Powerful Pedagogy in the Science-and-Religion Classroom

This essay is a discussion of effective teaching in the science-and-religion classroom. I begin by introducing Alfred North Whitehead's three stages of learning—romance, discipline, and generalization—and consider their implications for powerful pedagogy in science and religion. Following Whitehead's three principles, I develop a number of additional heuristics that deal with active, visual, narrative, cooperative, and dialogical learning styles. Finally, I present twelve guidelines for how to use e-mail and class-based listserves to achieve some of these outcomes.     

Polanyi's Finalism

Although Michael Polanyi's model of science and his construal of the nature of the real are usually thought to be congenial to religion and although Polanyi himself says that "the stage on which we thus resume our full intellectual powers is borrowed from the Christian scheme of Fall and Redemption" (Polanyi 1958, 324), theologians have given little attention to the model of God he presents. The metaphysical and theological vision unfolded in part 4 of Personal Knowledge is a thoughtful alternative to materialist versions of neo-Darwinism and provides a platform for revisiting four long-standing controversies at the interface of science and religion: whether life and mind can be completely specified in terms of physical analysis, whether nature can be adequately understood without appeal to final causes, whether natural selection adequately explains life's diverse forms, and whether knowledge can be fully objectified. Through an exploration of Polanyi's contribution to these discussions, we undertake to show not only that his treatment of God as a cosmic field is strikingly original but also that in reinstating activity as a metaphysical category, he reconstructs our understanding of our creaturely hope and calling.     

INCREASING REQUESTS BY ADULTS WITH DEVELOPMENTAL DISABILITIES USING INCIDENTAL TEACHING BY PEERS

A peer-delivered incidental-teaching procedure was used to instruct appropriate requesting in adults with moderate to severe mental retardation or autism. Three pairs of group-home residents participated in an incidental-teaching procedure to increase appropriate requesting, prompting, and responding of residents during lunch-preparation sessions. An increase in the number of incidental-teaching episodes during dinner was obtained, and remained high when lunch-making training sessions were withdrawn. In addition, during the incidental-teaching phase, an increase in appropriate requests and overall verbalizations occurred for the peer learners. Changes in appropriate requesting and overall verbalizations also remained higher than baseline when training was withdrawn.     

THE DOCTRINE OF THE TRINITY AS A MODEL FOR STRUCTURING THE RELATIONS BETWEEN SCIENCE AND THEOLOGY

Abstract. A strategy for deeding systematically with such complex relationships as those between science and theology is presented after a brief overview of the historical record and illustrated in terms of the concept of divinity. The application of that strategy to the title relationships yields a multilogical/multilevel solution which presents certain analogies to or isomorphisms with the doctrine of the Trinity. These concern mainly the multilogical/multilevel character of both conceptualizations and the relational and contextual reasoning required to conceive them. Furthermore, certain characteristics of the doctrine facilitate the dialogue between theologians and scientists on account of their similarity with such scientific concepts as diversity in unity, multiplicity of relationships, nonseparability, and nonclassical logic.     

The logics of orthoalgebras

The notion of unsharp orthoalgebra is introduced and it is proved that the category of unsharp orthoalgebras is isomorphic to the category of D-posets. A completeness theorem for some partial logics based on unsharp orthoalgebras, orthoalgebras and orthomodular posets is proved.     

Teaching simple addition to children with mental retardation using a microcomputer

Computer assisted instruction (CAI) was used for improving the efficiency of simple addition (single-digit without carrying) computation in three children with mental retardation. The training program, conducted on a portable personal computer, consisted of demonstrations and repetitive practices on simple addition presented in a vertical format. A number of behavioral instruction techniques such as direct feedback, corrective demonstration, verbal association, and token reinforcement were also included. To evaluate the effects of the CAI package, a multiple-baseline across subjects design with followup was employed. Results showed that performances of children improved with training and were maintained at 1-week, 4-week, and 12-week followups. Generalization of the learned skills was evident when children were assessed on a paper-and-pencil addition test in a vertical format. The skills were also transferable, with initial prompting, to a computerized addition test in a horizontal format. These findings reaffirmed the applicability of CAI and behavioral techniques for teaching math skills to children with mental retardation.     

Undecidability and intuitionistic incompleteness

Let S be a deductive system such that S-derivability (s) is arithmetic and sound with respect to structures of class K. From simple conditions on K and s, it follows constructively that the K-completeness of s implies MP(S), a form of Markov's Principle. If s is undecidable then MP(S) is independent of first-order Heyting arithmetic. Also, if s is undecidable and the S proof relation is decidable, then MP(S) is independent of second-order Heyting arithmetic, HAS. Lastly, when s is many-one complete, MP(S) implies the usual Markov's Principle MP.An immediate corollary is that the Tarski, Beth and Kripke weak completeness theorems for the negative fragment of intuitionistic predicate logic are unobtainable in HAS. Second, each of these: weak completeness for classical predicate logic, weak completeness for the negative fragment of intuitionistic predicate logic and strong completeness for sentential logic implics MP. Beth and Kripke completeness for intuitionistic predicate or sentential logic also entail MP.These results give extensions of the theorem of Gödel and Kreisel (in [4]) that completeness for pure intuitionistic predicate logic requires MP. The assumptions of Gödel and Kreisel's original proof included the Axiom of Dependent Choice and Herbrand's Theorem, no use of which is explicit in the present article.     

On maximal intermediate predicate constructive logics

We extend to the predicate frame a previous characterization of the maximal intermediate propositional constructive logics. This provides a technique to get maximal intermediate predicate constructive logics starting from suitable sets of classically valid predicate formulae we call maximal nonstandard predicate constructive logics. As an example of this technique, we exhibit two maximal intermediate predicate constructive logics, yet leaving open the problem of stating whether the two logics are distinct. Further properties of these logics will be also investigated.Presented by H. Ono