Excerpt: I claim that a mechanism that reconstructs and re-coordinates processes, rather than stores and retrieves labeled descriptions or procedures, is more consistent with what we know about human memory and perception (Clancey 1991, 1994). Such a process memory possibly cannot be built today, because we don’t know how to build the kind of self-organizing mechanism that is required (cf. Freeman 1991). But articulating how human cognition is different from a classical architecture helps delineate what aspects of situated robotic designs are still cast in the classical mold and remain to be freed of prevailing assumptions about the nature of memory and representations.

Demonstrates that Vygotskian theory can support two opposing interpretations: supporting reform and undermining reform. Discussion is organized by: sociocultural perspectives, Marxist influences on historical analysis and the role of labor, semiotics and psychological tools, dialectic of thought and language, conceptual development, and learning and development.

Presents a theory of intellectual development in which human development depends on environment, self is autonomous and communal, diversity and dissent are anticipated, emotional intelligence is acknowledged, abstraction is reconceptualized and placed in a dialectic, learning is a reciprocal activity, and classrooms are interactions among interactions.

Excerpt: I draw from recent developments in philosophy, biology, ecological thought, phenomenology, and curriculum theory in an effort to re-formulate a response to the question, Why teach mathematics?

This article focuses on an artificial life approach to some important problems in machine learning such as statistical discrimination, curve approximation, and pattern recognition. We describe a family of models, collectively referred to as semi-algebraic networks (SAN). These models are strongly inspired by two complementary lines of thought: the biological concept of autopoiesis and morphodynamical notions in mathematics. Mathematically defined as semi-algebraic sets, SANs involve geometric components that are submitted to two coupled processes: (a) the adjustment of the components (under the action of the learning examples), and (b) the regeneration of new components. Several examples of SANs are described, using different types of components. The geometric nature of SANs gives new possibilities for solving the bias/variance dilemma in discrimination or curve approximation problems. The question of building multilevel semi-algebraic networks is also addressed, as they are related to cognitive problems such as memory and morphological categorization. We describe an example of such multilevel models.

The unsolved problem of induction is closely linked to “the unreasonable effectiveness of mathematics in the natural sciences” (Wigner 1960) and to the question “why the universe is algorthmicly compressible” (Davies 1960). The problem of induction is approached here by means of a constructivist version of the Evolutionary Epistemology (CEE) considering both, the perceived regularities we condense to the laws of nature and the mathematical structures we condense to axioms, as invariants of inborn cognitive and mental operators. A phylogenetic relationship between the mental operators generating the perceived and the mathematical regularities respectively may explain the high suitability of mathematical tools to extrapolate observed data. The extension of perceptional operators by means of experimental operators, i.e., by means of measurement devices) would lead to the completion of the classical world picture if both the cognitive and the physical operators are commutable in the sense of operator algebra (quantitative extensions). Otherwise the physical operators will have invariants which no longer can be described in classical terms, and, therefore, would require the formation of non-classical theories (qualitative extension), exceeding the classical world picture. The mathematical analogon would be the algorithmic extension of elementary mathematical thinking exceeding the axiomatic basis previously established according to Gödel’s incompleteness theorem. As a consequence there will be neither a definitive set of axioms in mathematics, nor will be there a definitive theory of everything in physics.