A design approach to research in technology enhanced mathematics education
Year: 2010
Type: dissertation
Abstract: This thesis explores the prospect of a design science of technology enhanced mathematics education \n(TEME), on three levels: epistemological, methodological and pedagogical. Its primary domain is the \nidentification of scientific tools for design research in TEME. The outputs of this enquiry are \nevaluated by a demonstrator study in the domain of secondary school mathematics. \nA review of existing literature establishes a need for a design perspective in TEME research, but at \nthe same time suggests a need for a consensual epistemic infrastructure for the field: a shared set of \nrules, processes and representations which bound and support its scientific discourse. Three \nconstructs are proposed towards such an infrastructure: design narratives, design patterns, and the \ncycles of design research in which they are embedded. The first two are representations of domain \ndesign knowledge; the latter is a description of a design-centred scientific process. \nThe three constructs identified at the epistemological level are operationalised as a methodological \nframework by projecting them into a specific research setting of the demonstrator study. \nAppropriate methods and procedures are identified for collecting data, organising and interpreting \nthem as design narratives, and extracting design patterns from these narratives. \nThe methodological framework is applied in the demonstrator domain to the question of learning \nabout number sequences. A review of the educational research on number sequences identifies \nchallenges in this area related to the tension between learners' intuitive concept of sequences and \nthe dominant curricular form. The former appears to be recursive in nature and narrative in form, \nwhereas the latter is a function of index expressed in algebraic notation. The chosen design \napproach combines construction, collaboration and communication. It highlights the need for \nrepresentations and activities which lead learners from intuitive concepts to formal mathematical \nstructures. \nThree interleaved themes connect the primary and the demonstrator domains: narrative, \nsystematisation and representation. Narrative emerges as a key element in the process of deriving \nknowledge from experience. Systemisation concerns the structured organisation of knowledge. The \ntension between the two calls for representations which support a trajectory from the intuitive to \nthe structural. \nThe main outcome of this study is a methodological framework for design science of TEME which \ncombines design narratives and design patterns into structured cycles of enquiry. This framework is \nsupported both theoretically and empirically. Inter alia, it is used to derive a contribution towards a \npedagogical pattern language of construction, communication and collaboration in TEME.
Source: IOE EPrints
Author: Yishay Mor
Language: English
Subfield: Education
Field: Social Sciences
Domain: Social Sciences
SDG: Quality education
Open Access status: green
OpenAlex ID: W160371084