Open peer commentary on the article “Enactive Metaphorizing in the Mathematical Experience” by Daniela Díaz-Rojas, Jorge Soto-Andrade & Ronnie Videla-Reyes. Abstract: Welcoming their scholarly focus on metaphorizing, I critique Díaz-Rojas, Soto-Andrade and Videla-Reyes’s selection of the hypothetical constructs “conceptual metaphor” and “enactive metaphor” as guiding the epistemological positioning, educational design, and analytic interpretation of interactive mathematics education purporting to operationalize enactivist theory of cognition - both these constructs, I argue, are incompatible with enactivism. Instead, I draw on ecological dynamics to promote a view of metaphors as projected constraints on action, and I explain how mathematical concepts can be grounded in perceptual reorganization of motor coordination. I end with a note on how metaphors may take us astray and why that, too, is worthwhile.
Abrahamson D. (2021) Grasp actually: An evolutionist argument for enactivist mathematics education. Human Development, online first. https://cepa.info/7084
What evolutionary account explains our capacity to reason mathematically? Identifying the biological provenance of mathematical thinking would bear on education, because we could then design learning environments that simulate ecologically authentic conditions for leveraging this universal phylogenetic inclination. The ancient mechanism coopted for mathematical activity, I propose, is our fundamental organismic capacity to improve our sensorimotor engagement with the environment by detecting, generating, and maintaining goal-oriented perceptual structures regulating action, whether actual or imaginary. As such, the phenomenology of grasping a mathematical notion is literally that – gripping the environment in a new way that promotes interaction. To argue for the plausibility of my thesis, I first survey embodiment literature to implicate cognition as constituted in perceptuomotor engagement. Then, I summarize findings from a design-based research project investigating relations between learning to move in new ways and learning to reason mathematically about these conceptual choreographies. As such, the project proposes educational implications of enactivist evolutionary biology.
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.
Ackermann E. K. (2010) Constructivism(s): Shared roots, crossed paths, multiple legacies. In: Clayson J. & Kalas I. (eds.) Constructionist approaches to creative learning, thinking and education: Lessons for the 21st century. Proceedings of Constructionism 2010. Comenius University, Bratislava: 1–9. https://cepa.info/6082
This paper examines the shared roots and crossed paths between Jean Piaget’s constructivism, what Seymour Paper refers to as “constructionism,” and socio-cultural theories as epitomized by Lev Vygotsky. We do so in the light of more situated, pragmatic, and ecological approaches to human cognition. All these views are developmental (stressing the genesis children’s interests and abilities over time), experiential (in the sense that knowledge is rooted in sensori-motor activity) and interactionist (people are seen as constructing their knowledge by transforming the world). Yet, the views also differ, each highlighting some aspects of how children grow and learn, while leaving other questions unanswered. Piaget’s main contribution was to flesh out what is common in children’s ways of thinking at different stages of their cognitive development and, more important, how consistent, robust, and generally “adapted” their views are. The theory stresses the progressive de-contextualization of knowledge (from here-and-now to then-and-there) and identifies some of the hidden mechanisms (internal reorganizations) that drive human cognitive development. Papert, in contrast, stresses how individuals learn in context and how they use their own – and other people’s – externalizations as objects to think with, especially as their convictions break down. His approach is more situated. Papert is particularly interested the role of new media in human learning. Both Papert and Vygotsky shed light on the articulations between direct and mediated experience (from action and tool-use to enactments, language, and symbol-use). Yet Vygotsky and the Russian school have paid much closer attention to the role of caring adults and peers in a child’s initiation to her culture. They remind us that it takes a whole village to raise a child. Integrating the views helps rethink how children come to make sense of their experiences, and how they find their own places – and voices – in the world. At once world-makers, world-readers, and dwellers in the world, human infants are granted from birth with the abilities to optimize exchanges with people and things by moving in and out of contexts, by shifting perspectives, and by switching roles or standpoint. They are extraordinary learners, and much can be learned from them. Lastly, while mostly inner-driven and curious, children need caring adults, secure grounds, and engaging peers and props to thrive and grow. Tools, media, and cultural artifacts are the tangible forms through which they explore their surrounds, express their thoughts, and share the fun with others – and the traces left by those who came before (cultural heritage) become a terrain for newcomers to create their paths.
On the 50th anniversary of its publication, we look back on some of the intellectual contributions of Gibson’s (1966) The Senses Considered as Perceptual Systems. This work is often seen as contributing a new perspective to our understanding of the 5 senses. In this paper, we explore another intellectual contribution: Gibson’s treatment of perception–action as an irreducible, functional system. We review select examples of systems thinking from the physical, animal, and human social domains. Our suggestion is that a systems-level approach to social interactions would have been a natural extension of Gibson’s ideas.
Arango A. (2018) From sensorimotor dependencies to perceptual practices: Making enactivism social. Adaptive Behavior 27(1): 31–45.
Proponents of enactivism should be interested in exploring what notion of action best captures the type of action–perception link that the view proposes, such that it covers all the aspects in which our doings constitute and are constituted by our perceiving. This article proposes and defends the thesis that the notion of sensorimotor dependencies is insufficient to account for the reality of human perception and that the central enactive notion should be that of perceptual practices. Sensorimotor enactivism is insufficient because it has no traction on socially dependent perceptions (SDPs), which are essential to the role and significance of perception in our lives. Since the social dimension is a central desideratum in a theory of human perception, enactivism needs a notion that accounts for such an aspect. This article sketches the main features of the Wittgenstein-inspired notion of perceptual practices as the central notion to understand perception. Perception, I claim, is properly understood as woven into a type of social practices that includes food, dance, dress, and music. More specifically, perceptual practices are the enactment of culturally structured, normatively rich techniques of commerce of meaningful multi- and intermodal perceptible material. I argue that perceptual practices explain three central features of SDP: attentional focus, aspects’ salience, and modal-specific harmony-like relations.
Arango A. (2019) From sensorimotor dependencies to perceptual practices: Making enactivism social. Adaptive Behavior 27(1): 31–45. https://cepa.info/6199
Proponents of enactivism should be interested in exploring what notion of action best captures the type of action–perception link that the view proposes, such that it covers all the aspects in which our doings constitute and are constituted by our perceiving. This article proposes and defends the thesis that the notion of sensorimotor dependencies is insufficient to account for the reality of human perception and that the central enactive notion should be that of perceptual practices. Sensorimotor enactivism is insufficient because it has no traction on socially dependent perceptions (SDPs), which are essential to the role and significance of perception in our lives. Since the social dimension is a central desideratum in a theory of human perception, enactivism needs a notion that accounts for such an aspect. This article sketches the main features of the Wittgenstein-inspired notion of perceptual practices as the central notion to understand perception. Perception, I claim, is properly understood as woven into a type of social practices that includes food, dance, dress, and music. More specifically, perceptual practices are the enactment of culturally structured, normatively rich techniques of commerce of meaningful multi- and intermodal perceptible material. I argue that perceptual practices explain three central features of SDP: attentional focus, aspects’ salience, and modal-specific harmony-like relations.
While structured as an autobiography, this memoir exemplifies ways in which classic contributions to cybernetics (e.g., by Wiener, McCulloch & Pitts, and von Neumann) have fed into a diversity of current research areas, including the mathematical theory of systems and computation, artificial intelligence and robotics, computational neuroscience, linguistics, and cognitive science. The challenges of brain theory receive special emphasis. Action-oriented perception and schema theory complement neural network modeling in analyzing cerebral cortex, cerebellum, hippocampus, and basal ganglia. Comparative studies of frog, rat, monkey, ape and human not only deepen insights into the human brain but also ground an EvoDevoSocio view of “how the brain got language.” The rapprochement between neuroscience and architecture provides a recent challenge. The essay also assesses some of the social and theological implications of this broad perspective.
Atkinson B. J. & Heath A. W. (1990) Further thoughts on second-order family therapy – This time it’s personal. Family Process 29: 145–155. https://cepa.info/4097
A series of articles has recently appeared in which implications of second-order cybernetics for the practice of family therapy have been discussed. In this article, we attempt to advance the discussion by addressing ideas that we think have not been adequately emphasized thus far. Specifically proposed are ideas about conditions that might facilitate the emergence of consciously pragmatic strategy informed by the kind of systemic wisdom that delicately balances natural systems without the benefit of human planning. It is argued that a shift in the personal habits of knowing and acting that typically organize individual human experience is required. After attempting to specify what this shift might involve, implications of these ideas for the practice of family therapy and for human action in general are discussed.
Avenier M. J. & Parmentier Cajaiba A. (2012) The dialogical model: Developing academic knowledge for and from practice. European Management Review 9(4): 199–212.
We propose a methodological framework for developing and communicating academic knowledge relevant for practice: the dialogical model. This model of engaged scholarship comprises five activities: specifying a research question, elaborating local knowledge, developing conceptual knowledge, communicating knowledge, and activating knowledge. The current article focuses on the early stage of research question design and presents the epistemological framework in which the model was initially developed. It also offers guidance on how to maintain academic value and practical relevance in tension throughout the research process. Examples illustrate how to construct research questions relevant both for academia and practice, and how to justify validity in pragmatic constructivism. This model can likewise be mobilized in other epistemological frameworks, particularly for knowledge generation purposes. It enriches the researchers’ methodological toolbox by adding a new procedural tool that provides valuable guidelines from the very start of research projects. Relevance: The first part of this article is dedicated to presenting and discussing what internal validity, external validity, and reliability mean specifically in pragmatic constructivism, which is another name for radical constructivism. This naming is consistent with the radical constructivist view of the relationship between knowledge and action, and has the advantage of being free from all the misinterpretations associated with the term “radical.”