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

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.

Key words: Constructivism, Piaget, Papert, Vygotsky, situated learning, embodied cognition, ecology of mind

In the drive to improve standards, the collection and dissemination of numerical data still directs much contemporary educational policy. However, recent publications and debates seemingly attempt to reorient discussion from performance to learning. In support, constructivism is often referenced as a contributor in this endeavour. However, constructivism is not a single unified theory either of knowledge or pedagogy. This article identifies one version of constructivist thinking, social constructivism, both in terms of its underlying epistemology (theory of knowledge) and related pedagogy. Contemporary educational theories are then outlined to demonstrate that many practical solutions and theoretical ideas now presented as ‘good learning and teaching’ have much in common with social constructivist thinking. Finally, the article concludes by identifying two issues that require further discussion and debate if pedagogy of a social constructivist nature is to be considered.

In the drive to improve standards, the collection and dissemination of numerical data still directs much contemporary educational policy. However, recent publications and debates seemingly attempt to reorient discussion from performance to learning. In support, constructivism is often referenced as a contributor in this endeavour. However, constructivism is not a single unified theory either of knowledge or pedagogy. This article identifies one version of constructivist thinking, social constructivism, both in terms of its underlying epistemology (theory of knowledge) and related pedagogy. Contemporary educational theories are then outlined to demonstrate that many practical solutions and theoretical ideas now presented as ‘good learning and teaching’ have much in common with social constructivist thinking. Finally, the article concludes by identifying two issues that require further discussion and debate if pedagogy of a social constructivist nature is to be considered.

Education has institutionalized a process that reifies cultures, ecological communities, and ultimately evolution itself. This enclosure has lessened our sensitivity to the pedagogical (eteragogical) nature of our lived relations with other people and with other living beings. By acknowledging that learning and teaching go on between species, humans can regain an eteragogical sense of the interspecies curricula within which they exist. This article explores interspecies lived curricula through a selection of ideas from ecopragmatist Anthony Weston, and cybernetician Gregory Bateson, and through lived experiences with shorebirds of Lake Ontario. Some gulls and a tern teach the author to enrich and diversify, rather than constrict, the potentiality of life. In so doing, being ecological and being educative become unified concepts. Relevance: The publication is concerned with the relational implications between humans and other species of Bateson’s cybernetic theory of learning.

This paper defines a theoretical framework aiming to support the actions and reflections of researchers looking for a “method” in order to critically conceive the complexity of a scientific process of research. First, it starts with a brief overview of the core assumptions framing Morin’s “paradigm of complexity” and Le Moigne’s “general system theory.” Distinguishing “methodology” and “method,” the framework is conceived based on three moments, which represent recurring stages of the spiraling development of research. The first moment focuses on the definition of the research process and its sub-systems (author, system of ideas, object of study and method) understood as a complex form of organization finalized in a specific environment. The second moment introduces a matrix aiming to model the research process and nine core methodological issues, according to a programmatic and critical approach. Using the matrix previously modeled, the third moment suggests conceiving of the research process following a strategic mindset that focuses on contingencies, in order to locate, share and communicate the path followed throughout the inquiry. Relevance: This paper provides the readers with a constructivist methodology of research inspired by Morin’s paradigm of complexity and Le Moigne’s general system theory.

Excerpt: Education has failed to show steady progress because it has shifted back and forth among simplistic positions such as the associationist and rationalist philosophies. Modern cognitive psychology provides a basis for genuine progress by careful scientific analysis that identifies those aspects of theoretical positions that contribute to student learning and those that do not. Radical constructivism serves as the current exemplar of simplistic extremism, and certain of its devotees exhibit an antiscience bias that, should it prevail, would destroy any hope for progress in education.

For some years, there have been in‐service efforts to help teachers become familiar with constructivist ideas about learning, and to apply them in their science teaching. This study is a vignette of one teacher’s science teaching some time after such an in‐service activity. It explores the ways in which the teacher implemented his perceptions of constructivist ideas about learning in his teaching of a topic. The extent to which the teacher used teaching principles based on constructivism was influenced by his views of science and of learning, how he usually planned his teaching, and his confidence in his own understanding of the topic. Features of the teaching which reflect a constructivist view of learning are discussed and some problems are identified. We conclude with some reflections about in‐service programs within a constructivist framework.

This paper aims at shedding light on what students can “construct” when they learn science and how this construction process may be supported. Constructivism is a pluralist theory of science education. As a consequence, I support, there are several points of view concerning this construction process. Firstly, I stress that constructivism is rooted in two fields, psychology of cognitive development and epistemology, which leads to two ways of describing the construction process: either as a process of enrichment and/or reorganization of the cognitive structures at the mental level, or as a process of building or development of models or theories at the symbolic level. Secondly, I argue that the usual distinction between “personal constructivism” (PC) and “social constructivism” (SC) originates in a difference of model of reference: the one of PC is Piaget’s description of “spontaneous” concepts, assumed to be constructed by students on their own when interacting with their material environment, the one of SC is Vygotsky’s description of scientific concepts, assumed to be introduced by the teacher by means of verbal communication. Thirdly, I support the idea that, within SC, there are in fact two trends: one, in line with Piaget’s work, demonstrates how cooperation among students affects the development of each individual’s cognitive structures; the other, in line with Vygotsky’s work, claims that students can understand and master new models only if they are introduced to the scientific culture by their teacher. Fourthly, I draw attention to the process of “problem construction” identified by some French authors. Finally, I advocate for an integrated approach in science education, taking into account all the facets of science learning and teaching mentioned above and emphasizing their differences as well as their interrelations. Some suggestions intended to improve the efficiency of science teaching are made.

Key words: science learning science teaching, personal constructivism, social constructivism, cooperation, enculturation, problem construction.