The Vice: Some Historically Inspired and Proof-Generated Steps to Limits of Sequences

This paper proposes a genetic development of the concept of limit of a sequence leading to a definition, through a succession of proofs rather than through a succession of sequences or a succession of εs. The major ideas on which it is based are historical and depend on Euclid, Archimedes, Fermat, Wallis and Newton. Proofs of equality by means of inequalities precede the notion of limit. For example, the determination of the volume of a pyramid precedes the definition of limit. The algebraic details given here are anachronistically modern, and the notion of a vice between two inequalities which provides the distinctive perspective of this paper would not have been recognized in this form by any of the named mathematicians since it presumes the existence of negative numbers and their comparability in a modern sense with positive numbers.     

THE USES OF TELEVISION IN TEACHING PSYCHIATRY

The A.U.T.P. Working Party on the Applied Uses of Television was set up after the A UTP/ASME Conference on Undergraduate Education in Psychiatry and Behavioural Science held in Manchester in 1971. A group of Position Papers on the Uses of Television in Teaching Psychiatry has been published by the Working Party (AUTP, 1977), under the chairmanship of Professor David Goldberg. By his kind permission, two of these papers are here reprinted: one concerns the uses of television in undergraduate teaching of psychiatry; the other, ethical aspects of the use of television in psychiatry.     

Development of Oral Reading Fluency in Young Children at Risk for Failure

The body of knowledge on critical components of reading instruction is broad and deep with phonemic awareness, phonics, fluency, vocabulary, and comprehension serving as building blocks for literacy. The importance of fluent reading (i.e., with speed, accuracy, and proper expression, as well as comprehension) in the formula for success is widely accepted. The purpose of this study was to evaluate oral reading rates in a sample of 2nd-grade children. Using growth curve analysis, we identified models for a combined sample of at-risk and not-at-risk children. Large and important differences in oral reading were evident, but the growth rates remained the same throughout the 2nd- grade; in fact, the gap between at-risk and not-at-risk students remained constant. We discuss the implications of our findings for future research and the improvement of practice.