This thesis explores the prospect of a design science of technology enhanced mathematics education (TEME), on three levels: epistemic, methodological and pedagogical. The primary domain of the thesis 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 on TEME research, but at the same time suggests a need for a consensual epistemic infrastructure for the field: an agreed 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 epistemic level are operationalised as a methodological framework by projecting them into a specific research setting defined by the demonstrator study. Appropriate methods and procedures are identified for collecting data, organising and interpreting it 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 literature identifies challenges in this domain 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 later 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 Situated abstraction, forming a path from experience to knowledge. 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.