A three dimensional model for using case studies in the academic classroom

Abstract This paper studies metaphor use in British Public Bill Committee debates. It focuses on the way in which legislators frame their arguments in metaphorical terms under the form of figurative analogies. Because these figurative analogies can be misleading by oversimplifying the issue under discussion, resisting them by putting forward counter-argumentation is a crucial and necessary skill. The purpose of this paper is to explore the phenomenon of countering figurative analogies in legislative debates, and to show that resistance to figurative analogies is a complex phenomenon comprising various types of criticisms to different types of metaphor. To this end, we present qualitative analyses of a number of case studies of resistance to figurative analogies found in the British Public Bill Committee debates on the Education Bill 2010–11 by employing the three-dimensional model of metaphor (Steen, 2011) and the pragma-dialectical theory of argumentation (Van Eemeren, 2010).

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Community organizational learning: Case studies illustrating a three-dimensional model of levels and orders of change

Journal of Community Psychology ◽

10.1002/jcop.20150 ◽

2007 ◽

Vol 35 (3) ◽

pp. 303-328 ◽

Cited By ~ 16

Author(s):

Douglas D. Perkins ◽

Kimberly D. Bess ◽

Daniel G. Cooper ◽

Diana L. Jones ◽

Theresa Armstead ◽

...

Keyword(s):

Organizational Learning ◽

Case Studies ◽

Three Dimensional ◽

Dimensional Model ◽

Three Dimensional Model

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Paper, Plaster, Strings: Exploratory Material Mathematical Models between the 1860s and 1930s

Perspectives on Science ◽

10.1162/posc_a_00378 ◽

2021 ◽

Vol 29 (4) ◽

pp. 436-467

Author(s):

Michael Friedman

Keyword(s):

Nineteenth Century ◽

Mathematical Models ◽

Case Studies ◽

Hyperbolic Plane ◽

Three Dimensional ◽

Decisive Role ◽

Dimensional Model ◽

Three Dimensional Model ◽

The Status ◽

String Models

Abstract Does the materiality of a three-dimensional model have an effect on how this model operates in an exploratory way, how it prompts discovery of new mathematical results? Material mathematical models were produced and used during the second half of the nineteenth century, visualizing mathematical objects, such as curves and surfaces—and these were produced from a variety of materials: paper, cardboard, plaster, strings, wood. However, the question, whether their materiality influenced the status of these models—considered as exploratory, technical, or representational—was hardly touched upon. This article aims to approach this question by investigating two case studies: Beltrami’s paper models vs. Dyck’s plaster ones of the hyperbolic plane; and Chisini’s string models of braids vs. Artin’s and Moishezon’s algebraization of these braids. These two case studies indicate that materiality might have a decisive role in how the model was taken into account mathematically: either as an exploratory or rather as a technical or pedagogical object.

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