Context: The constructivist approach to the definition (or analysis) of the fundamental meanings of language in Ernst von Glasersfeld’s work. Problem: Has this approach achieved better results than other approaches? Method: Review of a book chapter by von Glasersfeld that is devoted to the analysis of the concepts of “unity,” “plurality” and “number.” Results: The constructivist approach to the semantics of the fundamental elements of language (some of which are fundamental for sciences too) seems to have produced positive results; moreover these are in a field where other approaches have produced results that do not objectively seem satisfactory.

Key words: semantics, numbers, mental operations, attention, language

Excerpt: The evidence I have reviewed – showing the distributed, visual, and physical nature of mathematical understanding – seems particularly significant when considering that mathematics, for most students, is taught as a series of numbers and abstract concepts. It is probably not surprising that so many students feel that mathematics is inaccessible and uninteresting when they are plunged into a world of abstraction and numbers. Most curriculum standards and published textbooks do not invite visual thinking. Many textbooks provide pictures, but they do not invite students to think visually or to draw their own representations of ideas. When textbook and classroom approaches do encourage visual work, it is usually encouraged as a prelude to the development of abstract ideas rather than a tool for seeing and extending mathematical ideas and strengthening important brain networks.

Educational technology is firmly grounded in the rational tradition. However, there are growing numbers of educational technologists who consider themselves constructivist in orientation. In this paper I look at design in the field of educational technology through the lens of an enactive constructivist framework in order to locate trends that suggest a convergence with the enactive position as explicated in the works of Humberto Maturana and Francisco Varela. The enactive position provides a coherent framewok within which to guide constructivist practice.

Constructivist educational principles suggest that educational environments should provide learners with personal control, authentic learning contexts, and diverse personal interactions including collaboration. How can such constructivist values be applied to mass Higher Education? Traditional methods cannot achieve it with large student numbers but computer‐based media are scaleable and may support constructivist learning. A new course for non‐science undergraduates provided an opportunity for a constructivist design using the World Wide Web, email, and video. The design of the course, its implementation and evaluation are described. Authentic assessment was critical. Web forms and e‐mail supported some necessary personal interactions, but collaborative work was problematical.

Chilean biology covers a wide disciplinary spectrum, where evolutionary biology has been able to gain an outstanding presence, despite its notably small number of practitioners. In this regard, however, numbers may appear deceptive. For instance, a review of the papers published from 1983 to 1995 in the Revista Chilena de Historia Natural, which covers all naturalist disciplines, showed that only 4. 7 %dealt with evolutionary aspects sensu lato, a very low percent in comparison to dominant disciplines such as botany, zoology and ecology (Camus 1995) Of course, Chilean evolutionists publish in other Chilean and foreign journals, and thus the above figure is just a vague reference on the relative importance of evolution. Nevertheless, quantitative estimations could not capture the real importance or the impact of evolutionary knowledge on the formation of Chilean naturalists, regardless any explicit or implicit consideration in their own studies. Very likely, Chilean naturalists do see in evolution the ultimate foundation for their work, as an echo of that legendary statement by T. Dobzhansky, and partly as a result of a long darwinian tradition in Chilean universities. In fact, Manrfquez & Rothhammer ( 1997) documented that Darwin’s theory was already incorporated in some school texts as early as 1866, and in 1917 it was approved as part of the official educational program for public schools. This certainly lead to intense public debates between lay and catholic sectors, which lasted for about 60 years. However, Manrfquez & Rothhammer (1997) also mentioned that such a debate not only was virtually absent in Chilean universities, but darwinian theory, and even the basic tenets of the rising synthetic theory of evolution, were formally included in university curricula during the first decades of the 20�h century.

This paper poses two problems for von Glasersfeld’s Radical Constructivism. The first problem concerns the rejection of the idea that it is possible to share meanings. The second problem is that Radical Constructivism rejects the notion of an objectively existing reality of which we can have objective knowledge. Yet with respect to mathematics, von Glasersfeld seems to claim that it is possible to obtain objective knowledge. We propose an alternative position – Constructive Realism – that gives a description of what mathematical objects are and gives an account of why knowledge in mathematics is objective. Furthermore, we argue that some of the assumptions, used in von Glasersfeld’s description of how numbers are formed, support the claim that some meanings are objective and that communication is possible. Finally, we consider some of the implications this position has for mathematics education.

Educational robotics (ER) is a subset of educational technology that includes robotic kits and social robots utilized with a goal to facilitate teaching and learning. Scientific publications on educational robotics are commonly anticipated by references to constructivism and constructionism. However, in philosophy, social sciences and cognitive science, constructivism is not a unified framework but a conglomerate of at least six different branches with diverse ontological, epistemological and pragmatic positions. This thesis takes a form of a critical survey where my aim was to map and to evaluate what constructivism means in and for educational robotics research. To meet this goal, I collected and studied 57 ER publications dated 2000–2018. Following an extended introduction into constructivist debates in philosophy and cognitive science, and the discussion how these in influenced contemporary educational paradigms in the first and second chapters of the thesis, in the third chapter I proceed to lay out the insights I gathered during my survey of educational robotics literature. As expected, interpretations ranged from less theoretically informed where constructivism is reduced to any instances of hands-on manipulations of robotic technology, to more informed where constructivism is interpreted through the lens of subject-centered constructivist strands (Piaget-derived cognitive constructivism and its spin-off constructionism). In the latter group, notions associated with authentic education paradigm, such as collaboration, personalization, exploratory learning, and others, are addressed either as pedagogical strategies or as objects of research on their own terms. Though fewer in numbers, the field is also represented by studies that integrate concepts from social constructivism with the overall authentic education orientation. Here, Vygotskian concepts such as zone of proximal development, more knowledgeable other and scaffolding are commonly referred to. The thesis concludes with a broader discussion and my suggestions for future research.

The non-adaptationist approach to evolutionary epistemology (EE) was born at the end of the 1970s as an alternative to traditional adaptationist EE. Despite the fact that non-adaptationist EE offers compelling interpretative models and its explanatory power is widely recognised, an organic overview of the broad non-adaptationist field is still lacking. In this paper, I propose to fill this gap. To this effect, after providing a systematisation of the perspectives that are commonly associated with non-adaptationist EE, I will discuss two recurring orders of arguments that non-adaptationist scholars, often independently of one another, put forward against their adaptationist rivals. By offering a way to conceive non-adaptationist evolutionary epistemological approaches as part of a structured whole, the resulting systematic account is meant to provide a reading grid, a compass for orienting oneself in the uneven territories of non-adaptationist EE. Moreover, the consequent identification of two recurring argumentative bodies is intended to add to the explanatory power of non-adaptationist EE, which in finding new strength in numbers eventually acquires a greater critical efficacy against its adaptationist counterpart.

Key words: evolutionary epistemology, non-adaptationism, adaptationism, overview, world-in-itself, epistemic circularity.

This book contains 15 essays written between 1969 through 1983. The essays included are: (1) “Semantic Analysis of Verbs in Terms of Conceptual Situations”; (2) "“Because” and the Concepts of Causation”; (3) “The Development of Language as Purposive Behavior”; (4) “Adaptation and Viability”; (5) “On the Concept of Interpretation”; (6) “Piaget and the Radical Constructivist Epistemology”; (7) “The Construct of Identity or the Art of Disregarding a Difference”; (8) “The Concepts of Adaptation and Viability in a Radical Constructivist Theory of Knowledge”; (9) “Cybernetics, Experience, and the Concept of Self”; (10) “An Introduction to Radical Constructivism”; (11) “Feedback, Induction and Epistemology”; (12) “An Interpretation of Piaget’s Constructivism”; (13) “An Attentional Model for the Conceptual Construction of Units and Numbers”; (14) “Subitizing-The Role of Figural Patterns in the Development of Numerical Concepts”; and (15) “Learning as Constructive Activity.” These essays are categorized in three sections: language and semantics; constructivist epistemology; and concepts of number. A list of 106 publications written by the author from 1960 to 1987 is provided.

Key words: philosophy, language, radical constructivism

The report contains a discursive description and flow diagrams of the machine program written for a GE 425 computer in order to implement the previously developed “Multistore Procedure.” Advances in several related problem areas are reported: Classification of words in terms of “correlation indices, i.e. by means of code numbers representing the words” possibilities of forming syntatic combinations with others; Reclassification, i.e. assignation of correlation indices to word combinations; Correlator range, i.e. the extent of syntactic government – in this case of prepositions – in English sentences; Grammatical and semantic factor analysis, i.e. analysis of grammatical functions and semantic content in terms of constant factors.

Key words: machine translation, cybernetics