By Wendy Lesley Millroy
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Extra info for An Ethnographic Study of the Mathematical Ideas of a Group of Carpenters (Journal for Research in Mathematics Education. Monograph, N.? 5)
Mathematics is presentedas an ever-increasing set of eternal,immutabletruths. (p. 142) 35 The book ProofsandRefutations(Lakatos,1976),most of which takesthe form of the of a discussionbetweena teacherandhis students,is a "rationalreconstruction" conjectureaboutthe relationship developmentof the prooffor the Descartes-Euler betweenthe numberof vertices(V), edges (E), andfaces (F) of polyhedra,namelythat V- E + F = 2. Lakatosgives a vivid illustrationof how mathematicalknowledgeis The studentsrepresent constructedfromthe interactionsof a groupof mathematicians.
The systemof symbolscomprisinga culturecan be November1988)to some (R. In the studyof culture,symbolicactsare"diagnosed"to "ferretout the importof things"in the processof analysisof social discourse,muchlike the unapparent way a physicianwoulddiagnosesymptomsin a patient(Geertz,1973). He describesthe conceptof cultureas being "strippedof or sociologicalobjectof study," its politicaldimensions,""reducedto an anthropological and"anapologyfor the statusquo"(Giroux,1981,p. 26). He calls for an acknowledgement thatany distinctionbetweencultureandpoweris false.
In this way, mentalenergywas usedin orderto save the physicaleffortof movingextracases. The workerswerefoundto rely on visualization,ratherthanon arithmetic,to solve problems. Examplesof researchof thiskindarecompellingbecausethey raisefundamental questionsaboutthe usefulnessof school-taughtformalmathematicsfor people's lives. Solvingwell-definedacademicmathematicsproblemsin the classroomdoes not adequatelyportraythekindof problemsolvingrequiredin everyday settings,wherethe situationmaybe anythingbutclear-cut.