I analyze the role of infinite idealizations used in the renormalization group (RG hereafter) method in explaining universality across microscopically different physical systems in critical phenomena. I argue that despite the reference to infinite limit systems such as systems with infinite correlation lengths during the RG process, the key to explaining universality in critical phenomena need not involve infinite limit systems. I develop my argument by introducing what I regard as the explanatorily relevant property in RG explanations: (...) linearization* property; I then motivate and prove a proposition about the linearization* property in support of my view. As a result, infinite limit systems in RG explanations are dispensable. (shrink)

Renormalization group (RG) theory, while proposed to study particle physics, has found its usage in a large variety of topics over the years, including other physics branches like solid state physics, fluid mechanics, cosmology, machine learning and even non-physics fields like biology, epidemiology, economics, psychology, sociology and so on. The omnipresence of renormalization group theory thus raises the philosophical question of what are the common features of the systems that enable the employment of RG theory and (...) what can be revealed by using the RG method, why renormalization group theory is the naturally approach to deal with these problems and what is the essential point that leads to organizing the system according to renormalization group flow, i.e., order and disorder. These question are addressed in this paper. (shrink)

Renormalisation Group (RG) methods are one of the theoretical masterpieces of postwar physics whose historical development still remains largely unexplored. This article traces the origins of Kenneth Wilson's RG from 1956 to 1965, with a particular focus on its relationship to Murray Gell-Mann and Francis Low's RG published in 1954. I argue that there is ultimately little methodological and conceptual continuity between their respective versions. The article briefly concludes with the evolution of the Wilsonian RG from 1965 to the (...) early 1970s. (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)

Batterman and Rice ([2014]) argue that minimal models possess explanatory power that cannot be captured by what they call ‘common features’ approaches to explanation. Minimal models are explanatory, according to Batterman and Rice, not in virtue of accurately representing relevant features, but in virtue of answering three questions that provide a ‘story about why large classes of features are irrelevant to the explanandum phenomenon’ ([2014], p. 356). In this article, I argue, first, that a method (the renormalization (...) class='Hi'>group) they propose to answer the three questions cannot answer them, at least not by itself. Second, I argue that answers to the three questions are unnecessary to account for the explanatoriness of their minimal models. Finally, I argue that a common features account, what I call the ‘generalized ontic conception of explanation’, can capture the explanatoriness of minimal models. (shrink)

It is commonly claimed that the universality of critical phenomena is explained through particular applications of the renormalization group. This article has three aims: to clarify the structure of the explanation of universality, to discuss the physics of such RG explanations, and to examine the extent to which universality is thus explained. The derivation of critical exponents proceeds via a real-space or a field-theoretic approach to the RG. Building on work by Mainwood, this article argues that these approaches (...) ought to be distinguished: while the field-theoretic approach explains universality, the real-space approach fails to provide an adequate explanation. (shrink)

The “sloppy models” program originated in systems biology, but has seen applications across a range of fields. Sloppy models are dependent on a large number of parameters, but highly insensitive to the vast majority of parameter combinations. Sloppy models proponents claim that the program may explain the success of science. I argue that the sloppy models program can at best provide a very partial explanation. Drawing a parallel with renormalization group realism, I argue that it would only give (...) us grounds for a minimal kind of scientific realism. Nonetheless, the program can offer certain epistemic virtues. (shrink)

Recently, many have argued that there are certain kinds of abstract mathematical explanations that are noncausal. In particular, the irrelevancy approach suggests that abstracting away irrelevant causal details can leave us with a noncausal explanation. In this paper, I argue that the common example of Renormalization Group explanations of universality used to motivate the irrelevancy approach deserves more critical attention. I argue that the reasons given by those who hold up RG as noncausal do not stand up to (...) critical scrutiny. As a result, the irrelevancy approach and the line between casual and noncausal explanation deserves more scrutiny. (shrink)

Diversity in Indonesia raises the tolerance problem. The research goal to find guidance and counseling services right to develop character tolerance. The goals of this research is developing of models group gudance with folklore methode as alternative developing tolerance character. This research use Research and development as an approach. Research and development steps include preliminary study, development hypothetical group guidance model-based folklore, validation of expert judgment and expert practitioners, experimental test form group guidance model- based folklore on (...) a limited basis — descriptive qualitative and descriptive quantitative in research analysis. Group guidance services consisted of 8-9 students from Yogyakarta City, Bantul Regency, Sleman Regency, Kulonpogo Regency, and Gunungkidul Regency (Indonesia Country The result from this research that group guidance with folklore methode can incrase the tolerance character of students. The result of the limited trial appears that there was a change of condition before pre-test with an average of 109 and an increase of 117.9 after post-test in implementation of group guidance service with folklore method. The T-test results also reveal significant changes from before to after the significance of 0.000 (<0.05). (shrink)

A method of identifying banks’ business models and studying the features of their risk profile, considering the system of indicators featuring the structure of assets, liabilities, income, expenses, and other qualitative indicators based on monthly statistical reporting. Kohonen's self-organizing maps (SOM) are used to process large data sets, revealing objects’ hidden features by forming homogeneous groups according to similar values of a large system of indicators. The choice of the system of indicators that play the most significant role in (...) describing the business models of modern banks is substantiated. The proposed method makes it possible to group banks with homogeneous characteristics into so-called structural-functional groups and studies the change in the characteristics of groups of banks over time to compare their behavior during periods of active development of the system and during a crisis. That approach is useful for studying the banking system at the macro level, as it provides a quantitative measure of its financial stability. The more banks are in groups with negative values of parameters, increased risks, and unprofitable performance, the worse the general state of the system. The method also allows studying the features of each structural and functional group and the business models’ features at the meso-level. The number and composition of banks inherent in any group change dynamically, which characterizes the features of the relevant business model in a particular period. The averages of each group reflect the objective changes in the banking system structure. In addition, the SOM trajectory can be built for each individual bank determining the development of its strategy, features of a particular business model, and risk profile. At the micro-level, it allows comparing the features of individual banks within the SFGB and models ways to improve efficiency and financial stability by forecast values for SOM. An extensive system of indicators used to form structural and functional groups of banks allows to quickly respond to changes in the banking system, identify areas of increased risk and explore the adequacy and effectiveness of banks’ business models. (shrink)

Contemporary philosophers and scientists have done much to expand our understanding of the structure and neural mechanisms of joint action. But the phenomenology of joint action has only recently become a live topic for research. One method of clarifying what is unique about the phenomenology of joint action is by considering the alternative perspective of agents subsumed in group action. By group action we mean instances of individual agents acting while embedded within a group agent, instead (...) of with individual coordination. Paradigm examples are educational bureaucracies, corporations, and nation states. There is a phenomenological difference between agents whose actions are subsumed within a group action (“the university did X”) as compared to agents who act jointly (“we did x”). Attending to this difference clarifies what is phenomenologically distinctive about joint action. Appealing to an Aristotelian account of agency and to the metaphysical concept of weak emergence, we argue that what makes paradigmatic group action distinctive is the relative inaccessibility, un-revisability, and evaluative simplicity of the group agent’s goal(s) from the perspective of individual agents. This suggests that a distinctive feature of joint agency is the maintenance of a greater sense of individual agency. Put simply, joint agency is often experienced as an enhancement of the individuals’ agency precisely because our paradigmatic agential powers are extended intersubjectively as we act together. In contrast, group agency often involves a loss of the sense of agency, precisely because it is the emergent group agent that maintains the agential powers. (shrink)

Recently, there has been growing concern that increased partisanship in news sources, as well as new ways in which people acquire information, has led to a proliferation of epistemic bubbles and echo chambers: in the former, one tends to acquire information from a limited range of sources, ones that generally support the kinds of beliefs that one already has, while the latter function in the same way, but possess the additional characteristic that certain beliefs are actively reinforced. Here I argue, (...) first, that we should conceive of epistemic bubbles and echo chambers as types of epistemically pernicious groups, and second, that while analyses of such groups have typically focused on relationships between individual members, at least part of what such groups epistemically pernicious pertains to the way that members rely on the groups themselves as sources of information. I argue that member reliance on groups results in groups being attributed a degree of credibility that outruns their warrant, a process I call groupstrapping. I argue that by recognizing the groupstrapping as an illicit method of forming and updating beliefs we can make progress on some of the open questions concerning epistemically pernicious groups. (shrink)

When members of a group doxastically disagree with each other, decisions in the group are often hard to make. The members are supposed to find an epistemic compromise. How do members of a group reach a rational epistemic compromise on a proposition when they have different (rational) credences in the proposition? I answer the question by suggesting the Fine-Grained Method of Aggregation, which is introduced in Brössel and Eder 2014 and is further developed here. I show (...) how this method faces challenges of the standard method of aggregation, Weighted Straight Averaging, in a successful way. One of the challenges concerns the fact that Weighted Straight Averaging does not respect the evidential states of agents. Another challenge arises because Weighted Straight Averaging does not account for synergetic effects. (shrink)

Trigonometry serves as an important precursor to calculus as well as college level courses. However, a possible factor that affects students from learning is teachers’ strategies in teaching. Several studies reveal that cooperative learning such as study group can increase achievement of students in mathematics. This study focused on the effects of study groups on the grade 9 students’ achievement in trigonometric problems. It sought to identify the achievement of the students in problem solving before and after the interventions (...) and to compare the interventions, the group taught with study groups and taught with the existing method. The study used true experimental design particularly pretest-posttest control group design. The study was analyzed through frequency count and percentage of scores, Wilcoxon rank test, and t-test for independents samples. The subjects of the study were the Grade 9 students in a public high school in Nueva Vizcaya, Philippines. The results revealed that majority of the students’ achievements increased. Moreover, the intervention with a study group and the existing method can improve the students’ performance in solving trigonometric problems. Furthermore, the result suggests that study group method was more effective than the existing method. (shrink)

When I ask students how they feel about group projects, the response is often negative. This is usually a result of bad experiences with problematic group members, such as free riders who do not contribute or members who bulldoze their ideas through while disregarding their peers. After many semesters mediating disputes within such groups, I have found that issues often stem from concerns about “saving face”. This leads to a lack of much-needed communication. In this article, I offer (...) three methods to facilitate effective group work by improving participation and communication between student peers. (shrink)

The field of this research is the area of Thrace in Greece, in which people from various ethnic groups coexist for almost a century. Most of these ethnic groups moved to the area, after voluntary migrations in 1923. The newcomers were classified as "refugees" and were treated hostilely by the locals. One of these ethnic groups that was treated hostilely was the Gagauz, a Turkish-speaking ethnic group. The aim of this research is to study the acculturation strategies of the (...) Gagauz in their attempt to be accepted in Greek society. This study attempts to investigate the way in which the Gagauz construct and reconstruct their ethnic identity through dance. Data was gathered through the ethnographic method as this is applied to the study of dance. The interpretation of the research data in order to approach the ethnic identity of the Gagauz was based on the theoretical perspective of cultural and social construction or constructivism. This theory, in order to highlight the ethnic identity of the Gagauz, is used under the analytical terms of "acculturation" according to the multicultural model proposed by Berry. From the analysis and interpretation of the ethnographic data, it was found that the construction of the ethnic identity of the Gagauz in Greece is a fluid process, in the reconstruction of which an important factor is the degree of its acculturation. The Gagauz, experiencing a social reality that seeks to have multiple identities at the same time, change the meanings of their actions always in relation to their social environment. Thus, on the one hand, they choose to have a Greek Thracian ethnic identity, on the other Gagauz ethnic identity, and on a third level they self-identify as Greek Gagauz. So, depending on their circumstances and feelings, they choose a different ethnic identity. (shrink)

Emergent religious groups (ERGs) are an innovative but chronically understudied and misunderstood realm of contemporary religion. This may be due to notorious difficulties encountered when estimating the size of populations involved with emergent religious groups at any given time. The purpose of this article is to estimate the percentage of the U.S. population involved with ERGs over the past 50 years. Findings from three national surveys suggest .2-2.2% of the United States population involved with ERGs regardless of year. ERGs are (...) a viable case for quantitative sociologists of religion, which has hitherto been dominated by qualitative case study, although creativity and further research is needed to verify the findings. (shrink)

Two families of mathematical methods lie at the heart of investigating the hierarchical structure of genetic variation in Homo sapiens: /diversity partitioning/, which assesses genetic variation within and among pre-determined groups, and /clustering analysis/, which simultaneously produces clusters and assigns individuals to these “unsupervised” cluster classifications. While mathematically consistent, these two methodologies are understood by many to ground diametrically opposed claims about the reality of human races. Moreover, modeling results are sensitive to assumptions such as preexisting theoretical commitments to certain (...) linguistic, anthropological, and geographic human groups. Thus, models can be perniciously reified. That is, they can be conflated and confused with the world. This fact belies standard realist and antirealist interpretations of “race,” and supports a pluralist conventionalist interpretation. (shrink)

At the end of the 19th century, most professional historians – wherever they existed – deemed history to be a form of knowledge ruled by a method that bears no resemblance with those most commonly traceable in the natural sciences. The bulk of the historian’s task was then frequently regarded as being the application of procedures frequently referred to as ‘historical method’. In the context of such an emerging interest on historical methods and methodology, at least three textbooks (...) stand out: Johann Gustav Droysen’s Grundriss der Historik (Outline of the Theory of History), Ernst Bernheim’s Lehrbuch der historischen Methode (Handbook of Historical Method), and Charles Langlois and Charles Seignobos’s Introduction aux études historiques (Introduction to the Study of History). These books were quite influential in Germany, France, and elsewhere, and they very much helped promote a general idea of historical method that would become relatively consensual among historians of many nationalities by the early 20th century. Such a relative agreement on historical method sponsored both the communication and the development of a sense of disciplinary identity among historians trained within different and sometimes conflicting national traditions. It was then partially extended, partially challenged, and surely made more complex when, from the 1920s on, social and economic historians became a good part of the historiographical establishment in many countries. -/- The three books by Droysen, Bernheim, and Langlois and Seignobos were already pieced together by Rolf Torstendahl, who studied them as a group of texts that, despite their differences, contributed to shape the developments outlined above. However, Torstendahl’s primary aim was to show how Droysen, Bernheim, and Seignobos all resorted to ‘method’ as a way to circumvent skepticism against the possibility of historical knowledge, rather than investigate the internal interrelationships between the three texts. In this chapter I follow precisely this latter, not yet taken, road, focusing on crucial cross-references between the Grundriss, the Lehrbuch, and the Introduction. I intend to show that, at a general level, the schemes of historical method found in these texts are largely convergent, and that this convergence is due to Bernheim’s reading of Droysen and to Langlois and Seignobos’s reading of Bernheim. I will attempt to do it through a regressive approach that starts with an analysis of the Introduction. Aspects of the editorial history and circulation of the three texts will also be briefly addressed, as a way to illustrate their special importance within the framework of early 20th century historical theory. Because my argument calls for a focus on the most general lines of Droysen’s, Bernheim’s, and Langlois and Seignobos’s schemes of historical method, I will, for the sake of consistency, refrain from analysing in-depth the complex epistemological and ontological arguments in which those schemes are nested. (shrink)

This study focuses on the step-to-step procedure in creating Facebook Social Learning Group (FBSLG) and the perception of students on using FBSLG as learning management tool. Descriptive method was employed in this study participated by two hundred eighty (280) teacher education students in Nueva Ecija University of Science and Technology – College of Education during the academic year 2020-2021 who were purposively selected based on the criteria set by the researcher. Five simple steps on creating FBSLG were discussed (...) by the researcher. Using the adapted survey questionnaire, the data revealed that the students strongly agreed on the four aspects of perception about FBSLG namely: pedagogical affordance, social affordance, technological affordance, and their overall perception on the platform. Some worries of the students on the platform were addressed like the safety of sharing ideas in the FBSLG and some technical difficulties were encountered. It is concluded that the FBSLG is a good platform of conducting classes during this time of pandemic, so the use of this platform to other subjects is highly recommended. (shrink)

I advocate the use of small group learning in the philosophy classroom because it engages a broad cross-section of students and because it proves to be an effective way to teach critical thinking. In this article, I suggest small group activities that are useful for developing philosophical skills, and I propose methods for circumventing common logistical problems that can arise when implementing small group learning in the classroom. Ultimately, I show that small group learning is a (...) pedagogically powerful and logistically feasible supplement to traditional teaching methods. (shrink)

This paper is devoted to present Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method for multi-attribute group decision making under rough neutrosophic environment. The concept of rough neutrosophic set is a powerful mathematical tool to deal with uncertainty, indeterminacy and inconsistency. In this paper, a new approach for multi-attribute group decision making problems is proposed by extending the TOPSIS method under rough neutrosophic environment. Rough neutrosophic set is characterized by the upper and lower (...) approximation operators and the pair of neutrosophic sets that are characterized by truth-membership degree, indeterminacy membership degree, and falsity membership degree. In the decision situation, ratings of alternatives with respect to each attribute are characterized by rough neutrosophic sets that reflect the decision makers’ opinion. Rough neutrosophic weighted averaging operator has been used to aggregate the individual decision maker’s opinion into group opinion for rating the importance of attributes and alternatives. Finally, a numerical example has been provided to demonstrate the applicability and effectiveness of the proposed approach. (shrink)

The notion of neutrosophic cubic set is originated from the hybridization of the concept of neutrosophic set and interval valued neutrosophic set. We define similarity measure for neutrosophic cubic sets and prove some of its basic properties. We present a new multi criteria group decision making method with linguistic variables in neutrosophic cubic set environment. Finally, we present a numerical example to demonstrate the usefulness and applicability of the proposed method.

There is a critical need to understand the effect of changing assessment methods on demonstrated competencies in teacher education. This study examined how the transition from online to in-person testing affects the measured teaching competencies of students who completed a Competency-Based Enhancement (CBE) program, aiming to identify factors contributing to performance differences and strategies for adaptation. Using a one-group pre-test-post-test design, the study involved 669 graduating teacher education students at Pangasinan State University. Participants completed online pre-tests and in-person post-tests, (...) with data analyzed through paired samples t-tests, multiple regression, and ANCOVA. Findings revealed a significant decline in post-test scores despite CBE participation, suggesting a substantial effect of the testing modality change. The change in the testing environment emerged as the most significant predictor of score differences, while student engagement levels were positively associated with minor score decreases. These results underscore the need for adaptive assessment strategies in competency-based education programs. While limited to a single institution, this study recommends implementing a scaffolded approach to assessment transitions and enhancing student support services to mitigate adverse effects on performance across different testing modalities. (shrink)

In real-time collaborative graphical editing systems, Object-based Group/Ungroup operations are frequently accessible and practically useful. However, the existing research on these operations of the graphical editing is rare and defective. In this paper, based on Multi-Version strategy and Address Space Transformation method, a new MVSDR algorithm, which is not only applied to simple operations (such as Create, Delete, ChangeATT, etc.), but also suitable for Group/Ungroup ones, is proposed to solve the consistency maintenance problem. The proposed algorithm abandons (...) previous attempts to divide conflict operations into Real-Conflict operations and Resolvable-Conflict ones and to deal with them separately, thus making the algorithm more simple and effective. In addition, an example analysis is also given in this paper to prove the algorithm’s correctness and effectiveness. (shrink)

The research on social science eventually comes through any meaning about the human and society. Its message is directed to the society and the principal object of research would be its components, generally research participants or samples in terms of research method. As for nature, it is per se obvious that humans or populace act on various factors to influence their decision. This complex nature of human strands generally prevail that the multivariate analysis is an usual challenge for the (...) social science researchers. For example, the researchers may like to know the relationship of special training on math and achievement of math score. He or she may apply a multivariate analysis from several variables, in which one may be controlled and pretest or post test will be administered. So he groups two classes in test and for a longitudinal study over one semester between the specially trained students and normal class. Then he adds one other variable of family income level that he supposes one important factor to affect the achievement of student in math subject. This would be quantitatively answered by applying a multivariate test, called specifically as factoral ANOVA. The simple ANOVA test may be dosed in several times to understand more a complex interaction or control among the variables. Nevertheless, it has the weakness that unnecessary time and effort would be consumed. Additionally, MANOVA or other multivariate analysis of data would lead us to the more intense and precise result when the variables in consideration all interact to affect the outcome variables. It can be made distinct from mere aggregation of each result from one way ANOVA or univariate and bivariate analysis. Like these, in various ways. the quantitative studies are used to find the scientific truth. Through the Quantitative Reasoning and Analysis (QRA), we could achieve much progress which would be helpful to accelerate the interest and skills in the empirical studies. Most of all, the studies in concern of quantitative method might be a leapfrog for one, who fears of the difficult quantitative skills of analysis. Many of researchers may be fragile since the math courses in the high school and one pass in the college days are all we may have experienced. It is challenging also because the days might be far gone of middle age. For this reason, it never is a puffery that we would fear of quantitative skills. I hope that this paper could be a small help to adapt with the quantitative paradigm. Additionally, it would be great to realize that the quantitative reasoning is fairly powerful and very persuasive to frame a scientific message not only for the peer professionals, but also for lay world. We don’t have to cite the belief of empiricists and its modern evolution backed up by the mathematicians and statisticians. The benefit from this research method is obvious from many realities. The SPSS program facilitates to save from the difficult hand-on works in the earlier quantitative research. The empirical studies, particularly in the sphere of quantitative studies, typically are related with a mass of survey experiment which flavors the kind of political engraft with the research circle. (shrink)

Althusius is undoubtedly the founder and connotation endower of the term “federation”. He explained the origin of the term as coming from “feudo”, which means feudal territory, covenant, agreement, and obligation. It is a group of people with a common purpose who, under the witness of God, sign a covenant stipulating that a ruler will be elected among them in some just manner, and the others will obey the ruler's commands. The author named this form of organization: federation. The (...) family is the most basic unit of a federation, or more bluntly, the family is the smallest federation. Can a king create another king with the same rights by transferring rights? Impossible. Because the rights of the recipient of the transferred rights are always less than those of the transferor. This is the process and essence of politics. In the author's view, politics, or rather, just politics, should be organized in the form of a federation. In this federal polity, the lower ranks are higher than the upper ranks, and the parts are greater than the whole. Because the lower ranks, parts, peripheries, and subordinates are eternal; while the upper ranks, the whole, the center, and the superiors are temporary, derivative, and created, and thus can also be taken away. Indeed, the authority of an individual citizen is less than that of the supreme magistrate as the head of the union. But the collective authority of the citizens is greater than the authority of the supreme magistrate. (shrink)

Groups have committed historical wrongs (e.g., genocide, slavery). We investigated why people blame current groups who were not involved in the original historical wrong for the actions of their predecessors who committed these wrongs and are no longer alive. Current models of individual and group blame overlook the dimension of time and therefore have difficulty explaining this phenomenon using their existing criteria like causality, intentionality, or preventability. We hypothesized that factors that help psychologically bridge the past and present, like (...) perceiving higher (a) connectedness between past and present perpetrator groups, (b) continued privilege of perpetrator groups, (c) continued harm of victim groups, and (d) unfulfilled forward obligations of perpetrator groups would facilitate higher blame judgments against current groups for the past. In two repeated-measures surveys using real events (N1 = 518, N2 = 495) and two conjoint experiments using hypothetical events (N3 = 598, N4 = 605), we find correlational and causal evidence for our hypotheses. These factors link present groups to their past and cause more historical blame and support for compensation policies. This work brings the dimension of time into theories of blame, uncovers overlooked criteria for blame judgments, and questions the assumptions of existing blame models. Additionally, it helps us understand the psychological processes undergirding intergroup relations and historical narratives mired in historical conflict. Our work provides psychological insight into the debates on intergenerational justice by suggesting methods people can use to ameliorate the psychological legacies of historical wrongs and atrocities. (shrink)

In this study, we propose a new approach based on fuzzy TODIM (Portuguese acronym for interactive and multicriteria decision-making) for decision-making problems in uncertain environments. Our method incorporates group utility and individual regret, which are often ignored in traditional multicriteria decision-making (MCDM) methods. To enhance the analysis and application of fuzzy sets in decision-making processes, we introduce novel entropy and distance measures for q-rung picture fuzzy sets. These measures include an entropy measure based on the sine function and (...) a distance measure derived from the Jensen-Shannon divergence. In our methodology, incorporating the sine function into the entropy measure stands out as a distinctive decision, grounded in a profound understanding of the inherent characteristics of fuzzy sets. Utilizing the sine function proves especially advantageous when handling fuzzy sets that exhibit cyclical variations or fluctuations in their membership degrees. We effectively weight the criteria for an improved evaluation by using this new entropy measure. The introduced distance measure finds application in the TODIM approach, allowing the execution of TODIM method steps within a fuzzy environment until the determination of one alternative’s dominance over another—an advancement beyond traditional approaches. We apply our enhanced fuzzy TODIM method to a real-life construction project management problem from the literature and compare the results with those in the literature and obtained from other MCDM methods. Our proposed measures are robust, as demonstrated by the sensitivity analysis that varied the weights of group utility and individual regret, with the results visualized in a 3D sensitivity plot. The findings demonstrate the superiority of our method in providing a more comprehensive evaluation of alternatives, making it a useful tool for decision-makers facing complex and uncertain decision-making problems. (shrink)

The aim of this paper is to show how PH II constitutes an original, ambitious, and unified skeptical inquiry into logic. My thesis is that Sextus’s argument in Book II is meant to accomplish both its stated goal (to investigate the topics typically grouped together by dogmatists under the heading of “logic”) and an unstated goal. The unstated goal is, in my view, interesting in itself and sheds new light on Sextus’s methodology. The goal is: to suspend judgement on the (...) effectiveness of dogmatic methodologies. (shrink)

India dropped its target of 500 GW of renewable energy capacity fossil fuel sources by 2030. Its responsibilities the United Nations Framework Convention Climate Change [UNFCCC],and reducing radiations by one billion tonnes by the end of the decade at the COP26 conference, held in Glasgow in November 2022. Researchers are continually searching for inexhaustible and reasonable energy sources. Solar energy is one of the greenest sources of energy and is also one of the cleanest. The most important factor in using (...) solar energy is the location of the solar power plant. The main objective of this study is to find the best location for a new solar power plant in a specific region called Bundelkhand region of Uttar Pradesh in India. Here we offer an extension of ELECTRE III method as two-phase Pythagorean neutrosophic elimination and choice translating reality PN-ELECTRE-III) method to adapt with fuzzy, ambiguous, unsure, and indeterminate criteria. The Pythagorean neutrosophic numbers [PNNs] used by the group decision support system of PN-ELECTRE III to measure performance of the alternatives. The options are entirely outclassed in the subsequent stage in view of the past stage's evaluations of them. By defining PNN we describe the technique of indifference threshold functions, preference treshold and veto threshold functions, which provide a more stable basis to drop outranking relations. By calculating the concordance credibility, discordance credibility and net credibility degrees of each alternative, the ranking module of the PN-ELECTRE III approach is made simpler. In order to confirm the applicability of the strategy suggested in this paper, the location selection problem for solar plants is finaly solved. (shrink)

While P.F. Strawson’s essay ‘Freedom and Resentment’ has had many commentators, discussions of it can be roughly divided into two categories. A first group has dealt with the essay as something that stands by itself in order to analyse Strawson’s main arguments and to expose its weaknesses. A second group of commentators has looked beyond ‘Freedom and Resentment’ by emphasizing its Humean, Kantian or Wittgensteinian elements. Although both approaches have their own merits, it is too often forgotten that (...) Strawson was an original thinker with his own views on the nature of philosophical problems and how to appropriately deal with them. The aim of this article is to remedy this forgetfulness and to make sense of ‘Freedom and Resentment’ from a Strawsonian perspective, by looking at Strawson’s own views on philosophical methodology. (shrink)

This paper presents an ethical framework designed to support the development of critical data literacy for research methods courses and data training programmes in higher education. The framework we present draws upon our reviews of literature, course syllabi and existing frameworks on data ethics. For this research we reviewed 250 research methods syllabi from across the disciplines, as well as 80 syllabi from data science programmes to understand how or if data ethics was taught. We also reviewed 12 data ethics (...) frameworks drawn from different sectors. Finally, we reviewed an extensive and diverse body of literature about data practices, research ethics, data ethics and critical data literacy, in order to develop a transversal model that can be adopted across higher education. To promote and support ethical approaches to the collection and use of data, ethics training must go beyond securing informed consent to enable a critical understanding of the techno-centric environment and the intersecting hierarchies of power embedded in technology and data. By fostering ethics as a method, educators can enable research that protects vulnerable groups and empower communities. (shrink)

This article proposes the comparison of two methods of analysis, semiotics, and hermeneutics, to address contemporary issues in ethical and political philosophy, through the study of the phenomenon of epistemic injustice. Conceptualized by Fricker (2007), epistemic injustice is synonymous with the denial of the value of knowledge that an individual possesses because of prejudices about the social group to which he or she belongs or is affiliated. When epistemic injustice is studied in the empirical world, it poses some crucial (...) issues in terms of interpreting the meaning that the individual gives to the experience of injustice that he or she experiences. Although the interpretation of injustice is central to the understanding of the phenomenon itself, little research in ethical and political philosophy addresses these aspects, because of the failure to sufficiently mobilize analytical methods such as semiotics and hermeneutics. However, these two methods, usually used in other fields to deal with these aspects, allow us to question the treatment and the interpretative scope of the epistemic injustice by the different interlocutors involved in the interaction in which it is reconducted. The comparison of these two methods in the analysis of epistemic injustice finally allows us to argue in favor of the hermeneutic method, as defined by Gadamer and rethought by Code (2003), to enhance Gadamer's legacy through the analysis of ethical and political issues in human sciences research. (shrink)

Many philosophers accept the idea that there are duties to promote or create just institutions. But are the addressees of such duties supposed to be individuals – the members of the citizenry? What does it mean for an individual to promote or create just institutions? According to the ‘Simple View’, the citizenry has a collective duty to create or promote just institutions, and each individual citizen has an individual duty to do their part in this collective project. The simple view (...) appears to work well with regard to – you guessed it – ‘simple’ scenarios but it is riddled with further questions and problems. In this chapter, we raise five problems for the Simple View: (a) We suggest that one cannot develop a view concerning the citizenry’s duty to promote just institutions in isolation from a conception of the ontological relationship between the state and its citizens; (b) We argue that it is not obvious that the citizenry is the right entity to be attributed duties in the first place; (c) We show that a plausible account of collective duties to promote just institutions must not remain silent on the complexities and difficulties amorphous, unorganized group face in vis-à-vis collective action; (d) We contend that without allocation principles for contributory duties amongst the citizenry, or – alternatively – a method for practical deliberation that is action-guiding in collective action contexts, the claim that the citizens have a collective duty to promote just institutions remains moot; and, finally, (e) We demonstrate that the problem of reasonable disagreement is a serious threat to a collective duty to promote or create just institutions – it potentially undermines such a duty altogether and allows for conflicting contributory duties amongst the citizenry. We hope that our discussion will ultimately help improve existing theories and conceptual frameworks with a view to better understanding citizens’ obligations to promote justice under non-ideal conditions. (shrink)

Among historians of philosophy it is often taken for granted that the “Brentano school” was one of the influential philosophical movements at the end of the nineteenth and the beginning of the twentieth century – but Brentano’s own contributions are often eclipsed by that of his direct students. This invites to reflect on the nature of and the unity within the school. Since Brentano’s conception of a rigorous, scientific philosophy had a strong impact on his students, it has been argued (...) that this conception constitutes a unifying element in an otherwise heterogeneous group. The scope of this article is to shed light on this thesis and to show its limits. I argue for a differentiated view: the Brentano school is best seen not as a compact movement, but as a heterogeneous group of scholars who approached, in a given historical and geographical period, similar topics in very similar ways. (shrink)

One of the great challenges for students of any discipline is to be able to put into practice the knowledge learned in theory. Public health does not escape this challenge. Research Methods for Public Health is a book that seeks to help students understand in a simple way how to enter into the practice of public health research. This book stands out for its easy reading, but especially because it emphasizes the existence of quantitative and qualitative methods, as well as (...) the combination of both methods. On the other hand, the authors show between the lines, and sometimes more clearly, the importance of teamwork in research groups, a key element to avoid errors, validate procedures or instruments and increase the reliability of the results, as well as the importance of criteria of validity, reliability, precision, relevance, transparency and credibility, among others. -/- Uno de los grandes retos para los estudiantes de cualquier disciplina es poder poner en práctica los conocimientos aprendidos en la teoría. La salud pública no se escapa de este desafío. Research Methods for Public Health es un libro que busca ayudar a comprender de manera sencilla cómo introducirse en la práctica de la investigación en salud pública. Este libro se destaca por su fácil lectura, pero especialmente porque pone el énfasis en la existencia de los métodos cuantitativos y cualitativos, así como en la combinación de ambos métodos. Por otro lado, los autores dejan ver entrelíneas, y a veces más claramente, la importancia del trabajo en equipo en los grupos de investigación, elemento clave para evitar errores, validar procedimientos o instrumentos y aumentar la confia-bilidad de los resultados, así como la importancia de criterios de validez, confiabilidad, precisión, relevancia, transparencia y credibilidad, entre otros. (shrink)

Presented at the 2010 Annual Meeting of the Association for Core Texts and Courses, New Brunswick, New Jersey, USA, April 2010. -/- René Descartes’ Discourse on Method is paradoxical in several respects: it was published anonymously, yet is rich in autobiographical detail; further, Descartes insists that “the power of judging well and of distinguishing the true from the false…is naturally equal in all men,” and also that “the world consists almost exclusively of … minds for whom [his method (...) of reasoning] is not at all suitable” (1, 9). The Discourse indicates both that the identity of a particular reasoning subject (such as the author of the text itself) does not matter—because all rational beings could come to the same conclusion if using their reason correctly—and yet also that who one is does indeed matter to showing that one counts as one of the select group of subjects who possess knowledge. The method and its results do not speak for themselves; rather, the author must speak for them, and legitimize his authority in the process. If it were the case that Descartes’ plan did not go beyond “trying to reform [his] own thoughts and building upon a foundation which is completely [his] own” (9), then he might rest content with his own convictions regarding the truth of his conclusions, but if he wants to be recognized by others as possessing knowledge then he must either appeal to existing standards of authority to legitimize his method and its conclusions, or argue for the validity of new ones. Either way, the Discourse demonstrates Michel Foucault’s claims that knowledge production is bound up in a social context that determines what counts as true knowledge and who has the authority to speak about it. Descartes’s text shows an author both boldly presenting revolutionary arguments and methods and revealing his awareness of the difficulties and dangers of resisting the accepted standards of knowledge. It can be used to spark discussion amongst students about whether, even if we believe anyone’s reason might produce knowledge, it is still the case today that only some count as “knowers” according to criteria that are socially determined (e.g., institutional affiliation, status within an institution, the acceptability of certain sorts of projects and methods as legitimate for knowledge). (shrink)

To date researchers planning experiments have always lived by the mantra that 'using equal sample sizes gives the best results' and although unequal groups are also used in experimentation, it is not the preferred method of many and indeed actively discouraged in literature. However, during live study planning there are other considerations that we must take into account such as availability of study participants, statistical power and, indeed, the cost of the study. These can all make allocating equal sample (...) sizes difficult, and sometimes near impossible. This, some might say, means that the study would not adhere to rigorous statistical standard (Rosenbaum and Rubin, 1985). However, here we present evidence that, not only is this a false assumption, but that we may actually gain more power in the study by actually using unequal groups. Here, data from a Sepsis Biomarker study is used, in which the aim is to predict, by biomarker level and presence, whether the patient would go on to develop sepsis. It was found that larger control groups may give more power to studies looking for an effect in the mid range but not for large or small effects. This study shows merit in the hypothesis that more power can be achieved when a larger control group is used. Published by the Ministry of Defence at dstl - Reference DSTLTR92592 P2PP2R-2016-02-23T13:39:45. (shrink)

This study aims to describe the cultural strategy of the Buginese people of Pagatan (one of ethnic group in Indonesia) in preserving their local wisdom living in a multicultural society. This research was conducted using qualitative descriptive method through three methods of data collection i.e. in-depth interview, observation and literature involving community leaders and ordinary people as informants. The historical-interpretative method was used to analyze the Data. The findings from this study indicate that the people of Buginese-Pagatan (...) use two strategies to preserve their Buginese identity in a pluralistic society i.e. the strategy of interaction patterns and the use of ethnic symbols. In the strategy of interaction patterns, they implement adaptive and inclusive interaction patterns. This strategy is represented by the mastery and the use of regional languages in addition to the Buginese language, cross-ethnic marriages, and participation in social activities. While in the strategy of using ethnic symbols, they form a distinct identity from the one existing in Sulawesi. This strategy is represented by the use of ethnic symbols such as wearing Bodo clothes, bone cap in the rituals of marriage and moving in new houses, preserving the ancient model of Buginese house for settlement, and forming a new cultural identity called Maccera Tasi. This research has identified local values preserved and held by its people as cultural strategies in building a harmonious society. We believe that the cultural strategies are useful not only to form a united, dignified and civilized local community of Indonesia, but also to serve as a model for other cultures to preserve their local wisdom. (shrink)

This study primarily assessed students' achievement in mathematics using a mobile educational application to help them learn and adapt to changes in education. The study involved selected Grade 9 students at a public high school in Nueva Vizcaya, Philippines. This study used a quasi-experimental method, particularly a post-test control group design. Descriptive statistics such as frequencies, percent, mean, and standard deviation were used to describe the achievement of the students in mathematics. A t-test for independent samples was also (...) computed to determine if there is a significant difference between the students’ achievement in mathematics after using the mobile educational application by the control and experimental groups. Results revealed that students' achievement in mathematics was very proficient after using the application. Moreover, the usage of educational mobile applications has a better impact on students' achievement in mathematics than the traditional approach to teaching. Teachers are encouraged to place priority on solving problems. Overall, the use of the mobile educational application can enhance learning in mathematics, thus the continued use of the said application is advised. (shrink)

To investigate cultural lifestyle preferences in different cultural contexts, a forced-choice questionnaire was constructed, based on Thurstone's Law of Comparative Judgement, an almost forgotten statistical method of 1927, which is a useful tool for assessing groups. This study's questionnaire items targeted job and living conditions in the spectrum from traditional to globalised lifestyles. Subjects were indigenous representatives at the UNO in Geneva, and students in Nigeria, Cameroon, South Africa and Germany. The preferences ascertained reflect attitudes on a scale ranging (...) from very traditional to very globalised lifestyles. Although being an uncommon assessment tool, Thurstone's Comparative Judgement indicates to yield highly valid outcomes, as the results of the African university students, though from three different countries, resembled each other, but were complementary to the results of the indigenous representatives, which, in turn, mirrored the Berlin controls' profiles, according to expectations. Findings are discussed in light of the Symbolic Self-Completion Theory. (shrink)

The majority of analyses investigating the professionalisation of scientific domains tend to assume the linear and general features of this transformation. These studies focus on the shift from a non-professionalised state to a professionalised state. This dual approach, however, crucially lacks some other aspects of the process of professionalisation. This issue is discussed within the context of the growth of prehistoric archaeology in France from the 1940s, by observing scientific societies, national research organisations and their social networks. Looking at the (...) scale of Georges Laplace’s career and that of his research group, which studied the typologie analytique method, this article demonstrates the benefits of a ternary model which also encompasses the modes of refusal of professionalisation. (shrink)

A resolution to the Russell Paradox is presented that is similar to Russell's “theory of types” method but is instead based on the definition of why a thing exists as described in previous work by this author. In that work, it was proposed that a thing exists if it is a grouping tying "stuff" together into a new unit whole. In tying stuff together, this grouping defines what is contained within the new existent entity. A corollary is that a (...) thing, such as a set, does not exist until after the stuff is tied together, or said another way, until what is contained within is completely defined. A second corollary is that after a grouping defining what is contained within is present and the thing exists, if one then alters what is tied together (e.g., alters what is contained within), the first existent entity is destroyed and a different existent entity is created. A third corollary is that a thing exists only where and when its grouping exists. Based on this, the Russell Paradox's set R of all sets that aren't members of themselves does not even exist until after the list of the elements it contains (e.g. the list of all sets that aren't members of themselves) is defined. Once this list of elements is completely defined, R then springs into existence. Therefore, because it doesn't exist until after its list of elements is defined, R obviously can't be in this list of elements and, thus, cannot be a member of itself; so, the paradox is resolved. This same type of reasoning is then applied to Godel's first Incompleteness Theorem. Briefly, while writing a Godel Sentence, one makes reference to a future, not yet completed and not yet existent sentence, G, that claims its unprovability. However, only once the sentence is finished does it become a new unit whole and existent entity called sentence G. If one then goes back in and replaces the reference to the future sentence with the future sentence itself, a totally different sentence, G1, is created. This new sentence G1 does not assert its unprovability. An objection might be that all the possibly infinite number of possible G-type sentences or their corresponding Godel numbers already exist somehow, so one doesn't have to worry about references to future sentences and springing into existence. But, if so, where do they exist? If they exist in a Platonic realm, where is this realm? If they exist pre-formed in the mind, this would seem to require a possibly infinite-sized brain to hold all these sentences. This is not the case. What does exist in the mind is the system for creating G-type sentences and their corresponding numbers. This mental system for making a G-type sentence is not the same as the G-type sentence itself just as an assembly line is not the same as a finished car. In conclusion, a new resolution of the Russell Paradox and some issues with proofs of Godel's First Incompleteness Theorem are described. (shrink)

Building on Philip Tagg’s timely intervention (2011), I investigate four things in relation to three dominant Anglophone popular music studies journals (Popular Music and Society, Popular Music, and the Journal of Popular Music Studies): 1) what interdisciplinarity or multidisciplinarity means within popular music studies, with a particular focus on the sites of research and the place of ethnographic and/or anthropological approaches; 2) the extent to which popular music studies has developed canonic scholarship, and the citation tendencies present within scholarship on (...) both Western and non-Western popular musics; 3) the motivations for two scholarly groups, Dancecult and ASARP, to breakaway from popular music studies; 4) the forms of music analysis and the kinds of musical material commonly employed within popular music studies. I suggest that the field would greatly benefit from a true engagement with anthropological theories and methods, and that the “chaotic conceptualization” of musical structuration and the critical discourse would likewise benefit from an attention to recorded sound and production aesthetics. (shrink)

Objective: The coronavirus disease 2019 (Covid-19) has significantly affected human health around the world, causing many complications. However, it is not fully understood how the body compositions of individuals affected in the short or long term after disease. In this study, we aimed to show the effects of Covid-19 on body composition and phase angle values, using Bioelectrical Impedance Analayser. -/- Methods: Subjects were selected from individuals in the 18-60 age group, who had survived COVID-19 disease. 33 individuals who (...) had survived it 1-3 months ago, and 30 individuals who had survived it 3-6 months ago were included in the study. -/- Results: Effects of COVID-19 on basal metabolism and body composition and the ratio of damaged cells in the body after the disease were determined. Basal metabolic rate, lean body mass, body cell mass, total body fluid, intracellular fluid, and phase angle values were found to be significantly changed in the 3-6 months range compared to that of 1-3 months. -/- Conclusion: These results indicate that the basal metabolism and body composition parameters of the body become better, and the proportion of damaged cells decreases as time goes on after suffering COVID-19, reaching values close to normal in 1-3 months and quite better values in 3-6 months. It can be concluded that, although covid-19 influences body composition parameters and cell integrity in survivors of Covid 19 disease, these effects are limited to 3-6 months. (shrink)

In recent decades, the analysis of phraseology has made use of the exploration of large corpora as a source of quantitative information about language. This paper intends to present the main lines of work in progress based on this empirical approach to linguistic analysis. In particular, we focus our attention on some problems relating to the morpho-syntactic annotation of corpora. The CORIS/CODIS corpus of contemporary written Italian, developed at CILTA – University of Bologna (Rossini Favretti 2000; Rossini Favretti, Tamburini, De (...) Santis in press), is a synchronic 100-million-word corpus and is being lemmatised and annotated with part-of-speech (POS) tags, in order to increase the quantity of information and improve data retrieval procedures (Tamburini 2000). The aim of POS tagging is to assign each lexical unit to the appropriate word class. Usually the set of tags is pre-established by the linguist, who uses his/her competence to identify the different word classes. The very first experiments we made revealed how the traditional part-of-speech distinctions in Italian (generally based on morphological and semantic criteria) are often inadequate to represent the syntactic features of words in context. It is worth noting that the uncertainties in categorisation contained in Italian grammars and dictionaries reflect a growing difficulty as they move from fundamental linguistic classes, such as nouns and verbs, to more complex classes, such as adverbs, pronouns, prepositions and conjunctions. This latter class, that groups together elements traditionally used to express connections between sentences, appears inadequate when describing cohesive relations in Italian. This phenomenon actually seems to involve other elements traditionally assigned to different classes, such as adverbs, pronouns and interjections. Recent studies proposed the class of ‘connectives’, grouping all words that, apart from their traditional word class, have the function of connecting phrases and contributing to textual cohesion. From this point of view, conjunctions can be considered as part of phrasal connectives, that can in turn be included in the wider category of textual connectives. The aim of this study is to identify elements that can be included in the class of phrasal connectives, using quantitative methods. According to Shannon and Weaver’s (1949) observation that words are linked by dependent probabilities, corroborated by Halliday’s (1991) argument that the grammatical “system” (in Firth’s sense of the term) is essentially probabilistic, quantitative data are introduced in order to provide evidence of relative frequencies. Section 2 presents a description of word-class categorisation from the point of view of grammars and dictionaries arguing that the traditional category of conjunctions is inadequate for capturing the notion of phrasal connective. Section 3 examines the notion of ‘connective’ and suggests a truth-function interpretation of connective behaviour. Section 4 describes the quantitative methods proposed for analysing the distributional properties of lexical units, and section 5 comments on the results obtained by applying such methods drawing some provisional conclusions. (shrink)

The untrained early childhood development education (ECDE) teacher tends to escape from children’s problems instead of dealing with them. They do not know how to deal with different age groups since they do not know what tasks to give which group of children. The type of training enables a teacher to escape the constraints of a curriculum. Once this issue can be established, preferably by research, it will ease the inconsistencies in the ECDE teacher training in Kenya. The purpose (...) of this study was to establish teacher factors that influence the choice of teaching methods used by ECDE teachers in Keiyo South District. This study was guided by the Learning Styles theory by McCarthy (1980) and adopted a descriptive survey design. The study targeted 126 public ECDE centres, 252 ECDE teachers and 126 ECDE head teachers in the public EDCE centres in the district. Simple random sampling technique was used to select 38 public ECDE centres. The study used the questionnaire, interview schedule and observation checklist to collect data. Data was analyzed using descriptive and inferential statistics and presented using frequencies and percentages. The availability of teaching /learning materials, age of the ECDE child, mastery of content and teacher’s experience influenced the choice of teaching method. Others such as teacher motivation, number of children and the school locality also tend to influence the choice of the teaching method. It was also established that there was a relationship between the factors and choice of teaching method. A teacher should embrace the use of a variety of teaching methods; they should appropriately choose the teaching methods in consideration of the learners’ needs. (shrink)

The philosophy of science has traditionally assumed that knowledge should be organized in the form of theories. From theories propositions can be deduced that can be tested in experiments. Most propositions deduced from theories take the form of if-then statements. For example, if variable A increases, what happens to variable B, assuming that all other variables are held constant? However, an alternative way of organizing knowledge, in the form of producer-product relationships, was proposed by the philosopher E.A. Singer, Jr. and (...) advocated by two of his students, C. West Churchman and Russell L. Ackoff. Whether to structure knowledge in the form of theories or methods is related to the question of whether there is a fundamental difference between the natural and the social sciences. As opposed to Karl Popper’s doctrine of the unity of method, this paper argues that structuring knowledge in the form of methods is appropriate in applied fields, particularly in management where a large part of the task is to achieve agreement among a group of knowing subjects on an appropriate set of actions. (shrink)

This study examined how senior high school teachers in Digos City develop their portfolios, focusing on documenting pedagogical content knowledge (PCK) and reflective practices and the relationship between these constructs and teaching experience. The study employed an embedded mixed-methods design, incorporating a quantitative survey to assess PCK, reflective practices, and qualitative focus group discussions (FGDs) to explore teachers' experiences and portfolio development strategies. The Quantitative data were analyzed using descriptive statistics and Pearson's correlation, while qualitative data from FGDs were (...) analyzed thematically using Colaizzi's phenomenological method. The study identified five key themes in portfolio development: a systematic approach, reflective practice as a guiding principle, the impact of professional development, external feedback, and teaching experience. Teachers demonstrated "extensive" PCK across content, pedagogical, and curriculum knowledge. A moderate positive correlation was found between years of teaching experience and PCK. Teachers showed "extensive" reflective practices in practical experience and metacognition but only "moderately extensive" in cognitive aspects. A strong positive correlation was also found between PCK and reflective practice. The study concludes that teacher portfolios are valuable tools for professional growth when developed systematically and supported by professional development, emphasizing the importance of strengthening teachers' PCK and reflective practices through comprehensive training and fostering a collaborative environment. (shrink)