This inaugural handbook documents the distinctive research field that utilizes history and philosophy in investigation of theoretical, curricular and pedagogical issues in the teaching of science and mathematics. It is contributed to by 130 researchers from 30 countries; it provides a logically structured, fully referenced guide to the ways in which science and mathematics education is, informed by the history and philosophy of these disciplines, as well as by the philosophy of education more generally. The first handbook to cover the (...) field, it lays down a much-needed marker of progress to date and provides a platform for informed and coherent future analysis and research of the subject. -/- The publication comes at a time of heightened worldwide concern over the standard of science and mathematics education, attended by fierce debate over how best to reform curricula and enliven student engagement in the subjects There is a growing recognition among educators and policy makers that the learning of science must dovetail with learning about science; this handbook is uniquely positioned as a locus for the discussion. -/- The handbook features sections on pedagogical, theoretical, national, and biographical research, setting the literature of each tradition in its historical context. Each chapter engages in an assessment of the strengths and weakness of the research addressed, and suggests potentially fruitful avenues of future research. A key element of the handbook’s broader analytical framework is its identification and examination of unnoticed philosophical assumptions in science and mathematics research. It reminds readers at a crucial juncture that there has been a long and rich tradition of historical and philosophical engagements with science and mathematics teaching, and that lessons can be learnt from these engagements for the resolution of current theoretical, curricular and pedagogical questions that face teachers and administrators. (shrink)

More than a hundred years ago, the American philosopher C. S. Peirce suggested the idea of pragmatism as a logical criterion to analyze what words and concepts express through their practical meaning. Many words have been spent on creative processes and reasoning, especially in the case of scientific practices. In fact, philosophers have usually offered a number of ways of construing hypotheses generation, but all aim at demonstrating that the activity of generating hypotheses is paradoxical, illusory or obscure, and thus (...) not analyzable. The “computational turn” gave us a new way to understand creative processes in a strictly pragmatic sense. Artificial Intelligence and Cognitive Science tools allow us to test concepts and ideas previously conceived in abstract terms. It is in the perspective of these actual models that we find the central role of abduction in the explanation of creative reasoning in science. What I call theoretical abduction certainly illustrates much of what is important in abductive reasoning, especially the objective of selecting and creating a set of hypotheses that are able to dispense good explanations of data, but fails to account for many cases of explanation occurring in science or in everyday reasoning when the exploitation of the environment is crucial. The concept of manipulative abduction is devoted to capture the role of action in many interesting situations: action provides otherwise unavailable information that enables the agent to solve problems by starting and performing a suitable abductive process of generation or selection of hypotheses. Many external things, usually inert from the epistemological point of view, can be transformed into what I call epistemic mediators, which are illustrated in the last part of the paper. (shrink)

Many important concepts of the calculus are difficult to grasp, and they may appear epistemologically unjustified. For example, how does a real function appear in “small” neighborhoods of its points? How does it appear at infinity? Diagrams allow us to overcome the difficulty in constructing representations of mathematical critical situations and objects. For example, they actually reveal the behavior of a real function not “close to” a point but “in” the point. We are interested in our research in the diagrams (...) which play an optical role –microscopes and “microscopes within microscopes”, telescopes, windows, a mirror role, and an unveiling role. In this paper we describe some examples of optical diagrams as a particular kind of epistemic mediator able to perform the explanatory abductive task of providing a better understanding of the calculus, through a non-standard model of analysis. We also maintain they can be used in many other different epistemological and cognitive situations. (shrink)

Work on analogy has been done from a number of disciplinary perspectives throughout the history of Western thought. This work is a multidisciplinary guide to theorizing about analogy. It contains 1,406 references, primarily to journal articles and monographs, and primarily to English language material. classical through to contemporary sources are included. The work is classified into eight different sections (with a number of subsections). A brief introduction to each section is provided. Keywords and key expressions of importance to research on (...) analogy are discussed in the introductory material. Electronic resources for conducting research on analogy are listed as well. (shrink)

Three studies were conducted to examine the relation of spatial visualization to solving kinematics problems that involved either predicting the two‐dimensional motion of an object, translating from one frame of reference to another, or interpreting kinematics graphs. In Study 1, 60 physics‐naíve students were administered kinematics problems and spatial visualization ability tests. In Study 2, 17 (8 high‐ and 9 low‐spatial ability) additional students completed think‐aloud protocols while they solved the kinematics problems. In Study 3, the eye movements of fifteen (...) (9 high‐ and 6 low‐spatial ability) students were recorded while the students solved kinematics problems. In contrast to high‐spatial students, most low‐spatial students did not combine two motion vectors, were unable to switch frames of reference, and tended to interpret graphs literally. The results of the study suggest an important relationship between spatial visualization ability and solving kinematics problems with multiple spatial parameters. (shrink)

A cognitive ethnography of how bioengineering scientists create innovative modeling methods. In this first full-scale, long-term cognitive ethnography by a philosopher of science, Nancy J. Nersessian offers an account of how scientists at the interdisciplinary frontiers of bioengineering create novel problem-solving methods. Bioengineering scientists model complex dynamical biological systems using concepts, methods, materials, and other resources drawn primarily from engineering. They aim to understand these systems sufficiently to control or intervene in them. What Nersessian examines here is how cutting-edge bioengineering (...) scientists integrate the cognitive, social, material, and cultural dimensions of practice. Her findings and conclusions have broad implications for researchers in philosophy, science studies, cognitive science, and interdisciplinary studies, as well as scientists, educators, policy makers, and funding agencies. In studying the epistemic practices of scientists, Nersessian pushes the boundaries of the philosophy of science and cognitive science into areas not ventured before. She recounts a decades-long, wide-ranging, and richly detailed investigation of the innovative interdisciplinary modeling practices of bioengineering researchers in four university laboratories. She argues and demonstrates that the methods of cognitive ethnography and qualitative data analysis, placed in the framework of distributed cognition, provide the tools for a philosophical analysis of how scientific discoveries arise from complex systems in which the cognitive, social, material, and cultural dimensions of problem-solving are integrated into the epistemic practices of scientists. Specifically, she looks at how interdisciplinary environments shape problem-solving. Although Nersessian’s case material is drawn from the bioengineering sciences, her analytic framework and methodological approach are directly applicable to scientific research in a broader, more general sense, as well. (shrink)

The central aim of science is to make sense of the world. To move forward as a community endeavor, sense-making must be systematic and focused. The question then is how do scientists actually experience the sense-making process? In this chapter we examine the “practice turn” in science studies and in particular how as a result of this turn scholars have come to realize that models are the “functional unit” of scientific thought and form the center of the reasoning/sense-making process. This (...) chapter will explore a context-dependent view of models and modeling in science. From this analysis we present a framework for delineating the different aspects of model-based reasoning and describe how this view can be useful in educational settings. This framework highlights how modeling supports and focuses scientific practice on sense-making. (shrink)

Our brains make up a series of signs and are engaged in making or manifesting or reacting to a series of signs: through this semiotic activity they are at the same time engaged in “being minds” and so in thinking intelligently. An important effect of this semiotic activity of brains is a continuous process of “externalization of the mind” that exhibits a new cognitive perspective on the mechanisms underling the semiotic emergence of abductive processes of meaning formation. To illustrate this (...) process I will take advantage of the analysis of some aspects of the cognitive interplay between internal and external representations. I consider this interplay critical in analyzing the relation between meaningful semiotic internal resources and devices and their dynamical interactions with the externalized semiotic materiality suitably stocked in the environment. Hence, minds are material, “extended” and artificial in themselves. A considerable part of human abductive thinking is occurring through an activity consisting in a kind of reification in the external environment and a subsequent re-projection and reinterpretation through new configurations of neural networks and chemical processes. I also illustrate how this activity takes advantage of hybrid representations and how it can nicely account for various processes of creative and selective abduction, bringing up the question of how multimodal aspects involving a full range of sensory modalities are important in hypothetical reasoning. (shrink)

Understanding nature of science is widely considered an important educational objective and views of NOS are closely linked to science teaching and learning. Thus there is a lively discussion about what understanding NOS means and how it is reached. As a result of analyses in educational, philosophical, sociological and historical research, a worldwide consensus about the content of NOS teaching is said to be reached. This consensus content is listed as a general statement of science, which students are supposed to (...) understand during their education. Unfortunately, decades of research has demonstrated that teachers and students alike do not possess an appropriate understanding of NOS, at least as far as it is defined at the general level. One reason for such failure might be that formal statements about the NOS and scientific knowledge can really be understood after having been contextualized in the actual cases. Typically NOS is studied as contextualized in the reconstructed historical case stories. When the objective is to educate scientifically and technologically literate citizens, as well as scientists of the near future, studying NOS in the contexts of contemporary science is encouraged. Such contextualizations call for revision of the characterization of NOS and the goals of teaching about NOS. As a consequence, this article gives two examples for studying NOS in the contexts of scientific practices with practicing scientists: an interview study with nanomodellers considering NOS in the context of their actual practices and a course on nature of scientific modelling for science teachers employing the same interview method as a studying method. Such scrutinization opens rarely discussed areas and viewpoints to NOS as well as aspects that practising scientists consider as important. (shrink)

Cases where analogy has played a significant role in the formation of a new scientific concept are well-documented. Yet, how is it that genuinely new representations can be constructed from existing representations? It is argued that the process of ‘generic modeling’ enables abstraction of features common to both the domain of the source of the analogy and of the target phenomena. The analysis focuses on James Clerk Maxwell's construction of the electromagnetic field concept. The mathematical representation Maxwell constructed turned out (...) to be a system of abstract laws that when applied to electromagnetic systems yield laws of a dynamical system that will not map back onto the mechanicals domains used in their construction. (shrink)

Although most philosophers are not aware of it, research in cognitive development and in learning in the last decade has made considerable use of the characterizations of the nature and development of scientific knowledge proffered by philosophers of science. In a “reflexive” move, Alison Gopnik proposes philosophers of science can profit from the research of psychologists investigating cognitive development-specifically from that group of researchers who advocate the “theory theory.”.

The extensive use of modelling in physics research has many implications on how it is used in physics education. An interesting case is the use of models in producing of new knowledge, which we here refer to as generative modelling. Generative modelling can serve as a cognitive tool bridging conceptual reality and real phenomena by mutually fitting of simulations and experiments. In this fitting process of fitting, pursuing partial mimetic similarity in simulations and experiments acquires a central epistemological role. At (...) the core of generative modelling is the creative use of theoretical and empirical elements of modelling as well as the explorative manipulation of real conditions to fit the models. We argue here that such modelling is also identifiable as authentic by the modelling practitioners themselves and that such a modelling approach supports constructively oriented and creative teaching solutions. (shrink)

Many important concepts of the calculus are difficult to grasp, and they may appear epistemologically unjustified. For example, how does a real function appear in “small” neighborhoods of its points? How does it appear at infinity? Diagrams allow us to overcome the difficulty in constructing representations of mathematical critical situations and objects. For example, they actually reveal the behavior of a real function not “close to” a point (as in the standard limit theory) but “in” the point. We are interested (...) in our research in the diagrams which play an optical role –microscopes and “microscopes within microscopes”, telescopes, windows, a mirror role (to externalize rough mental models), and an unveiling role (to help create new and interesting mathematical concepts, theories, and structures). In this paper we describe some examples of optical diagrams as a particular kind of epistemic mediator able to perform the explanatory abductive task of providing a better understanding of the calculus, through a non-standard model of analysis. We also maintain they can be used in many other different epistemological and cognitive situations. (shrink)

One approach to understanding model-based reasoning in science is to examine how it develops during infancy, childhood, and adolescence. The way in which thinking changes sometimes provides clues to its nature. This paper examines cognitive developmental aspects of modeling practices and discusses how a developmental perspective can enrich the study of model-based scientific reasoning in adults. The paper begins with issues concerning developmental change, followed by a model of model-based reasoning. The rest of the paper describes how several key concepts (...) from recent developmental work could contribute to current work on model-based reasoning. Specifically, developmental research shows that (a) social processes are involved in model-based reasoning and scientific discovery, (b) the development of a theory of mind contributes to the development of scientific reasoning, (c) changes in scientific reasoning are characterized by cognitive variability, and (d) microgenetic methods could clarify conceptual change during model-based reasoning. (shrink)

Cases where analogy has played a significant role in the formation of a new scientific concept are well-documented. Yet, how is it that genuinely new representations can be constructed from existing representations? It is argued that the process of ‘generic modeling’ enables abstraction of features common to both the domain of the source of the analogy and of the target phenomena. The analysis focuses on James Clerk Maxwell's construction of the electromagnetic field concept. The mathematical representation Maxwell constructed turned out (...) to be a system of abstract laws that when applied to electromagnetic systems yield laws of a dynamical system that will not map back onto the mechanicals domains used in their construction. (shrink)

Philosophers of science today by and large reject the cataclysmic and irrational interpretation of the scientific enterprise claimed by Kuhn. Many computational models have been implemented to rationally study the conceptual change in science. In this recent tradition a key role is played by the concept of abduction as a mechanism by which new explanatory hypotheses are introduced. Nevertheless some problems in describing the most interesting abductive issues rise from the classical computational approach. It describes a cognitive process (and so (...) abduction) by the manipulation of internal symbolic representations of external world. This view assumes a discrete set of representations fixed in discrete time jumps, and cannot adequately account for the issue of anticipation and causation of a new hypothesis. An integration of the traditional computational view with some ideas developed inside the so-called dynamical approach can suggest some important insights. The concept of attractor is very significant. It permits a description of the abductive generation of new hypotheses in terms of a catastrophic rearrangement of the parameters responsible for the behavior of the system. (shrink)

Computational philosophy (CP) aims at investigating many important concepts and problems of the philosophical and epistemological tradition in a new way by taking advantage of information-theoretic, cognitive, and artificial intelligence methodologies. I maintain that the results of computational philosophy meet the classical requirements of some Peircian pragmatic ambitions. Indeed, more than a 100 years ago, the American philosopher C.S. Peirce, when working on logical and philosophical problems, suggested the concept of pragmatism(pragmaticism, in his own words) as a logical criterion to (...) analyze what words and concepts express through their practical meaning. Many words have been spent on creative processes and reasoning, especially in the case of scientific practices. In fact, many philosophers have usually offered a number of ways of construing hypotheses generation, but they aim at demonstrating that the activity of generating hypotheses is paradoxical, obscure, and thus not analyzable. Those descriptions are often so far from Peircian pragmatic prescription and so abstract to result completely unknowable and obscure. To dismiss this tendency and gain interesting insight about the so-called logic of scientific discovery we need to build constructive procedures, which could play a role in moving the problem-solving process forward by implementing them in some actual models. The computational turn gives us a new way to understand creative processes in a strictly pragmatic sense. In fact, by exploiting artificial intelligence and cognitive science tools, computational philosophy allows us to test concepts and ideas previously conceived only in abstract terms. It is in the perspective of these actual computational models that I find the central role of abduction in the explanation of creative reasoning in science. I maintain that the computational philosophy analysis of model-based and manipulative abduction and of external and epistemic mediators is important not only to delineate the actual practice of abduction, but also to further enhance the development of programs computationally adequate in rediscovering, or discovering for the first time, for example, scientific hypotheses or mathematical theorems. The last part of the paper is devoted to illustrating the problem of the extra-theoretical dimension of reasoning and discovery from the perspective of some mathematical cases derived from calculus and geometry. (shrink)