Like the learning abilities of their students, the teaching abilities of college professors seem to develop in stages. In this paper I want to offer an account of how this development sometimes, and perhaps often, proceeds. Typically, when they begin their teaching careers, professors focus their concern primarily on their own role in the classroom (stage I: self). When they have mastered this role, at least to their own satisfaction, the focus of their concern shifts, first to their understanding of the subject matter they teach (stage 2: subject) and then to their students" ability to absorb what they have been taught (stage 3: student). With this last shift comes a more general shift of focus from teaching to learning, that begins, in stage 3, with a focus on helping their students become more absorbent (stage 3: student as receptive). Concern then typically shifts to helping students learn to use what they have been taught (stage 4: student as active) and then to helping them to learn on their own (stage 5: student as independent). My account of this development is based on the informal observation of a few cases and it suggests a framework for thinking about the development of professors as teachers. With further work, it might lead to theories that will describe what does happen and predict what will happen.

The uncomputable parts of thinking (if there are any) can be studied in much the same spirit that Turing (1950) suggested for the study of its computable parts. We can develop precise accounts of cognitive processes that, although they involve more than computing, can still be modelled on the machines we call 'computers'. In this paper, I want to suggest some ways that this might be done, using ideas from the mathematical theory of uncomputability (or Recursion Theory). And I want to suggest some uses to which the resulting models might be put. (The reader more interested in the models and their uses than the mathematics and its theorems, might want to skim or skip the mathematical parts.)

The indicativity of a type of catalog information (or catalog field) is intended as a measure of how well the information in the field conveys the contents of the document it represents. In the experiments reported here, indicativity is measured for several catalog fields by comparing users' evaluations of the relevance of documents on the basis of the information in a given field with their judgments on the basis of full text. A small but statistically significant increase in indicativity is found as the length of a catalog field (as measured by the number of different content‐word stems) is increased. The title field is found to have an indicativity of 0.64; matching subjects, 0.67; subjects, 0.70; abstract, 0.73. Despite the relatively small gain in indicativity for the longer fields, users value the longer fields highly for determining relevance if one judges by the amount of time they spend on them. Support for the hypothesis that the indicativity measure does not fully reflect the value of the fields is developed. Thus, the question of the cost effectiveness of the longer fields is unresolved. Other aspects of catalog field utility studied under the Project Intrex equipments are also reported.

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