Inspired by Enactivist philosophy yet in dialog with it, we ask what theory of embodied cognition might best serve in articulating implications of Enactivism for mathematics education. We offer a blend of Dynamical Systems Theory and Sociocultural Theory as an analytic lens on micro-processes of action-to-concept evolution. We also illustrate the methodological utility of design-research as an approach to such theory development. Building on constructs from ecological psychology, cultural anthropology, studies of motor-skill acquisition, and somatic awareness practices, we develop the notion of an “instrumented field of promoted action”. Children operating in this field first develop environmentally coupled motor-action coordinations. Next, we introduce into the field new artifacts. The children adopt the artifacts as frames of action and reference, yet in so doing they shift into disciplinary semiotic systems. We exemplify our thesis with two selected excerpts from our videography of Grade 4–6 volunteers participating in task-based clinical interviews centered on the Mathematical Imagery Trainer for Proportion. In particular, we present and analyze cases of either smooth or abrupt transformation in learners’ operatory schemes. We situate our design framework vis-à-vis seminal contributions to mathematics education research.

Key words: mathematics, education, motor learning, conceptual learning, motor problem, conceptual metaphor

Open peer commentary on the article “Developing a Dialogical Platform for Disseminating Research through Design” by Abigail C. Durrant, John Vines, Jayne Wallace & Joyce Yee. Upshot: My comments should contribute to making the next RTD conference even more “successful.” If we are to advance design research, changing the format of conferencing is secondary to changing the culture of inquiry, although they surely intertwine.

Open peer commentary on the article “Design Research as a Variety of Second-Order Cybernetic Practice” by Ben Sweeting. Upshot: I claim that the parallels between design research, second-order cybernetics (SOC) and second-order science (SOS), as discussed by Sweeting in the target article, are more explicit in digital design. The discussion of SOC and SOS can point towards the creation of an epistemological foundation to digital design, where self-reflexivity and the inclusion of the observer are central questions.

Open peer commentary on the article “Design Research as a Variety of Second-Order Cybernetic Practice” by Ben Sweeting. Upshot: It is suggested that the main arguments of the target article could be constructed in an easier way and would become even more compelling if a radical consideration of the systemic nature of design were taken into account.

Context: Practice-based design research is becoming more widely recognized in academia, including at doctoral level, yet there are arguably limited options for dissemination beyond the traditional conference format of paper-based proceedings, possibly with an exhibition or “demonstrator” component that is often non-archival. Further, the opportunities afforded by the traditional-format paper presentations is at times at odds with practice-based methodologies being presented. Purpose: We provide a first-hand descriptive account of developing and running a new international conference with an experimental format that aims to support more analogously the dissemination of practice-based design research. Method: Our approach herein is broadly interpretative, phenomenological and critically reflective in orientation, to analyze our own experiential insights from the conference conception, through to the event itself and post-conference reflections, alongside the reflections fed back by conference delegates. Results: We have found the roundtable format continues to function well for creating a discursive interactional context. However issues arose around the crucial nature of the session chair’s role in enabling rich and multi-voiced discussion and how presenters’, organizers’ and delegates’ voices were captured and documented, with implications for further developing the conference design. Looking forward, there are also questions raised about: balancing the stringency of a rigorous review process with provision of an encouraging platform for early-career researchers; and balancing the need for clear criteria and formatting standards (for assessing quality and rigor in submitted work) with the “openness” of the submission template and formatting guidelines (to encourage pioneering developments in visual argumentation. Implications: The article provides a valuable resource for practice-based design researchers who are committed to generating research understanding through applied endeavors (making things) and/or writing. This includes designers who are new to research cultures. It should also appeal to those working in interdisciplinary research in collaboration with design practitioners (but who may not be practitioners themselves. The conference aims to foster and support a burgeoning “research through design” academic community and to provide a fitting dissemination platform for this community. We hope that the conference will encourage academic communities to give proper consideration to the concept of design as a knowledge-generating activity. Constructivist content: Knowledge about design research is generated from meaningful interaction between people and artifacts as part of the unfolding conference experience. The organizational features of the conference aim to support knowledge dissemination through dialogical relations between people and things in particular contexts of interaction.

Key words: Research through design, practice-based research, dialogical relationships, embodied knowledge, new materialities, discursive dissemination platform

Open peer commentary on the article “Developing a Dialogical Platform for Disseminating Research through Design” by Abigail C. Durrant, John Vines, Jayne Wallace & Joyce Yee. Upshot: The commentary reflects on Durrant et al. from the perspective of a conference participant. It also addresses the dynamics at the meeting point of multidisciplinary practice-led design research.

Much design research, including much research in the computer-aided architectural design field, is based on the assumption that the process of designing is observable and that what happens in designing can be known, explicitly described and shared. In this paper I examine this assumption from my subjective viewpoint and conclude that designing occurs behind a blind spot. It can be concluded that existing design process models used in the “science of design” are based on invention rather than on empirical evidence, which in turn suggests that science should be studied as a form of design instead of studying designing scientifically.

Key words: design research, observation, design process, language

Presenting a hard-to-predict typography-varying system predicated on Nazi-era cryptography, this paper illustrates conditions under which unrepeatable phenomena can arise, even from straight-forward mechanisms. such conditions arise where systems are observed from outside of boundaries that arise through their observation, and where such systems refer to themselves in a circular fashion. This illustration aims to show the dilemma of scientific design research: Objective outsiders are mystified while those subjectively involved understand.

Key words: system boundaries, design, objectivity, subjectivity.

Purpose: The scientific criterion of determinability (predictability) can be framed in realist or in constructivist terms. This can pose a challenge to design researchers who operate between scientific research (which favors a realist view of determinism/indeterminism) and design practice (which favors a constructivist view of determinability/indeterminability). This paper aims to develop a framework to navigate this challenge. Design/methodology/approach – A critical approach to “scientific” design research is developed by examining the notion of (in)determinism, with particular attention to the observer-based projection of systemic boundaries, and the constructivist understanding of how such boundaries are constituted. This is illustrated using automata theory. A decision-making framework is then developed based on a diagram known as the epistemological triangle. Findings: The navigation between determinism as a property of the observed, and determinability as a property of the observer follows the navigation between realist and constructivist perspectives, and thus has a bearing on the navigation of the kinds of design research distinguished by Frayling, and their implied primary evaluation criteria. Research limitations/implications – The presented argument advocates a constructivist view, which, however, is not meant to imply a rejection of, but rather, an additional degree of freedom extending the realist view. Originality/value – This discussion contributes to the establishment of observational determinability as observer-dependent. The proposed framework connects the navigation between deterministic observables and determining observers to the navigation between the design criteria form, meaning and utility. This may be of value within and beyond design research.

There are many possible arguments the author of a chapter on design research might make, other than the one I chose to make here. And I have no doubt that what I have written will not sit comfortably or properly, in the minds of some readers. I can imagine the instantly dismissive tone of a certain type of response, precisely the sort of response I am trying to argue against. None of this makes my account wrong: it merely makes it contentious. It may be seen as contentious in what it includes, but also, and perhaps more so, in what and who it does not mention. The difficulty in any attempt to provide a position – or a review – is to find a line and then to hang a convincing and interesting story on it. In finding that line, any author will accommodate many views, but inevitably not all, and will feature the work of some, but not most, authorities. A further difficulty is not to drown the narrative of the story in reference, while yet showing the story is justifiable. And it is also to make space to include your own view, as author, without overplaying it. The real test of a text like this is, I believe, whether the argument helps you (the reader, but the author also) better to understand, and to act better. This is a reader’s judgement: like a placebo, the question is not what design research ‘really’ is, but how this account helps readers themselves understand and go forward.