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An Appreciation of Efraim Fischbein, 1920-1998Author(s): Dina TiroshSource: Educational Studies in Mathematics, Vol. 37, No. 1 (1998 - 1999), pp. ix-xPublished by: SpringerStable URL: http://www.jstor.org/stable/3482679

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AN APPRECIATIONOF EFRAIMFISCHBEIN,1920-1998

EfraimFischbeindied on Wednesday,22 July 1998. His death is a greatloss to his family,to his studentsandcolleaguesatTel AvivUniversityandto the entire communityof mathematics ducators.Fischbeinwas bornin Romania, n 1920. He taughtmathematicsandphilosophyin high school. In 1949 he was offered the position of lec-turer at the departmentof Departmentof EducationalPsychology at theUniversityof Bucharest,and from 1959 to 1975 he served as the headof the EducationalPsychology department t the Instituteof Psychologyin Bucharest.His work in child development,cognitive psychology,andmathematics ducationduring hatperiod s characterized y theoriginal-ity of the questionshe asked,his systematicmethodsof explorationandtheinsightshe provided n the interpretationf the data.His manybooks andarticlescreated nternationalnterest,and he was frequently nvited,frombehindtheIronCurtain,o conferencesandmeetings n westerncountries.By 1975, Efraim Fischbeinwas internationallyknown as one of theleading researchersn mathematics ducation.After leavingRomaniaforIsrael,he was offered an appointment s professorof mathematics duca-tion at Tel Aviv Universitywhere he founded the Departmentof ScienceEducationand continuedto teach, be active and creative n research,andsupervisemany researchstudents,until his last moments.

Efraim Fischbein is best known for his creative, systematic,coherentand influentialcontribution o knowledgeabout, and understanding f therole of intuition n learningandteachingmathematics nd science.His firstcontributionsn this areaconcerned ntuitionsof probability ndcombinat-orics; they establisheda strongbridgebetween psychology andeducationand were published nternationallynjournals n both domains, ncludingEducationalStudies in Mathematicsand The British Journalof Educa-tionalPsychology.Inthe preface o Fischbein'sbook 'The intuitivesourcesof probabilistichinking n children'(Reidel, 1975), Hans Freudenthal e-latedwarmlyto Fischbein'sapproachandwrote: 'I interpret ndwelcomeFischbein'swork as a majorbreakthroughn mentalityof research n thefield of developmentalpsychology.... I considerFischbein's shiftingthestressfromconceptsto intuitionsas a cognitive advancewhich maybenefitteachingmathematics.'

Ad EducationalStudies in Mathematics 37: ix-x, 1999.

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Fischbein'sdesire to understandinghenatureof intuitive hinkingandtherelationshipbetween intuitive and other forms of thinkingis evidencedin his furtherwork on infinity,on implicit models of multiplicationanddivision, on irrationalnumbers,on the relationshipbetween intuitionsandproofs, on the interactionbetween the formal, the algorithmicand theintuitivecomponents n mathematicalactivities,andothertopics. In 'In-tuition in Science and Mathematics'(Reidel, 1987) Fischbeinproposeda theoretical,comprehensiveview of the domainof intuition,identifiedand organizedthe relatedexperimental indings,and described and dis-cussedtheireducationalanddidactic mplications. nthisbook,as in otherpublications,he coined new, useful terminology(e.g., primary ntuitions,secondary ntuitions),raisedproblematic ssues (e.g., the educationaldi-lemma) and stimulated urtherrelatedresearch,thus leadingthe field ofmathematicseducationforward.It is not surprising hathis articleswerepublished n fourlanguagesandtranslated ntomanyothers.Anothermajorcontribution f EfraimFischbein o thedomainof math-ematics educationrelates to the creation and the organizationof PME,The InternationalGroup for the Psychology of MathematicsEducation.He was theorganizer,he firstpresidentand anhonorarymemberof PME.He activelyparticipatedn almost all the annualmeetings of PME, andcontributeda great deal to the ongoing developmentof the organization.His imprinton this important onstituentof ourfieldwill be felt formanyyearsto come.At the beginningof 1998, EfraimFischbeinstartedworkingon a thirdbook entitled'Intuitions,SchemataandModels in Mathematical ndSci-entificReasoning'.Unfortunately, e was unable to finish this work.Buthis books, his articles,andmainlyhis ideas will stay with us forever,andhis contributiono mathematicseducationwill serve as a permanentme-morialto him, and as a never-ending ource of inspirationor us all.

DINA TIROSH