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)
In everydaysituationsin the grocerystore,school-taught arithmeticseemedratheruseless. In the studyby de la Rocha(1985)withparticipants in a WeightWatchersdieting of foods, the emphasiswas also on program,a programthatrequiresprecisemeasurement time savingandefficiencyandnot on employingschool-learnedarithmeticskills. The samecontainerwas then used repeatedlyto eliminatethe needfor continualmeasuring. Forinstance,insteadof collectingitemsfromshelves in the warehouse in the sequencelaid out by the orderforms,dairyworkersorganizedandcoordinatedtheir activitiesin such a way as to minimizethe distanceto be traveledaroundthe huge warehouse.
As with Lakatos,Tymoczko'sview of mathematicsdoes not seem to encompassthe creatorsandusersin theworldoutsideof the ivory tower:the children, 36 students,and"ordinary" peoplewho also createanduse mathematicsto explain,convince, andcommunicate. Steffe describesthis as partof the "mathematics of children"andvoices his explicitintentionthat"school mathematicswill at leastincludethe mathematicsof children"(1986, p. 138). Apartfromthe childrenandstudentswho havebeenleft out as genuinemakersand usersof mathematics,othergroupshavealso consistentlybeendeniedthe statusof fully Harris(1987)pointsoutthatin mosthistoriesof mathematics,women fledgedparticipants.
I intendin the presentstudyto drawupon my experiencesas a carpentryapprenticeto commenton how I believe some of the characteristicsof sucha teachingandlearningsituationcouldbe used in the mathematics classroom. Knowing-in-Actionand Reflection-in-Action Schon(1983, 1987),in his proposalto redesignprofessionaleducationfor "reflectivepractice,"has writtenextensivelyabouthis researchinto "theexperienceof learningby doingandthe artistryof good coaching"(1987, p. 17). Nobodyelse can see for him andhe cannotsee just by being"told,"althoughthe rightkindof tellingmay guidehis seeing andthushelphim to see whathe needsto see.
An Ethnographic Study of the Mathematical Ideas of a Group of Carpenters (Journal for Research in Mathematics Education. Monograph, N.? 5) by Wendy Lesley Millroy