Helping students connect: architecting learning spaces for experiential and transactional reflection

Given the complex and varied contexts that inform students’ consciousness and occasion their learning, learning spaces are more than physical and virtual spaces. Learning spaces are also a range of situations sedimented in our continuum of experiences that shape our philosophical orientations. As such, this article, written from the perspectives of two faculty members in an English department at a four-year public university, describes our efforts to do the following. First, to draw upon models of instructional design we have experienced in our own educational backgrounds; and equally importantly, to develop learning spaces that support learning that is continuous, situated, and personal. Specifically, we critique the ways in which learning has been segregated from the rest of our life contexts for us throughout our educational histories. The irony is that this de-segregation has motivated us to create diverse learning spaces that provide our students with a more realistic set of tools and techniques for integrative life-long learning

Hierarchical Bayes Modeling for Large-Scale Inference

Bayesian modeling is now ubiquitous in problems of large-scale inference even when frequentist criteria are in mind for evaluating the performance of a procedure. By far most popular in the statistical literature of the past decade and a half are empirical Bayes methods, that have shown in practice to improve significantly over strictly-frequentist competitors in many different problems. As an alternative to empirical Bayes methods, in this paper we propose hierarchical Bayes modeling for large-scale problems, and address two separate points that, in our opinion, deserve more attention. The first is nonparametric "deconvolution" methods that are applicable also outside the sequence model. The second point is the adequacy of Bayesian modeling for situations where the parameters are by assumption deterministic. We provide partial answers to both: first, we demonstrate how our methodology applies in the analysis of a logistic regression model. Second, we appeal to Robbins's compound decision theory and provide an extension, to give formal justification for the Bayesian approach in the sequence case

Relevant Consequence and Empirical Inquiry

A criterion of adequacy is proposed for theories of relevant consequence. According to the criterion, scientists whose deductive reasoning is limited to some proposed subset of the standard consequence relation must not thereby suffer a reduction in scientific competence. A simple theory of relevant consequence is introduced and shown to satisfy the criterion with respect to a formally defined paradigm of empirical inquiry

Notes on Hierarchies and Inductive Inference

The following notes rework a discussion due to Kevin Kelly on the application of topological notions in the context of learning (see Kelly (1990)). All the results except for (2), (4) and (9) are due to Kelly, but are proved differently

Synthesizing inductive expertise

AbstractWe consider programs that accept descriptions of inductive inference problems and return machines that solve them. Several design specifications for synthesizers of this kind are considered from a recursion-theoretic perspective

A Universal Inductive Inference Machine

A paradigm of scientific discovery is defined within a first-order logical framework. It is shown that within this paradigm there exists a formal scientist that is Turing computable and universal in the sense that it solves every problem that any scientist can solve. It is also shown that universal scientists exist for no regular logics that extend first order logic and satisfy the Lowenheim-Skolem condition

Uniform Inductive Improvement

We examine uniform procedures for improving the scientific competence of inductive inference machines. Formally, such procedures are construed as recursive operators. Several senses of improvement are considered, including (a) enlarging the class of functions on which success is certain, and (b) transforming probable success into certain success