The ability to learn and the passion to do so may be innate human characteristics. Education, on the other hand, concerns identifying specific structures of knowledge and directing learning towards them by assembling resources and activities under cultural, institutional, social, and psychological constraints. In other words, education is designed learning, and as such, an incredibly complex and inherently multidisciplinary endeavour. Any framework attempting to address this domain needs to identify methodological tools which allow it to confront these complexities. Such tools need to balance the need for a crisp directive for action with a rich representation of context, intentions and possible solutions. The characterisation of education as designed learning establishes a multi-faceted link between design and epistemology, or the creation of knowledge. This link is a motif that weaves through this thesis. Design emerges as a method of study, an object of study and an outcome of study, leading to an overarching theme of this thesis:
consider the study of technology-enhanced mathematics education as a design
science; highlight the implications of such a paradigm, and propose ways to
theorize design in a manner which draws both on educational research and
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. The
pragmatist nature of a design stance in educational research entails a tight
dependency between the three levels of epistemology: the method by which we
study education (its normative epistemology) links our understanding of how
people learn (genetic epistemology) to how we design artefacts for learning
(generative epistemology). The specific aims of this thesis are derived from
this realisation, namely, to:
potential elements of an epistemic
infrastructure for a design science of TEME.
elaborate the elements identified into a coherent methodological framework in a given research TEME context.
methodology in a problem domain and demonstrate its potential by producing a
contribution towards a language of pedagogical
patterns for TEME.
characteristics of design science, derived from Herbert Simon’s work (1969),
were found to be highly relevant to the study of education: a value-driven
agenda, a functional axis of decomposition and the role of representation. The
value dimension is reflected in education’s remit to improve the life of
individuals and communities. A functional axis of decomposition means that the
objects of educational research should be categorized and analysed according to
their effect rather than their structure. The importance of role of
representation is generally accepted in the learning sciences. Iterative
methodologies are gaining ground, in particular where technology is involved.
design approach was found to be better adapted to the complex and dynamic
nature of the circumstances and questions studied by educational science. This
approach has the potential to offer a cohesive paradigm, bridging across
practice and multiple theories. These
advantages are even more salient in the face of the rapid pace of change
induced by technological developments, calling for agile, responsive and
proactive approaches to educational research.
argument for an inherently iterative method of inquiry resonates well with the
growing tradition of design-based research (DBR) in TEME. DBR was characterised
as pragmatic, committed to theoretical as well as practical innovation, highly
interventionist, iterative. DBR produces modest theories, constrained to
well-defined domains of learning and contexts of design. A design science of
TEME produces design knowledge characterised as: problem driven, solution
oriented, value laden; Situated in context; and holistic, i.e. inherently
review of the field identified the need for a clearly articulated consensual
epistemic infrastructure; the explicit and implicit rules and assumptions which
bound the discourse of the scientific community, and a logical system by which
claims are presented and justified, independently of their content. Some
desirable features of such an infrastructure emerged from the discussion:
arguments should be accessible to the
scientific community, as well as by practitioners and by policy makers; the
processes of design study should be transparent
and traceable; the forms used for communicating results should be
sufficiently expressive to articulate
all that is needed to support the above requirements. These forms should
promote cumulativity and aggregation
of knowledge, and its organisation should follow a functional-pragmatist orientation aligned with the functional axis
of design knowledge.
review of existing design approaches to educational research identified common
methodological characteristics, including a dual focus on practical and
theoretical contributions, a highly interventionist and agile attitude, and a
cycle of iterative research. This cycle includes phases of theory, design,
implementation, execution (experiment / practice), articulation of experience,
interpretation, evaluation and analysis, and feedback to both theory and
design. The products of this cycle are validation or critique of existing
theory, evidence regarding the effectiveness of artefacts and practices in
well-defined settings, and innovations in practice and theory. A frequent
by-product of research is the synthesis of multiple frameworks. This cycle is
embedded in a meta-cycle, which includes a framing phase, an empirical phase
and a retrospective analysis phase.
was identified as a powerful epistemic form, leading to a proposal for a
formalisation of design narratives as a form of scientific discourse. Design
patterns, organised into pattern languages, emerged as a promising form for
encoding design knowledge in educational research. The constructs identified at
the epistemological level were operationalised as a methodological framework by
projecting them into a specific research setting of the demonstrator study.
the research setting was described, it was used to illustrate how these
constructs interact in practice. Special attention was given to the trajectory
from experience to structured theory, focusing on the processes by which data
was collected and how design narratives and design patterns were produced from the
data and validated. The result is a description of a methodological framework
and a set of instruments for the demonstrator study, from data collection and
management, through interpretation and systemisation of observations as design
narratives and on to the formalisation of research outcomes as design patterns.
The latter provided a full specification for implementation of the analytical
hemicycle of the design experiment cycle and of the retrospective analysis
phase of the design research meta-cycle.
structured process of selection and construction of design narratives was
identified, using Bruner’s ten principles (1991) as guidelines. These principles,
adapted to the needs of scientific form, were expressed in the design narrative
template. Design patterns were extracted from design narratives through a six-step
process devised to capture, systemise and substantiate the key design elements.
This was followed by a phase of refactoring: structural manipulations which gave
the pattern language as a whole greater coherence.
methodological framework was applied in the demonstrator domain to the question
of learning about number sequences. The demonstrator study followed the design
research cycle and meta-cycle noted above. The framing phase produced a
pragmatic review of the literature, whose aim was to identify key challenges in
the domain and raise conjectures as to ways in which they may be addressed.
These conjectures were translated into the design of activities and the
technology to support them. The iterative process of design, implementation and
evaluation was captured as a set of design narratives that were analysed to
produce the collection of design patterns. 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.
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. Number patterns and sequences are
broadly accepted as a viable gateway to advanced mathematical subjects which is
intuitively appealing to learners. Yet the review exposed several pedagogical
and epistemic issues concerning this topic. Foremost among these are the
difficulties of formulating a structural view of sequences, specifically with
respect of the process-product duality and recursive vs. closed form. These
difficulties were linked to a dissonance between intuitive perceptions and the
prevalent school representations of mathematical objects. This observation was
inspected in the broader context of the relationship between communication,
representation and meaning in mathematical learning. Combining the
communicational approach with the concept of situated abstraction led to
considering narrative as a fundamental social and cognitive epistemic force.
Narrative form would appear to be at odds with the nature of mathematics,
raising the question of their reconciliation – which has been a central
question of the demonstrator study. Bringing narrative into the domain of
constructionist learning and educational programming raised questions regarding
its manifestation in computer-based representations, specifically, the
representatiuon of number sequences. The Streams
design pattern was proposed as a promising candidate. The union of the various
approaches calls for educational designs which weave construction,
communication and collaboration.
observations and conjectures emerging from the review of the literature were
translated into design of activities and tools. These were tested and refined
in two sites over three years. The process of design and the outcomes of
testing were captured as series of nine design narratives which form the
empirical content of this thesis. They are the first tier of interpretation,
not the data itself. Each narrative recounts a particular incident, defined by
a single problem to be solved or task to be accomplished.
generalisable observations stood out: the potential of the Streams design pattern, the roles and
characterisations of narrative, the importance of combining construction, communication
and collaboration, and the recursive intuition of sequences. Among the more
general themes that surfaced were the co-evolution of technology and pedagogy,
the interdependence of interface and substance, and consequently the fluidity
of design and the need for flexibility and malleability.
Applying the methodological framework to a
demonstrator study yielded a contribution towards a pedagogical pattern
language of construction, communication and collaboration in TEME. This
contribution includes thirteen design patterns, supported by nine design
narratives. Seven of these patterns have been fully specified, while six others
are provided as thumbnails. The design patterns unpack the general themes
emerging from the design narratives, translating them into theoretically and
empirically substantiated context-aware guidelines for educational design. This
collection of design narratives and patterns demonstrates the validity of the
proposed approach in dealing with the immense complexity of designing for
learning, and calls for further work in this vein.
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 a design science of TEME which combines design narratives and
design patterns into structured cycles of enquiry. This framework is supported
both theoretically and empirically. It is, inter alia, used to derive a
contribution towards a pedagogical pattern language of construction,
communication and collaboration in TEME.