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.