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.

Blind and visually impaired mathematics students must rely on accessible materials such as tactile diagrams to learn mathematics. However, these compensatory materials are frequently found to offer students inferior opportunities for engaging in mathematical practice and do not allow sensorily heterogenous students to collaborate. Such prevailing problems of access and interaction are central concerns of Universal Design for Learning (UDL), an engineering paradigm for inclusive participation in cultural praxis like mathematics. Rather than directly adapt existing artifacts for broader usage, UDL process begins by interrogating the praxis these artifacts serve and then radically re-imagining tools and ecologies to optimize usability for all learners. We argue for the utility of two additional frameworks to enhance UDL efforts: (a) enactivism, a cognitive-sciences view of learning, knowing, and reasoning as modal activity; and (b) ethnomethodological conversation analysis (EMCA), which investigates participants’ multimodal methods for coordinating action and meaning. Combined, these approaches help frame the design and evaluation of opportunities for heterogeneous students to learn mathematics collaboratively in inclusive classrooms by coordinating perceptuo-motor solutions to joint manipulation problems. We contextualize the thesis with a proposal for a pluralist design for proportions, in which a pair of students jointly operate an interactive technological device.

It is characteristic of Heinz von Foerster’s approach to the cybernetics of cybernetics that it combines a sense of tight reasoning with the acknowledgment of fundamental ignorance. The article attempts to uncover an epistemological relationship between the reasoning and the ignorance. The relationship is provided for by a razor which reads: what can be described in relation to its composition, is described in vain in relation to its substance. The razor asks for second-order terms instead of first-order terms, or for ontogenetics instead of ontology.

Key words: closure, communication, composition, epistemology

My colleagues and I have begun to build a model of the development of young infants’ physical reasoning. The model is based on the assumption that infants are born not with substantive beliefs about objects (e.g., intuitive notions of impenetrability, continuity, or force), as researchers such as Spelke and Leslie have proposed, but with highly constrained mechanisms that guide the development of infants’ reasoning about objects. The model is derived from findings concerning infants’ intuitions about different physical phenomena (e.g., support, collision, and unveiling phenomena). Comparison of these findings points to two developmental patterns that recur across ages and phenomena. We assume that these patterns reflect, at least indirectly, the nature and properties of infants’ learning mechanisms. In this review, I describe the patterns and summarize some of the evidence supporting them.

The classical formulation of the object of ethics refers to a knowledge of the rules of the adaptation of the human species to their natural environments, to normative expectations supposed in the others and to the biographical evolution of the self. Accordingly, a doctrine of the duties was edified on three pillars, embracing a reference to the duties towards nature, towards the others and towards oneself. Notwithstanding the fact that human action obeys to a variety of factors including bio-physiological conditions and the dimensions of the social environment, ancient and modern metaphysical models of ethics favored the commendatory discourse about the predicates “right” and “wrong,” concurring to ultimate goals. The ethical discussions consisted chiefly in the investigation of the adequacy of the subordinate goals to the final ends of the human action or in the treatment of the metaphysical questions related to free will or determinism, the opposition of the intentionality of the voluntary conduct of man to the mechanical or quasi-mechanical responses of the inferior organisms or machines. From a “second order” approach to the ethical action and imperatives, I propose with this book a critical analysis of the metaphysical and the Kantian ethics. Relevance: In “Ethics and Second-Order Cybernetics” (1992) Heinz von Foerster referred the importance of the application of his notion of “second-order cybernetics” to ethics and moral reasoning. Initially, second-order cybernetics intended an epistemological discussion of recursive operations in non-trivial machines, which were able to include in their evolving states their own self-awareness in observations. The application of his views to ethics entails new challenges. After H. von Foerster essay, what I mean with “second-order ethics is an attempt to identify the advantages of the adoption of his proposal, some consequences in the therapeutically field and lines for new developments.

Key words: Ethics, moral discourse, commendations, second-order cybernetics, observer, objectivity

The article considers peculiarities of modern subject-object relation son the basis of radical constructivism and their key question – the problem of verity. It reveals that the vector of a new definition of subjectivity through epistemology of radical constructivism is risky for false subject-object relations picture, due to the loss of differences between real and virtual reality, limitation of postmodern tendencies to stop the gap between the reality and the world of simulacris. Ourvisionofpeculiaritiesofsubjectivenatureofcognitionandaman’ssubjectivityfromthepointofviewof subjective and objective dialectics in the verity as well as their criteria, suggests the reasoning of introducing the term “criteria of mistaking” into epistemology. As we see the problem, radical constructivism uses just on criteria of versions of mistaking, though it rejects the problem of grounds of cognition. Moreover, it is clear that radical constructivism stands for general line of modern social epistemologies, it revealed the vector of postmodernist culture as a tendency for cognition to alter into pure game with its constant and changing simulacris – rules, ideas, signs, reflecting the reality in a distorted way, without any connection with it, and even hiding the reality, sometimes.…

Key words: subject, object, subjectivity of knowledge, truth, radical constructivism, the criterion of error, virtual reality, simulacris

Excerpt: My purpose in this paper is to show that the two major options on which the current debate on the interpretation of quantum mechanics relies, namely realism and empiricism (or instrumentalism), are far from being exhaustive. There is at least one more position available; a position which has been widely known in the history of philosophy during the past two centuries but which, in spite of some momentous exceptions, has only attracted little interest until recently in relation to the foundational problems of quantum mechanics. According to this third position, one may provide a theory with much stronger justifications than mere a posteriori empirical adequacy, without invoking the slightest degree of isomorphism between this theory and the elusive things out there. Such an intermediate attitude, which is metaphysically as agnostic as empiricism, but which shares with realism a commitment to considering the structure of theories as highly significant, has been named transcendentalism after Kant. Of course, I have no intention in this paper to rehearse the procedures and concepts developed by Kant himself; for these particular procedures and concepts were mostly adapted to the state of physics in his time, namely to Newtonian mechanics. I rather wish to formulate a generalized version of his method and show how this can yield a reasoning that one is entitled to call a transcendental deduction of quantum mechanics. This will be done in three steps. To begin with, I shall define carefully the word “transcendental,” and the procedure of “transcendental deduction,” in terms which will make clear how they can have a much broader field of application than Kant ever dared to imagine. Then, I shall show briefly that the main structural features of quantum mechanics can indeed be transcendentally deduced in this modern sense. Finally, I shall discuss the significance, and also the limits, of these results.

Given the centrality of arguments from vicious infinite regress to our philosophical reasoning, it is little wonder that they should also appear on the catalogue of arguments offered in defense of theses that pertain to the fundamental structure of reality. In particular, the metaphysical foundationalist will argue that, on pain of vicious infinite regress, there must be something fundamental. But why think that infinite regresses of grounds are vicious? I explore existing proposed accounts of viciousness cast in terms of contradictions, dependence, failed reductive theories and parsimony. I argue that no one of these accounts adequately captures the conditions under which an infinite regress – any infinite regress – is vicious as opposed to benign. In their place, I suggest an account of viciousness in terms of explanatory failure. If this account is correct, infinite grounding regresses are not necessarily vicious; and we must be much more careful employing such arguments to the conclusion that there has to be something fundamental.

Open peer commentary on the article “Elementary Students’ Construction of Geometric Transformation Reasoning in a Dynamic Animation Environment” by Alan Maloney. Upshot: This commentary assumes a constructionist perspective to discuss the choice of methods, conclusions and design goals that Panorkou and Maloney make in their study of students’ activities with the Graph ’n Glyphs microworld.

Although the core of Jean Piaget’s scientific legacy is his stage model of intellectual ontogenesis and his studies of the reasoning skills that figure in those stages, his impact on education, especially American education, has been vast. Thirty years ago, his theory of cognitive development stimulated revolutionary changes in preschool and elementary school curriculum practices, and in the ensuing decades, Piagetian thought has continued to foment major changes in American education, with the whole language approach to reading instruction being a recent illustration. The aim of the present chapter is to focus attention on those aspects of Piaget’s contributions that have proven to be of greatest significance for educational psychology. The chapter begins with a biographical sketch. The rest of the chapter deals with Piaget’s views on learning. This material is divided into 2 sections. The first section presents Piagetian ideas about the relation between cognitive development and learning, and it summarizes findings from classical experiments that tested those ideas. The second section presents Piagetian ideas about instructional methodology and also summarizes findings from classical experiments that tested those ideas.