Tacit Model Research Articles

Exploring the relationship between tacit models and mathematical infinity through history

In this article we address the historical and epistemological study of infinity as a mathematical concept, focusing on identifying difficulties, counter-intuitive ideas and paradoxes that constituted implicit, unconscious models faced by mathematicians at different times in history, representing obstacles in the rigorous formalization process of this mathematical concept. It is shown how the active and conscious questioning of these models led to a process of axiomatization of mathematical infinity, which was completed with the works of Cantor (1883) and Robinson (1974). The implemented methodology is supported by a qualitative and argumentative bibliographic research based on content analysis from a meta-ethnography. From this research, information is obtained about the unconscious mathematical structures students are confronted with and the conscious patterns of reasoning they must develop to overcome difficulties and obstacles that these models produce, and thus achieve an adequate understanding of mathematical infinity.

Getting Fra Angelico’s splotch out: rehabilitating visual cognitive semiotics

Abstract Most contemporary approaches to meaning presume the limitation of semiotics (Didi-Huberman, Gumbrecht, Belting). The question of what kind of “semiotics” is required has not been asked. However, without some general science of meaning it is impossible to reform theory without committing past errors or ignoring progress. In the interest of reconnecting contemporary interests in “presence” to long-evolving needs, I review the ossification and decline of one theory of semiotics that serves as the tacit model rejected today. I return to problems of the nature of the sign – whether it is “digital” or “analog” and conceived as “communication” or merely “meaning.” I then reconstitute a workable visual cognitive semiotics based on phenomenological premises.

Conceptual Metaphors and Tacit Models in the Study of Mathematical Infinity

This work shows the connections between conceptual metaphors and uncon-scious, tacit models that benefit our understanding of mathematical infinity in the university classroom. From the perspective of cognitive linguistics, it is argued that conceptual metaphors play a key role in explaining how this mathematical concept is grounded in our experience, simultaneously providing a mechanism to address these tacit models in a more conscious way. Moreover, it is shown that conceptual metaphors can be built from the conflicting cognitive structures un-derlying these models, specifying obstacles and difficulties that teachers must consider when designing activities aimed at achieving an adequate understanding of mathematical infinity. This type of study allows us to improve our teaching practice, making us aware and stimulating students to become aware, to reflect on the inconsistencies of their own thoughts and intuitions regarding this mathemati-cal concept. At the same time, it allows us to show the validity of these inconsist-encies by revealing how our cognitive processes are constrained by bodily-grounded experiences determined by the complexity of our human nervous sys-tem. The use of technology would also engage students in these reflections and could also help them by fostering new ways of thinking about mathematical infin-ity. This perspective would be of interest in the current context of digital technol-ogy in mathematics education research.

Eliciting experts’ tacit models for the interpretation of soil information, an example from the evaluation of potential benefits from conservation agriculture

We examined a procedure to elicit the tacit models underlying expert opinions on environmental factors that affect the absolute yield benefits expected from the adoption of conservation agriculture (CA) practices in southern Africa. The procedure is based on expert evaluation of the expected improvement in crop yield on adoption of CA in a particular scenario or ‘state’, a state being a specified set of soil conditions captured by a standard soil profile description from a specified agroecological zone (AEZ) of Zambia. Mixed groups of scientists including soil scientists, agronomists, agricultural economists and other environmental scientists, facilitated by experienced senior researchers, were presented with multiple subsets each of three states, and asked to rank the states in each subset with respect to expected yield improvement under CA. The groups of scientists could be divided into two sets. Each set comprised two groups, and the agreement on ranking between groups within each set was larger than would be expected if the ranking were done at random. For both sets of groups the ranking could be modelled with respect to properties of the soil, and the contrast between AEZ. The models revealed two contrasting groups of conceptual assumptions. One group broadly expected larger absolute yield improvements from conservation agriculture in settings where water is most likely to be limiting and the carbon status of the soil is poor. By contrast, the other group expected larger improvements where water was less likely to be limiting. These contrasting views are relevant to current discussions as to whether conservation agriculture, which is promoted as a ‘climate smart’ strategy for cropping, is sufficiently attractive for smallholder producers in conditions where crop production is already challenging, and whether the potential benefits in areas where water availability is not of itself a common limitation should be considered. The elicited models could be translated directly into competing hypotheses to be tested, perhaps in on-farm trials of conservation agriculture practices over contrasting soils in the different AEZ. The method, based on modelling the ranking process, could be of more general interest for the elicitation of expert opinion about complex soil, crop and environmental systems.

Victorian Feminist Criticism: Recovery Work and the Care Community

It is fitting that this article emerged from a conference in which the orderly progression of speakers was continually modified by exchanges within the conference space, for these two ways of organizing information form the subject of this article. When we aim to recover Victorian women writers, we often imagine a particular case in a timeline, selecting and extracting in a tacit model of linear orderliness. This is particularly significant in what we might call “recovery feminism,” the practice of salvaging texts that have been lost to history. Recovery feminism has dominated Victorianist feminist criticism since its development in the late 1970s, and I practiced it enthusiastically in my first book,The Forgotten Female Aesthetes. In this article, I want to acknowledge what recovery feminism has given us, but I also want to delineate the profound and often unarticulated ways it continues to structure our work, often with unintended consequences. In order to explore alternative forms of feminism, I assess theories of influence and intertextuality, and I use Charlotte M. Yonge'sThe Heir of Redclyffe(1853) as an example that both thematizes this issue and acts as a case study of forms of feminist criticism. A viable feminist criticism, I contend, ought to be able to address a novel likeHeir, andHeiritself may be able to provide a model for how to do that. Such a model of feminist practice might actually resemble the simultaneous, atemporal, interactive model of the conference day. In the digital era, we occupy an alternative chronology, in which we envision ourselves not as strenuously excavating the last disintegrating relics of the past, but rather as choosing among multiple simultaneous virtual texts, severed from markers of time or space. What might be a feminist critical practice for the way we work now?

Tacit Models that Govern Undergraduate Reasoning about Subspaces

This study is concerned with the reasoning that undergraduates apply when deciding whether a prompt is an example or non-example of the subspace concept. A qualitative analysis of written responses of 438 students revealed five unconventional tacit models that govern their reasoning. The models account for whether a prompt is a subset of a vector space, whether the zero vector is included, the structure of vectors, their number in the formula for the general solution to the system of linear equations, and the corresponding coefficient matrix. Furthermore, a conception was identified in students’ responses, according to which the algebraic structure of a vector space passes from a ‘parent’ space to its subset, turning automatically it into a subspace. For many students this conception of an inheriting structure was instrumental for identifying and reasoning around subspaces. Polysemy of the prefix ‘sub’ and students’ prior experiences in identifying concept examples are used for offering explanations for the emergence of the conception.

Global Mental Health: Anthropological Perspectives

Global Mental Health: Anthropological Perspectives

Uncertainty in mapped geological boundaries held by a national geological survey:eliciting the geologists' tacit error model

Abstract. It is generally accepted that geological line work, such as mapped boundaries, are uncertain for various reasons. It is difficult to quantify this uncertainty directly, because the investigation of error in a boundary at a single location may be costly and time consuming, and many such observations are needed to estimate an uncertainty model with confidence. However, it is recognized across many disciplines that experts generally have a tacit model of the uncertainty of information that they produce (interpretations, diagnoses, etc.) and formal methods exist to extract this model in usable form by elicitation. In this paper we report a trial in which uncertainty models for geological boundaries mapped by geologists of the British Geological Survey (BGS) in six geological scenarios were elicited from a group of five experienced BGS geologists. In five cases a consensus distribution was obtained, which reflected both the initial individually elicited distribution and a structured process of group discussion in which individuals revised their opinions. In a sixth case a consensus was not reached. This concerned a boundary between superficial deposits where the geometry of the contact is hard to visualize. The trial showed that the geologists' tacit model of uncertainty in mapped boundaries reflects factors in addition to the cartographic error usually treated by buffering line work or in written guidance on its application. It suggests that further application of elicitation, to scenarios at an appropriate level of generalization, could be useful to provide working error models for the application and interpretation of line work.

Relazioni sistemiche tra imprenditorialità interna e gemmazione d’impresa: una ricerca empirica sulla natura cognitiva delle nuove imprese

The management of knowledge is increasingly considered as a main source of competitive advantage for corporations. It is argued that companies enjoy a competitive advantage if they know how to expand, disseminate and exploit organizational knowledge internally. Moreover, to achieve those goals the executive body is required to encourage knowledge sharing, flexibility, and adaptation to change, by spreading the entrepreneurial learning throughout all the levels of the organization. Although this attitude has positive results as it favours a better circulation of know-how within the company, on the other hand it may also generate upsetting behaviours leading to hostile spin off processes, as a result of the employees’ stratification of tacit knowledge and of cognitive maps. Then, this study assumes and empirically tests the possible relationships between firm specific knowledge stratification and corporate spin offs. By the way, spin off is assumed to be an adequate instrument for the spontaneous or induced transfer outside the parent company of tacit behavioural models, apparently similar to organizational routines, but as a matter of fact much more complex and refined: the cognitive scripts.

Tacit models, treasured intuitions and the discrete—continuous interplay

We explore conditions for productive synthesis between formal reasoning and intuitive representations through analysis of college students’ understanding of the limit concept in the definition of the derivative. In particular, we compare and contrast cognitive processes that accompany different manifestations of persistence of intuitions and tacit models that coexist with students’ logical reasoning. The students are highly trained in mathematics. We encounter expressions of the persistence and impact of intuitions and tacit pictorial models as described by Fischbein. But we also observe some new characterization of persistence of tacit models in which the tacit pictorial model continues to interfere in the student’s reasoning process, coexists with a logical reasoning but does not prevent the student from reaching a feeling of logical consistency. The empirical analysis and the theoretical discussion offered in the present paper permit us to highlight this very special integration of the formal and the intuitive components of the reasoning process.

The Overgeneralization of Linear Models among University Students' Mathematical Productions: A Long-Term Study

Over the past several years, we have been exploring and researching a phenomenon that occurs among undergraduate students that we called extension of linear models to non-linear contexts or overgeneralization of linear models. This phenomenon appears when some students use linear representations in situations that are non-linear. In a first phase, we recognized and characterized the overgeneralization among agronomy majors while working with different kinds of problems. This process let us raise some conjectures about the statement of the problems that were studied in a second phase. In a third phase we conducted some interviews in order to deepen our understanding. The study allowed us to discuss: (a) the robustness and broadness of the linear models as tacit models among university students, (b) the emergence of a tension between unrealistic tasks posed by the teacher/researcher and the students' realistic interpretation of it, and (c) some considerations about the teaching environment at university level.

Combining different theoretical perspectives for analyzing students’ difficulties in vector spaces theory

This paper originates from our doctorate research project, in which we investigated graduate and undergraduate students’ errors and difficulties in vector space theory (VST). After a brief account of the whole study, we will focus on the analyses carried out through the lenses of two different theoretical frameworks: Fischbein’s Theory of Tacit Models and Sfard’s process/object duality theory. We also propose a retrospective reflection concerning the reasons why we chose to carry out our analysis according to more than one theoretical framework and why we chose those specific theoretical frameworks as well. Hence this contribution has a double focus: on the one hand it reports on the results drawn from our study on students’ difficulties in VST; on the other hand it presents a personal retrospective reflection on the use of theoretical frames within that study.

Evaluation of support groups for women with breast cancer: importance of the navigator role

BackgroundAt least some forms of breast cancer are increasingly being viewed as a chronic illness, where an emphasis is placed on meeting the various ongoing needs of people living with cancer, their families and other members of their social support networks. This commentary outlines some approaches to the evaluation of cancer-related support groups, with a particular emphasis on those designed to provide long-distance support, via the internet, for women with breast cancer.DiscussionThe literature on evaluations of community-based cancer support groups indicates that they offer a number of benefits, and that it is more reasonable to expect an impact of such interventions on psychosocial functioning and/or health-related quality of life than on survival. The literature on both face-to-face and online social support groups suggests that they offer many advantages, although evaluation of the latter delivery mechanism presents some ethical issues that need to be addressed. Many popular online support groups are peer-moderated, rather than professionally-moderated. In an evaluation of online support groups, different models of the role of the "navigator" need to be taken into account. Some conceptual models are outlined for the evaluation of the "navigator role" in meeting the informational, decisional and educational needs of women with breast cancer. The Breast-Cancer Mailing List, an example of an unmoderated internet-based peer-support group, is considered within the context of a Shared or Tacit Model of the navigator role.ConclusionApplication of the concept of a "navigator role" to support groups in general, and to unmoderated online ones in particular, has received little or no attention in the research literature. The navigator role should be taken into account in research on this increasingly important aspect of cancer communication.

A “CONCEPTS-ON” PROJECT ON UNDERGRADUATE CONTROL EDUCATION

The relevance of the conceptual learning in control education is analyzed in this paper. It indicates a concepts-on view of control education. This approach, that already is the tacit model of classroom education, tries to complement recent control educational trends. In this context, it presents a recent project called “Virtual Control School” in development at the Federal University of Santa Catarina. This project tries to integrate pedagogical, computational and epistemological aspects in order to assist the control teaching and learning processes.

Tacit Models and Infinity

The paper analyses several examples of tacit influences exerted by mental models on the interpretation of various mathematical concepts in the domain of actual infinity. The influences of the respective tacit models, being generally uncontrolled consciously, may lead to erroneous interpretations, to contradictions and paradoxes. The paper deals especially with the unconscious effect of the figural-pictorial models of statements related to the infinite sets of geometrical points (on a segment, a square, or a cube) related to the concepts of function and derivative and to the spatial interpretation of time and motion in Zeno's paradoxes.

Narrative Research in Design Practice: Capturing Mental Models of Work Environments

Within practice, designers are increasingly pressured to establish proofs and utilize quantitative data to guide solutions. Analyzing the human component within an organization, however, may require adopting qualitative research tools that redefine performance beyond the limitations of quantitative tools. This report examines STUDIOS Architecture's use of narrative research in practice. Narrative research is utilized in situations when STUDIOS examines mental models of work environments held by clients and end–users. STUDIOS’ definition of a mental model of work is the set of work–related beliefs, motives, and behaviors from which an organization or individuals operate. Narratives gleaned from a wide range of individuals define the organization within a collective voice. STUDIOS’ approach to narrative is related to holistic–content methodologies (Liebich, Tuval–Mashiach, & Zilber, 1998) and incorporates traditional content analysis (Weber, 1990) to deconstruct and analyze narrative content. A predetermined research scope determines the initial parameters of analysis to be most meaningful to the client. Domains, or categories of meaning, are established to fit the project objectives while patterns within and between these domains are then identified within the narratives to capture mental models of work environments. Narrative research allows the designer and client to discover these tacit models and make inferences as to the connection of beliefs, motives, and behaviors to the physical environment. Future exploration in adapting narrative research methods for design, within both education and practice, will increase the body of knowledge that informs design, allowing the designer to better understand the relationship between people and the workplace.

The Mathematical Concept of set and the 'Collection' Model

Analysing the various misconceptions held by students with regard to the mathematical set concept, the authors hypothesized that these misunderstandings may be explained by the initial ‘collection’ model. Even after learning the formal properties of a set in the mathematical sense, the students are still influenced in their reactions by the collection representation, which acts ‘from behind the scenes’ as a tacit model. If the mathematical concept is not continually reinforced through systematic use, it is the initial figural interpretation which will replace, as an effect of time, the formal one. The findings confirmed this hypothesis.

WHY HORROR? THE PECULIAR PLEASURES OF A POPULAR GENRE

What is the appeal of horror? Various attempts have been made to answer this question, generally combining arguments about the nature of horror texts with arguments about the distinctive character of horror consumers. The most common attempts at general explanation are grounded in concepts drawn from psychoanalytic theory, some depending quite directly on Freud's ‘return of the repressed’ argument in his discussion of ‘the uncanny’, others utilizing the framework of ‘structural psychoanalysis’ to explore the ways in which the unconscious structures forms of representation. Examples of both forms of analysis are discussed – largely in relation to horror movies – exemplified in the recent work of Wood, Twitchell, Creed and Clover. General explanations which do not use psychoanalytic arguments are less common, though Carroll has recently offered one such approach which is given consideration here. It is argued that these attempts at posing general explanations of the appeal of horror are, at worst, inappropriately reductive and, at best, insufficiently specific, failing to distinguish the diverse pleasures that heterogeneous horror audiences take from their active involvement in the genre. Alternative, more particularistic approaches are considered (exemplified in aspects of work by Biskind, Carroll, Dika, Jancovich and Tudor) which seek to relate textual features to specific social circumstances. It is argued that such approaches pre-suppose a social ontology centred upon active social agents who use cultural artefacts as resources in rendering coherent their everyday lives. This is in some contrast to attempts to provide general explanations of horror's appeal where the tacit model is one in which human agents are pre-constituted in key respects, horror appealing, therefore, because it gratifies pre-established desires. It is suggested that the former, active and particularistic conception is to be preferred and that this necessitates a renewed attempt to grasp the diversity of what is, after all, a heterogenous audience capable of taking diverse pleasures from their favoured genre.

Tacit models of disability underlying health status instruments

In recent years much attention has been paid to the development of measures of subjective health status yet, although statistical criteria of reliability and validity have been quite rigourously tested, there has been little consideration of the different theories of disability which underlie the design. The sociology of disability may illuminate such tacit theories. It is suggested that the development of health status questionnaires has not been one of simple rational accumulation in response to methodological advances. Through an examination of the content of health assessment questionnaires, four distinct models of disability are indentified. These are shown to influence not only the focus of the content and phrasing of the questions but also, crucially, the way that they perform and how responsive they are to change. The models (the functional, subjective distress, comparative and dependence) are illustrated and discussed in terms related to research design.

Anthropology and psychiatry. The role of culture in cross-cultural research on illness.

To illustrate the contribution anthropology can make to cross-cultural and international research in psychiatry, four questions have been put to the cross-cultural research literature and discussed from an anthropological point of view: 'To what extent do psychiatric disorders differ in different societies?' 'Does the tacit model of pathogenicity/pathoplasticity exaggerate the biological aspects of cross-cultural findings and blur their cultural dimensions?' 'What is the place of translation in cross-cultural studies?' and 'Does the standard format for conducting cross-cultural studies in psychiatry create a category fallacy?' Anthropology contributes to each of these concerns an insistence that the problem of cross-cultural validity be given the same attention as the question of reliability, that the concept of culture be operationalised as a research variable, and that cultural analysis be applied to psychiatry's own taxonomies and methods rather than just to indigenous illness beliefs of native populations.