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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)
The impetusfor thesestudieshascome froma concernaboutthe failureof mathematicseducationfor groupssuchas ethnicminorities,oppressed majorities,women,girls, andworking-classchildren(Brodie,1988). 2.
Gerdes(1986, p. 12) claimsthatby "unfreezingthis frozenmathematics," peoplecan be encouragedthattheywerecapableof developingmathematicsin the pastand can continueto do so. Gerdes(1988b,p. 6) suggeststhatpupilscould be given opportunitiesto "reinvent"traditionaltechniquesof, for instance,housebuildingand and"explore"the frozenmathematics. Forinstance,Fasheh(1988) observedthathis illiterateseamstress motherhada richandcomplexrelationshipto mathematicsandthatthe mathematicsshe used was integratedinto herworldin sucha way thatit remainedout of his grasp.
The simplemodelof actionandreflectionon a problematicin the constructivist cycle has practicaluses duringfieldworkdesignedto recognizeanddescribethe mathematicalpracticesof a communityof people,since problemsolving is one of the occasionsduringwhichtheirmathematizing is demonstrated. It is in reflectingon the actionsandthereflectionsobservedthatthe possibility of describingthe tacitknowledgedevelops. Traditional appreciatethe powerof constructingmultiplerepresentations school mathematicscan moreeasily be seen as one possibleconceptionof mathematicsand benchmarkaccordingto whichall the mathematicalendeavorsof not an international humankindmustbe judgedrightor wrong.