First Published in 1984. Routledge is an imprint of Taylor & Francis, an informa company.

Chemistry seeks to provide qualitative and quantitative explanations for the observed behaviour of elements and their compounds. Doing so involves making use of three types of representation: the macro (the empirical properties of substances); the sub-micro (the natures of the entities giving rise to those properties); and the symbolic (the number of entities involved in any changes that take place). Although understanding this triplet relationship is a key aspect of chemical education, there is considerable evidence that students find great difficulty in achieving mastery of the ideas involved. In bringing together the work of leading chemistry educators who are researching the triplet relationship at the secondary and university levels, the book discusses the learning involved, the problems that students encounter, and successful approaches to teaching. Based on the reported research, the editors argue for a coherent model for understanding the triplet relationship in chemical education.

This volume is important because despite various external representations, such as analogies, metaphors, and visualizations being commonly used by physics teachers, educators and researchers, the notion of using the pedagogical functions of multiple representations to support teaching and learning is still a gap in physics education. The research presented in the three sections of the book is introduced by descriptions of various psychological theories that are applied in different ways for designing physics teaching and learning in classroom settings. The following chapters of the book illustrate teaching and learning with respect to applying specific physics multiple representations in different levels of the education system and in different physics topics using analogies and models, different modes, and in reasoning and representational competence. When multiple representations are used in physics for teaching, the expectation is that they should be successful. To ensure this is the case, the implementation of representations should consider design principles for using multiple representations. Investigations regarding their effect on classroom communication as well as on the learning results in all levels of schooling and for different topics of physics are reported. The book is intended for physics educators and their students at universities and for physics teachers in schools to apply multiple representations in physics in a productive way.

How human musical experience emerges from the audition of organized tones is a riddle of long standing. In The Musical Representation, Charles Nussbaum offers a philosophical naturalist's solution. Nussbaum founds his naturalistic theory of musical representation on the collusion between the physics of sound and the organization of the human mind-brain. He argues that important varieties of experience afforded by Western tonal art music since 1650 arise through the feeling of tone, the sense of movement in musical space, cognition, emotional arousal, and the engagement, by way of specific emotional responses, of deeply rooted human ideals. Construing the art music of the modern West as representational, as a symbolic system that carries extramusical content, Nussbaum attempts to make normative principles of musical representation explicit and bring them into reflective equilibrium with the intuitions of competent listeners. Nussbaum identifies three modes of musical representation, describes the basis of extramusical meaning, and analyzes musical works as created historical entities (performances of which are tokens or replicas). In addition, he explains how music gives rise to emotions and evokes states of mind that are religious in character. Nussbaum's argument proceeds from biology, psychology, and philosophy to music--and occasionally from music back to biology, psychology, and philosophy. The human mind-brain, writes Nussbaum, is a living record of its evolutionary history; relatively recent cognitive acquisitions derive from older representational functions of which we are hardly aware. Consideration of musical art can help bring to light the more ancient cognitive functions that underlie modern human cognition. The biology, psychology, and philosophy of musical representation, he argues, have something to tell us about what we are, based on what we have been.

Marx Wartofsky has been working for many years within an unusual confluence of philosophical problems. He brings to these intersecting problems his comprehensive intelligence, at once imaginative and rigorous, analytic and historical. He is a philosopher's philosopher, but also Everyman's. Wartofsky is philosopher of the natural and the social sciences, of perception, esthetics and the creative arts, of the 18th century French and the 19th century Germans, of politics and morality, ofthe methods and morals of medicine, and it is plain, of all human existence. To a colleague, he seems Jack-of-all-philosophical-trades, and master of them too. The reader soon will learn that Wartofsky is a genial, lucid and relaxed philosophical companion, deeply serious but without noticeable anxiety. I need not highlight these selected epistemological papers gathered as, and about, Models, since Wartofsky's own introductory remarks are helpful and stimulating in that respect. I need only, after 21 years of friendship and collaboration with him, warn the reader to beware of how profound and provocative these papers will show themselves to be beneath their good-humored and swiftly-flowing surface. And I must publicly note the pleasure with which I welcome Marx Wartofsky's volume to our Boston Studies. Boston University R.S.C. Center for the Philosophy and History of Science September 1979 vii TABLE OF CONTENTS EDITORIAL PREFACE VII xi AC K NOWLEDGEMENTS xiii INTRODUCTION The Model Muddle: Proposals for an Immodest Realism 1.

Instruction is an effort to assist or to shape growth. In devising instruction for the young, one would be ill advised indeed to ignore what is known about growth, its constraints and opportunities. And a theory of instruction - and this book is a series of exercises in such a theory - is in effect a theory of how growth and development are assisted by diverse means.