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Mathematics at work: a study of mathematical organisations in Rwandan workplaces and educational settings
Linköping University, Department of Behavioural Sciences and Learning, Studies in Adult, Popular and Higher Education. Linköping University, Faculty of Educational Sciences.
2010 (English)Doctoral thesis, monograph (Other academic)
Abstract [en]

To make mathematics more significant for the beneficiaries, the problem studied in this thesis is to investigate how to connect mathematical daily practices with educational contexts. The overarching aim is to investigate how to contextualise school mathematics within Rwandan cultural mathematics practices. The content of the thesis reports on the characteristics of mathematical organisations in three workplace settings (taxi driving, house construction and restaurant management) which in turn serve as source for the design of contextualised mathematical activities for student teachers in a teacher education programme. Three levels of mathematical practices are described: (1) mathematical practices that are performed by workers within their respective workplaces, (2) mathematical practices that are performed by student teachers while solving and posing contextualised mathematical tasks for secondary school students, (3) mathematical practices that are carried out by secondary school students. Data gathered from individual and group interviews, transcripts of group discussions and students’ written reports of mathematical work were analysed from the perspective of both activity theory and anthropological theory of didactics. Findings from workplace settings revealed that mathematical organisations performed by workers are characterised by techniques which are functional to the problem at hand, the cultural constraints and the educational background of the workers. As long as they are pragmatic towards the goals of the activity no further justification of the techniques used is needed, resulting in a mathematical organisation with undeveloped know-why (logos). On the contrary, at university and secondary school settings, students justified the used techniques throughout the related taught content of the subject mathematics. Also from each category of mathematical practice, it is shown that while connecting workplaces and educational settings the didactic transposition process was much influenced by the institutional conditions and constraints.

Abstract [sv]

För att göra matematiken betydelsefull för avnämarna är problemområdet som studeras i denna avhandling hur den matematik som finns i samhället kan överbryggas till en undervisningskontext. Syftet med avhandlingen är att undersöka hur man kan kontextualisera skolmatematik i kulturella praktiker i Rwanda. I avhandlingen belyses först matematisk organisation på tre arbetsplatser – i en taxiverksamhet, hos en byggmästare och hos en restaurangägare. Matematik i dessa verksamheter utgör underlag för att konstruera uppgifter för lärarstudenter inom ämnet matematik som först löser uppgifterna och sedan i sin tur konstruerar uppgifter för elever motsvarande årskurs nio i grundskolan. Uppgifterna konstrueras med utgångspunkt i den information studenterna fått om de tre verksamheterna. Datainsamlingen skedde med hjälp av individuella intervjuer, gruppintervjuer och bandinspelade gruppdiskussioner samt studenters och elevers nedtecknade lösningar på respektive uppgifter. Data analyserades med hjälp av aktivitetsteori och antropologisk didaktisk teori. Resultaten från arbetsplatserna visade att matematisk organisation kännetecknades av tekniker som är funktionella för de problem som behövde lösas, de kulturella villkor som förelåg och deltagarnas utbildningsbakgrund. Så länge som teknikerna ledde till önskade mål för verksamheten fanns inga behov att utveckla tekniken som kännetecknades av en matematisk organisation med outvecklad logos. I kontrast till denna strategi sågs studenter och elever i respektive miljöer redovisa de tekniker som användes och motivera dem i enlighet med vad som krävs inom matematikämnet. Den matematiska transpositionsprocessen som utfördes av deltagarna i de olika miljöerna influerades i hög grad av rådande institutionella villkor och begränsningar.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press , 2010. , 160 p.
Series
Linköping Studies in Behavioural Science, ISSN 1654-2029 ; 150
Keyword [en]
Workplace mathematics, school mathematics, activity theory, anthropological theory of didactics, mathematical organisation, didactic transposition, contextualised mathematical tasks.
Keyword [sv]
Skolmatematik, arbetsplatsmatematik, aktivitetsteori, antropologisk didaktisk teori, matematisk organisation, didaktisk transposition, kontextualiserade uppgifter
National Category
Social Sciences
Identifiers
URN: urn:nbn:se:liu:diva-60260ISBN: 978-91-7393-459-6 (print)OAI: oai:DiVA.org:liu-60260DiVA: diva2:355786
Public defence
2010-02-19, Lecture Hall I: 101, House I, Campus Valla, Linköpings universitet, Linköping, 13:00 (English)
Supervisors
Available from: 2010-10-08 Created: 2010-10-08 Last updated: 2016-11-30Bibliographically approved

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