Design-based research studies are conducted as iterative implementation-analysis-modification cycles, in which emerging theoretical models and pedagogically plausible activities are reciprocally tuned toward each other as a means of investigating conjectures pertaining to mechanisms underlying content teaching and learning. Yet this approach, even when resulting in empirically effective educational products, remains under-conceptualized as long as researchers cannot be explicit about their craft and specifically how data analyses inform design decisions. Consequentially, design decisions may appear arbitrary, design methodology is insufficiently documented for broad dissemination, and design practice is inadequately conversant with learning-sciences perspectives. One reason for this apparent under-theorizing, I propose, is that designers do not have appropriate constructs to formulate and reflect on their own intuitive responses to students’ observed interactions with the media under development. Recent socio-cultural explication of epistemic artifacts as semiotic means for mathematical learners to objectify presymbolic notions (e.g., Radford, Mathematical Thinking and Learning 5(1): 37–70, 2003) may offer design-based researchers intellectual perspectives and analytic tools for theorizing design improvements as responses to participants’ compromised attempts to build and communicate meaning with available media. By explaining these media as potential semiotic means for students to objectify their emerging understandings of mathematical ideas, designers, reciprocally, create semiotic means to objectify their own intuitive design decisions, as they build and improve these media. Examining three case studies of undergraduate students reasoning about a simple probability situation (binomial), I demonstrate how the semiotic approach illuminates the process and content of student reasoning and, so doing, explicates and possibly enhances design-based research methodology.

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.

Key words: constructivism, design, education, enactivism, mathematics

Enactivism theorizes thinking as situated doing. Mathematical thinking, specifically, is handling imaginary objects, and learning is coming to perceive objects and reflecting on this activity. Putting theory to practice, Abrahamson’s embodied-design collaborative interdisciplinary research program has been designing and evaluating interactive tablet applications centered on motor-control tasks whose perceptual solutions then form the basis for understanding mathematical ideas (e.g., proportion). Analysis of multimodal data of students’ handand eyemovement as well as their linguistic and gestural expressions has pointed to the key role of emergent perceptual structures that form the developmental interface between motor coordination and conceptual articulation. Through timely tutorial intervention or peer interaction, these perceptual structures rise to the students’ discursive consciousness as “things” they can describe, measure, analyze, model, and symbolize with culturally accepted words, diagrams, and signs – they become mathematical entities with enactive meanings. We explain the theoretical background of enactivist mathematics pedagogy, demonstrate its technological implementation, list its principles, and then present a case study of a mathematics teacher who applied her graduate-school experiences in enactivist inquiry to create spontaneous classroom activities promoting student insight into challenging concepts. Students’ enactment of coordinated movement forms gave rise to new perceptual structures modeled as mathematical content.

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.

Purpose: Complexity is the real beast that baffles everybody. Though there are increasing inter-disciplinary discussions on it, yet it is scantly explored. The purpose of this paper is to bring a new and unique dimension to the discourse assimilating the important ideas of two towering scientists of their time, Newton and Heinz von Foerster. In the tradition of Foersterian second-order cybernetics the paper attempts to build a bridge from a cause-effect thinking to a thinking oriented towards “understanding understanding” and in the process presents a model of “Cybernetics of Simplification” indicating a path to simplicity from complexity. Design/methodology/approach – The design of research in the paper is exploratory and the paper takes a multidisciplinary approach. The model presented in the paper builds on analytics and systemics at the same time. Findings: Simplicity can be seen in complex systems or situations if one can construct the reality (be that the current one that is being experienced or perceived or the future one that is being desired or envisaged) through the Cybernetics of Simplification model, establishing the effect-cause-and-effect and simultaneously following the frame of iterate and infer as a circular feedback loop; in the tradition of cybernetics of cybernetics. Research limitations/implications – It is yet to be applied. Practical implications: The model in the paper seems to have far reaching implications for complex problem solving and enhancing understanding of complex situations and systems. Social implications – The paper has potential to provoke new ideas and new thinking among scholars of complexity. Originality/value – The paper presents an original idea in terms of Cybernetics of Simplification building on the cybernetics of the self-observing system. The value lies in the unique perspective that it brings to the cybernetics discussions on complexity and simplification.

Key words: causality, complexity, second-order cybernetics, cybernetics of simplification, self-observing system, simplification

Over the past decades many teaching strategies have been proposed by various educators to improve education of all students including students with special needs. No single one of these proposed teaching strategies meets the needs of all students. The new Every Student Succeeds Act, successor to No Child Left behind Law, which transfers oversight from federal level back to states, could be a benefactor for constructivism and special education. Educators are also optimistic that the new Every Student Succeeds Act will be better for vulnerable students in special education because it will introduce more flexibility in how individual states carry out evaluation of students and teachers. In addition, it will provide more flexibility on testing and adapt the curriculum to student’s needs. It would further reduce time and energy for students preparing for standardized tests or statewide exams. It will also end “Adequate Yearly Progress” – a measure that required schools to show test score gains. Constructivist teaching philosophy is all about accepting student autonomy where student thinking drives the lessons, where dialogue, inquiry, and puzzlement are valued and assessing student learning is in the context of teaching. It helps teachers to draw on new ideas as they make decisions about which teaching techniques are most appropriate for all students to learn. Now is the time to revisit the great debate of constructivism versus teacher-centered instruction and special education. Time has come to effectively explore our educational system and examine the core unit of the whole enterprise, the textbook, the classroom, a setting that is often dominated by teacher talk and students listen.

Key words: constructivist teaching strategies, student with special needs, academic outcomes, students with learning disabilities, positive learning, policy makers, indirect instruction, every student succeeds act.

The emergence of mind is a central issue in cognitive philosophy. The main working assumption of the present paper is that several important insights in answering this question might be provided by the nature of life itself. It is in this line of thinking that this paper compares two major philosophical conceptualizations of the living in the history of theoretical biology, namely those of Maturana and Aristotle. The present paper shows how both thinkers describe the most fundamental properties of the living as autonomous sustenance. The paper also shows how these theoretical insights might have a consequence upon our understanding of a specific constructiveness of human cognition, here referred to as enarrativity, if this can be considered in a structural as well as evolutionary connection with the structure of life as such. The paper finally suggests that the structural connection made here can be traced from the fundamental organization of self-preservation to survival behaviors to constructive orientation and action.

Key words: autopoiesis, soul, system theory, organism, cognitive philosophy, enarrativity, theoretical biology.

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.

The nature of cognition is being re-considered. Instead of emphasizing formal operations on abstract symbols, the new approach foregrounds the fact that cognition is, rather, a situated activity, and suggests that thinking beings ought therefore be considered first and foremost as acting beings. The essay reviews recent work in Embodied Cognition, provides a concise guide to its principles, attitudes and goals, and identifies the physical grounding project as its central research focus.