EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Mor, Yishay

OpenGrey Repository

A design approach to research in technology enhanced mathematics education

This thesis explores the prospect of a design science of technology enhanced mathematics education
(TEME), on three levels: epistemological, methodological and pedagogical. Its primary domain is the
identification of scientific tools for design research in TEME. The outputs of this enquiry are
evaluated by a demonstrator study in the domain of secondary school mathematics.
A review of existing literature establishes a need for a design perspective in TEME research, but at
the same time suggests a need for a consensual epistemic infrastructure for the field: a shared set of
rules, processes and representations which bound and support its scientific discourse. Three
constructs are proposed towards such an infrastructure: design narratives, design patterns, and the
cycles of design research in which they are embedded. The first two are representations of domain
design knowledge; the latter is a description of a design-centred scientific process.
The three constructs identified at the epistemological level are operationalised as a methodological
framework by projecting them into a specific research setting of the demonstrator study.
Appropriate methods and procedures are identified for collecting data, organising and interpreting
them as design narratives, and extracting design patterns from these narratives.
The methodological framework is applied in the demonstrator domain to the question of learning
about number sequences. A review of the educational research on number sequences identifies
challenges in this area related to the tension between learners' intuitive concept of sequences and
the dominant curricular form. The former appears to be recursive in nature and narrative in form,
whereas the latter is a function of index expressed in algebraic notation. The chosen design
approach combines construction, collaboration and communication. It highlights the need for
representations and activities which lead learners from intuitive concepts to formal mathematical
structures.
Three interleaved themes connect the primary and the demonstrator domains: narrative,
systematisation and representation. Narrative emerges as a key element in the process of deriving
knowledge from experience. Systemisation concerns the structured organisation of knowledge. The
tension between the two calls for representations which support a trajectory from the intuitive to
the structural.
The main outcome of this study is a methodological framework for design science of TEME which
combines design narratives and design patterns into structured cycles of enquiry. This framework is
supported both theoretically and empirically. Inter alia, it is used to derive a contribution towards a
pedagogical pattern language of construction, communication and collaboration in TEME

UCL Discovery

http://discovery.ucl.ac.uk/10006478/1/__d6_Shared%24_SUPP_Library_User%20Services_Circulation_Inter-Library%20Loans_IOE%20ETHOS_ETHOS%20digitised%20by%20ILL_MOR%2C%20Y.pdf

A design approach to research in technology enhanced mathematics education

Abstract

Similar works

Full text

Available Versions

OpenGrey Repository

UCL Discovery