Thesis (PhD)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: The special needs community is in the midst of a philosophical and physical shift from a segregated system to an integrated system, not only in placement, but more importantly, in terms of learning and affording learners with special needs access to mainstream curricular materials. Mathematical modelling, or challenging mathematics problems solved in small groups, is part of the Australian mainstream curriculum. The purpose of the study was to investigate the way special needs learners learn mathematics from a modelling learning environment. To do this, it was necessary to identify the critical characteristics of the best practice in teaching and learning for learners with special needs, and the critical features of modelling. One theory of learning that has the capacity to promote special needs learners' interaction with mathematical modelling is Feuerstein’s theory of Structural Cognitive Modifiability. A hypothetical learning trajectory was designed for special needs learners at middle school according to general design principles from theory, which was adapted to the learning characteristics of the class. The learning environment comprised of three challenging modelling tasks, together with recommended implementation and support conditions in the classroom. Specifically, the research sought to investigate the ways in which special needs educators can support the higher reasoning processes of special needs students during modelling through design in general, and through mediation specific to each learner. The research took the form of a qualitative study, combining the phases of design-based research with a multiple case study approach. Three cases were analysed in depth. Empirical data were collected through a range of qualitative methods, which included data from student files, field observations, video and audio recordings, focus group interviews with students, and the input of various collaborators across the different phases of planning, design, implementation, and revision. Data were coded and analysed inductively according to emerging patterns and themes. Findings suggest that the use of modelling was successful when implemented with certain characteristics defined in the literature, and that it enabled learners to learn mathematics and also to develop additional outcomes such as social skills and language. During this study, learners' higher-order reasoning was supported through dynamic assessment and subsequent mediation. / AFRIKAANSE OPSOMMING: Die onderwysgemeenskap vir leerders met spesiale behoeftes bevind hulle in die middel van filosofiese en fisiese verskuiwings van 'n geskeide sisteem na 'n geïntegreerde sisteem. Dit omvat die plasing van leerders, maar meer belangrik ook die bemoontliking van toegang van hierdie leerders tot hoofstroom kurrikulêre materiale. Wiskundige modellering, en uitdagende wiskundeprobleme wat deur leerders in klein groepies opgelos word, is deel van die Australiese hoofstroomkurrikulum. Die doel van die studie was om die wyse te ondersoek waarvolgens leerders met spesiale behoeftes wiskunde in 'n modelleringsomgewing leer. Dit is gedoen deur die belangrike kenmerke van beste praktyk vir onderrig en leer in spesiale onderwys, asook die kritiese kenmerke van modellering, te vind. Een leerteorie wat die interaksie van leerders met spesiale behoeftes met wiskunde bevorder, is Feuerstein se teorie van Strukturele Kognitiewe Modifieerbaarheid. 'n Hipotetiese leertrajek was ontwerp vir leerders met spesiale behoeftes op middelskoolvlak. Empiriese data is deur 'n reeks kwalitatiewe aksies: data van studentelêers, veldwaar-nemings, video en klankopnames, fokusgroeponderhoude met studente, asook die insette van verskeie medewerkers oor die verskillende fases van beplanning, ontwerp, implementering en hersiening gegenereer. Die spesifieke leerkenmerke van hierdie leerders volgens algemeen-teoretiese en lokaalgekontekstualiseerde ontwerpbeginsels is nagekom. Die leertrajek het bestaan uit drie uitdagende modelleringsprobleme met aanbevole implementering en ondersteuningsriglyne in die klaskamer. Die navorsing het spesifiek gesoek na wyses waarop hierdie leerders se hoër beredeneringsvaardighede deur hul onderwysers, volgens elkeen se eie behoefte gedurende modellering, deur ontwerp in die algemeen en mediasie in die besonder, ondersteun kan word. Die navorsing, 'n kwalitatiewe studie, was gekombineer met fases van ontwikkelingsgebaseerde ontwerp wat uitgespeel het in 'n veelvuldige gevallestudiebenadering. Drie gevalle is in diepte ondersoek. Data was induktief gekodeer en geanaliseer volgens ontluikende patrone en temas. Bevindinge wys uit dat die gebruik van modellering suksesvol was wanneer die implementering volgens spesifieke kenmerke in die literatuur was. Dit het leerders instaat gestel om wiskunde te leer asook om addisionele uitkomste soos sosiale vaardighede en taal te ontwikkel. In hierdie studie is hoër-orde denke ondersteun deur dinamiese assessering en voortspruitende mediasie.