Model-based learning has an established position within science education. It has been found to enhance conceptual understanding and provide a way for engaging students in authentic scientific activity. Despite ample research, few studies have examined the cognitive processes regarding learning scientific concepts within MBL. On the other hand, recent research within cognitive science has examined the learning of so-called relational categories. Relational categories are categories whose membership is determined on the basis of the common relational structure. In this theoretical paper, (...) I argue that viewing models as relational categories provides a well-motivated cognitive basis for MBL. I discuss the different roles of models and modeling within MBL and discern the related cognitive aspects brought forward by the reinterpretation of models as relational categories. I will argue that relational knowledge is vital in learning novel models and in the transfer of learning. Moreover, relational knowledge underlies the coherent, hierarchical knowledge of experts. Lastly, I will examine how the format of external representations may affect the learning of models and the relevant relations. The nature of the learning mechanisms underlying students’ mental representations of models is an interesting open question to be examined. Furthermore, the ways in which the expert-like knowledge develops and how to best support it is in need of more research. The discussion and conceptualization of models as relational categories allows discerning students’ mental representations of models in terms of evolving relational structures in greater detail than previously done. (shrink)

The omnipresence of the same basic equations, function forms, algorithms, and quantitative methods is one of the most spectacular characteristics of contemporary modeling practice. Recently, the emergence of the discussion of templates and template transfer has addressed this striking cross-disciplinary reach of certain mathematical forms and computational algorithms. In this paper, we develop a notion of a model template, consisting of its mathematical structure, ontology, prototypical properties and behaviors, focal conceptualizations, and the paradigmatic questions it addresses. We apply this notion (...) to three widely disseminated and powerful model templates: the Sherrington-Kirkpatrick model of spin glasses, scale-free networks, and the Kuramoto model of synchronization. We argue that what appears to be an interdisciplinary model transfer between different domains turns out, from a broader perspective, to be the application of transdisciplinary model templates across a multitude of domains. We also point out a further feature of template-based modeling that so far has not been discussed: template entanglement. Such entanglement enhances and makes manifest the conceptual side of model templates. (shrink)

One striking feature of the contemporary modelling practice is its interdisciplinary nature. The same equation forms, and mathematical and computational methods, are used across different disciplines, as well as within the same discipline. Are there, then, differences between intra- and interdisciplinary transfer, and can the comparison between the two provide more insight on the challenges of interdisciplinary theoretical work? We will study the development and various uses of the Ising model within physics, contrasting them to its applications to socio-economic systems. (...) While the renormalization group methods justify the transfer of the Ising model within physics – by ascribing them to the same universality class – its application to socio-economic phenomena has no such theoretical grounding. As a result, the insights gained by modelling socio-economic phenomena by the Ising model may remain limited. (shrink)

Points of view are a central phenomenon in human cognition. Although the concept of point of view is ambiguous, there exist common elements in different notions. A point of view is a certain way to look at things around us. In conceptual points of view, things are looked at or interpreted through conceptual lenses. Conceptual points of view are important for epistemology, cognitive science, and philosophy of science. In this article, a new method to formalize conceptual points of view is (...) introduced. It is based on the conceptual space approach, where concepts are regions of multi-dimensional quality spaces. Points of view, as defined in this article, consist of a selection of relevant dimensions, referred to here as determinables, and of a certain supposition, referred to here as a theory, about the subject content. After considering some early efforts to formalize points of view, the notion of conceptual space is defined and explored. One concept of point of view is defined and developed in the framework of conceptual space, and a new logic for points of view is also outlined. The problem of mind–body correlation is discussed as an example of the application of the notion of points of view. To conclude, the meaning and applications of the new concepts and tools developed in the article are discussed. (shrink)

We introduce ‘model migration’ as a species of cross-disciplinary knowledge transfer whereby the representational function of a model is radically changed to allow application to a new disciplinary context. Controversies and confusions that often derive from this phenomenon will be illustrated in the context of econophysics and phylogeographic linguistics. Migration can be usefully contrasted with concept of ‘imperialism’, that has been influentially discussed in the context of geographical economics. In particular, imperialism, unlike migration, relies upon extension of the original model (...) via an expansion of the domain of phenomena it is taken to adequately described. The success of imperialism thus requires expansion of the justificatory sanctioning of the original idealising assumptions to a new disciplinary context. Contrastingly, successful migration involves the radical representational re-interpretation of the original model, rather than its extension. Migration thus requires ‘re-sanctioning’ of new ‘counterpart idealisations’ to allow application to an entirely different class of phenomena. Whereas legitimate scientific imperialism should be based on the pursuit of some form of ontological unification, no such requirement is need to legitimate the practice of model migration. The distinction between migration and imperialism will thus be shown to have significant normative as well as descriptive value. (shrink)

While many recent accounts of scientific representation have given a central role to the agency and intentions of scientists in explaining representation, they have left these agential concepts unanalyzed. An account of scientific, representational actions will be a useful piece in offering a more complete account of the practice of representation in science. Drawing on an Anscombean approach to the nature of intentional actions, the Means-End Account of Scientific, Representational Actions describes three features of scientific, representational actions: the final description (...) in the means-end ordering of descriptions is some scientific aim; that interaction with a vehicle distinct from its target stands as an earlier description which is ordered toward the final description as means to end; and the means-end structure is licensed by scientific practice. After describing each of the components of the Means-End Account in greater detail through the example of the representational use of a mathematical model, I explain how it can demarcate scientific, representational actions from other sorts of actions. I close by describing some payoffs of the account, showing how it contributes to a more thorough understanding of the practice of representation in science and how it can be of use in understanding the close connection between representation and other forms of scientific activity. (shrink)

While many recent accounts of scientific representation have given a central role to the agency and intentions of scientists in explaining representation, they have left these agential concepts unanalyzed. An account of scientific, representational actions will be a useful piece in offering a more complete account of the practice of representation in science. Drawing on an Anscombean approach to the nature of intentional actions, the Means-End Account of Scientific, Representational Actions describes three features of scientific, representational actions: (I) the final (...) description in the means-end ordering of descriptions is some scientific aim; (II) that interaction with a vehicle distinct from its target stands as an earlier description which is ordered toward the final description as means to end; and (III) the means-end structure is licensed by scientific practice. After describing each of the components of the Means-End Account in greater detail through the example of the representational use of a mathematical model, I explain how it can demarcate scientific, representational actions from other sorts of actions. I close by describing some payoffs of the account, showing how it contributes to a more thorough understanding of the practice of representation in science and how it can be of use in understanding the close connection between representation and other forms of scientific activity. (shrink)