An Ethnographic Study of the Mathematical Ideas of a Group by Wendy Lesley Millroy

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)

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The researchprogramis beingcarriedoutby collectingexampleson the mathematical groupsandlinkingthesepracticesto patternsof practicesof culturallydifferentiated reasoningandmodesof thought. Ethnomathematics portrayedsimultaneouslyas the studyof mathematicswithina cultural,historical,and framework,as well as "themathematicswhichis practicedamong anthropological identifiableculturalgroups"(1985, p. , the mathematicsitself is also called D'Ambrosiogives few practicalguidelinesas to whatspecifically ethnomathematics).

26) remindsus thatalthougha classroomis partof theinstitutionof the school,each classroom groupis a uniquecombinationof people,with"itsown identity,its own atmosphere,its own significantevents,its own pleasuresandits own crises.... 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.

Instructioncan be conceivedof as a complex, tacitprocessdevelopedin the particularproblemsituation,ratherthanas an explicitrecipefor problemsolutionthatis availableout of the contextof action. (pp. The integrationof explanation,demonstration, apprenticeship participationin the modelis an importantpointthatis not madeexplicitin otherdiscussions modelof teachingandlearning,such as the work of the wideruse of the "apprenticeship" by Brown,Collins,andDuguid(1989). Brownet al. (1989), drawingon theresearchintocognitionin everydayactivity, as an proposethe ideas of "situatedcognition"4andof "cognitiveapprenticeship" alternativeto conventionalschoolpractices,arguingthat"knowledgeis situated,beingin parta productof the activity,contextandculturein whichit is developedandused"(p.

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