This article examines the intellectual and institutional factors that contributed to the col- laboration of neuropsychiatrist Warren McCulloch and mathematician Walter Pitts on the logic of neural networks, which culminated in their 1943 publication, “A Logical Calculus of the Ideas Immanent in Nervous Activity.” Historians and scientists alike often refer to the McCulloch–Pitts paper as a landmark event in the history of cybernetics, and fundamental to the development of cognitive science and artificial intelligence. This article seeks to bring some historical context to the McCulloch–Pitts collaboration itself, namely, their intellectual and scientific orientations and backgrounds, the key concepts that contributed to their paper, and the institutional context in which their collaboration was made. Al- though they were almost a generation apart and had dissimilar scientific backgrounds, McCulloch and Pitts had similar intellectual concerns, simultaneously motivated by issues in philosophy, neurology, and mathematics. This article demonstrates how these issues converged and found resonance in their model of neural networks. By examining the intellectual backgrounds of McCulloch and Pitts as individuals, it will be shown that besides being an important event in the history of cybernetics proper, the McCulloch– Pitts collaboration was an important result of early twentieth-century efforts to apply mathematics to neurological phenomena.

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

Purpose: To show the convergences between Josef Mitterer’s non-dualizing way of speaking and actor-network theory. Method: Comparative analysis of Mitterer’s non-dualizing philosophy and actor-network philosophy. Findings: Profound convergences between the two accounts may lead to a unified account that could redefine traditional philosophical problems. Benefits: The paper extends the range of Mitterer’s non-dualizing philosophy and actor-network theory enabling both to face new problems. Among them, extended non-dualizing philosophy may undergo empirical investigations.

Key words: so far descriptions, from now on descriptions, dualism, actor-network theory

Open peer commentary on the article “Decentering the Brain: Embodied Cognition and the Critique of Neurocentrism and Narrow-Minded Philosophy of Mind” by Shaun Gallagher. Abstract: Simulation theory and theory theory are interaction accounts of theory of mind that have been neurocentrically characterized. A hybrid of these theories approximates the interaction theory of social cognition, and can be described in an indexical-symbolic processing framework.

Purpose: Appreciating the relationship between Sylvio Ceccato and Ernst von Glasersfeld, both as people and in their work. Approach: historical and personal accounts, archeological approach to written evidence. Findings: Ceccato’s work is introduced to an English speaking audience, and the roots of Glasersfeld’s work in Ceccato’s is explored. Flaws in Ceccato’s approach are indicated, together with how Glasersfeld’s work overcomes these, specially in language and automatic translation, and what became Radical Constructivism. Conclusion: Glasersfeld willingly acknowledges Ceccato, who he still refers to as the Master. But Ceccato’s work is little known, specially in the English speaking world. The introduction, critique and delineation of extension and resolution of Ceccato’s ideas in Glasersfeld’s work is the intended value of the paper.

Key words: philosophy, language, correlational grammar, Italian Operational School, attention/mind, mental operation, Ernst von Glasersfeld, Silvio Ceccato

Traditional views of knowledge are being challenged. An emerging “constructivist” perspective, as proposed by George Kelly, an engineer turned clinician, suggests that to a large degree we construct reality. In his “constructive alternativism” Kelly assumes that we validate our hypotheses and beliefs through subjectively construed goodness-of-fit criteria applied to perceived differences between anticipations and feedback. His model of construing is compatible with those emerging in the history and philosophy of science and in cognitive psychology. Nevertheless, constructivists must answer a perplexing question: How can fallible knowledge, constructed as it is from abstracted and incomplete representations of objects and events, capture and maintain our confidence, as it does, and furthermore prove highly functional, as it does?

An evolving theory known as “constructivism” challenges the traditional view of how we generate and revise knowledge. Constructivism helps address a major issue raised by modern scholars of the history and philosophy of science, and decision theory. The question is: How do we reduce the search and solution space of complex and changing environments to “mind size” (i.e., to fit our limited memory and computational capacity)? One emerging answer is that we rely heavily upon robust presuppositions and simplified representations of environmental structure. However, such constructed knowledge is likely to be highly fallible, relying as it must on impoverished data bases in the service of strong expectations or paradigms. In this paper we address two issues: Under what conditions can knowledge be highly fallible and at the same time be highly functional?; Can we make a plausible case, within this constructivist frame of reference, for realism, for knowledge that approximates “reality”?

For millennia people have wondered what makes the living different from the non-living. Beginning in the mid-1980s, artificial life has studied living systems using a synthetic approach: build life in order to understand it better, be it by means of software, hardware, or wetware. This review provides a summary of the advances that led to the development of artificial life, its current research topics, and open problems and opportunities. We classify artificial life research into 14 themes: origins of life, autonomy, self-organization, adaptation (including evolution, development, and learning), ecology, artificial societies, behavior, computational biology, artificial chemistries, information, living technology, art, and philosophy. Being interdisciplinary, artificial life seems to be losing its boundaries and merging with other fields. Relevance: Artificial life has contributed to philosophy of biology and of cognitive science, thus making it an important field related to constructivism.

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.

This paper reports a study on conceptions of assessment held by students and instructors. The conceptions of assessment are considered to be one of the four interrelated sets of conceptions which together constitute the conception of education. The three other sets are the conceptions of (1) knowledge, (2) learning, and (3) instruction. Conceptions of knowledge were measured using an adapted version of the Epistemic Beliefs Questionnaire (EBQ). Conceptions of learning and instruction were measured with the Teaching and Learning Conceptions Questionnaire (TLCQ) developed by Elliott (2002)1, and Chan (2004)2. Since no instrument was available to measure conceptions of assessment, an experimental Conceptions of Assessment Scale (CAS) was developed and tested. Students filled out a 32-item forced-choice version, while instructors filled out a 25-item version in a four-point rating format. On all three instruments a dichotomy was created to distinguish subjects with ‘traditional’ conceptions from the ones with more ‘constructivist’ views. Results indicate that students and instructors hold different conceptions of assessment. Students have more traditional conceptions of assessment than instructors. With regard to conceptions of knowledge, students are more traditional than instructors. The conceptions of teaching and learning also show students to be more traditional than instructors. With respect to the congruency of conceptions of education, students seem to be equally (in) consistent as the instructors. An important implication of the present study is to pay more attention to the alignment between the educational philosophy of an institute and the conceptions of education held by its students and instructors.