An analysis of learning characteristics, processes, and representations in mathematical modelling of middle school learners with special educational needs

[摘要] ENGLISH ABSTRACT: The special needs community is in the midst of a philosophical and physical shift from asegregated system to an integrated system, not only in placement, but more importantly, interms of learning and affording learners with special needs access to mainstream curricularmaterials. Mathematical modelling, or challenging mathematics problems solved in smallgroups, is part of the Australian mainstream curriculum.The purpose of the study was to investigate the way special needs learners learn mathematicsfrom a modelling learning environment. To do this, it was necessary to identify the criticalcharacteristics 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 promotespecial needs learners' interaction with mathematical modelling is Feuerstein's theory ofStructural Cognitive Modifiability. A hypothetical learning trajectory was designed forspecial needs learners at middle school according to general design principles from theory,which was adapted to the learning characteristics of the class. The learning environmentcomprised of three challenging modelling tasks, together with recommended implementationand support conditions in the classroom. Specifically, the research sought to investigate theways in which special needs educators can support the higher reasoning processes of specialneeds students during modelling through design in general, and through mediation specific toeach learner. The research took the form of a qualitative study, combining the phases ofdesign-based research with a multiple case study approach. Three cases were analysed indepth. Empirical data were collected through a range of qualitative methods, which includeddata from student files, field observations, video and audio recordings, focus groupinterviews with students, and the input of various collaborators across the different phases ofplanning, design, implementation, and revision. Data were coded and analysed inductivelyaccording to emerging patterns and themes. Findings suggest that the use of modelling wassuccessful when implemented with certain characteristics defined in the literature, and that itenabled learners to learn mathematics and also to develop additional outcomes such as socialskills and language. During this study, learners' higher-order reasoning was supportedthrough dynamic assessment and subsequent mediation.

[发布机构] Stellenbosch University