversityofAuckland,NewZealand TheUniversityofAuckland,NewZealand [email protected] [email protected] Pollatsek,Alexander UniversityofMassachusetts,Amherst,USA [email protected] Foreword DavidS.Moore PurdueUniversity T his unique book is very welcome, for at least three reasons. The first is that teachers of statistics have much to learn from those whose primary expertise is the study of learning. We statisticians tend to insist that we teach first of all from the base of our knowledge of statistics, and this is true. Teachers at all levels must understandtheirsubject matter,andatadepthatleastsomewhat greaterthanthatof the content they actually teach. But teachers must also understand how students learn, be aware ofspecific difficulties, and consider meansto guide studentstoward understanding. Unaided, we gain skill intuitively, by observing our own teachers and by experience. Teachers below the university level receive specific instruction in teaching—this is, after all, their profession—and this book will improve that instruction where statistics is concerned. Teachers at the university level consider themselves first of all mathematicians or psychologists or statisticians and are sometimes slow to welcome pedagogical wisdom from other sources. This is folly, though a folly typical of professionals everywhere. I have learned a great deal from some of the editors and authors of this book in the past, and yet more from reading thisvolume. Second,thisbookistimelybecausedata-orientedstatisticshasatlastmovedinto the mainstream of mathematics instruction. In the United States, working with data is now an accepted strand in school mathematics curricula, a popular upper- secondary Advanced Placement syllabus adds a full treatment of inference, and enrollment inuniversity statisticscoursescontinuesto increase. (Indeed, statisticsis almost the only subject taught by university mathematics departments that is growing.) Similar trends, particularly in school mathematics, are evident in other nations.Thetitleofthisvolume,withitsemphasison“statisticalliteracy,reasoning, andthinking”reflectstheacceptanceofstatisticsasamainstreamsubjectratherthan ix
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