The Visibility of the State: Symbolic and Allegorical Representations in the Work of Carl Schmitt

Purpose– A need to renew music-related information notions arises from both information-seeking models and literature of musical semiotics. The purpose of this paper is to create a music information typology, which aims at facilitating the examination of music information types at varying levels of abstraction in the context of information seeking.Design/methodology/approach– Literature of musical semiotics and information seeking are juxtaposed to develop a novel approach to music-related information. The grounding concepts are Bruner’s enactive, iconic and symbolic modes of representation. The modes of representation offer a universal scheme of knowledge that is applied to the domain of music by defining their content through Tarasti’sTheory of Musical Semiotics.Findings– This conceptual paper results in a music information typology ranging from the enactive music information representations to the abstract ones as follows. Music making as the first mode of enactive representations; music listening as the second mode of enactive representations; iconic representations of music; technological models of music as the first mode of symbolic representations; and ideological models of music as the second mode of symbolic representations.Originality/value– The present paper develops a music information typology that encompasses broadly different music information facets by categorizing music information sources according to their level of abstraction. When applied into empirical research, the typology opens a new window into the perceived roles of music information types in the context of information seeking.

The paper reveals the structure, properties and main functions of modern political myth, in addition, it analyzes the relationship between modern and archaic myths. The basis of modern political myths is rationalized and expressed in symbolic form mythological archetype. Despite the fact that archaic mythology as an integral system of worldview is rationalized, desacralized and destroyed, mythological archetypes retain their social significance. That is, political myths are the result of rationalization and symbolic interpretation of mythological archetypes. The article describes the main symbols-archetypes being invariably present in political discourse. For example, the hero archetype symbol is used to create heroic political myths. This group of myths is necessary for the formation of the image of a political leader. The representation of a political leader in accordance with the symbol-archetype of the hero significantly increases his capabilities and powers. The symbol-archetype of the Golden age is used to construct the image of the ideal social and political system. This archetype is especially actively exploited in various utopian and revolutionary projects. The symbol-archetype of the Great Mother, also actively used by modern mythology, forms ideas about their native land and country creating a sense of unity and cohesion. Since archetypal symbols retain their social significance, political myths, by reproducing them, perform important social functions. Shaping a special symbolic and semantic reality modern myths perform the main function – meaning making. Modern political myths carry out their functions by acting on the unconscious level, thereby causing certain emotional experiences and pushing the masses to the required actions. Thus, it can be concluded that political myths are an integral component of modern social and political practice.

This study investigates the representational transition patterns of pre-service teachers in solving convergent-sequence problems, with a focus on how they utilize symbolic, visual, and verbal representations. Using a qualitative phenomenological design, seven pre-service mathematics teachers were purposively selected based on their dominant representation modes (symbolic, visual, verbal). Participants solved a convergent-sequence task, and their problem-solving processes were analyzed using a modified Colaizzi method, with triangulation ensuring the validity of the findings. Three key patterns emerged: a stagnant reliance on a single representation mode (symbolic or verbal), a linear transition from visual to symbolic forms, and a complementary use of symbolic and verbal representations. No cyclic or complex transition patterns were identified, indicating limited representational fluency. The findings highlight the dominance of symbolic representations among pre-service teachers, with some exhibiting limited representational flexibility. The study suggests that fostering representational fluency, where students can effectively transition between different forms, is crucial for deeper conceptual understanding, especially in abstract topics like convergent sequences. Pedagogically, the study underscores the importance of instructional strategies that encourage the integration and transition across symbolic, visual, and verbal representations. This research contributes to the understanding of representational transition patterns in real analysis, an area often underexplored in mathematics education, and offers insights for improving teacher preparation programs.

Background: Many students struggle to understand convergent sequences when they depend on only one form of mathematical representation, which limits how they interpret the idea of a sequence approaching its limit. Aim: This study explores how students who naturally rely on symbolic, visual, or verbal representations experience the process of solving convergent sequence problems. The goal is to understand how they construct meaning, the strategies they choose, and the points at which they feel uncertain when shifting between different modes of representation. Method: A descriptive phenomenological approach was used with seven participants selected through AHP–TOPSIS classification of Dominant Mathematical Representations. Data were gathered from written work, observations, and individual interviews, then analyzed using Colaizzi’s stages. Themes were refined through triangulation to ensure consistency and credibility. Results: Symbolic-oriented students tended to rely on procedural steps and showed little inclination to move beyond formulas. Students who preferred visual thinking used sketches to build intuition but hesitated when expressing their ideas in symbolic form. Those with a verbal orientation explained their reasoning narratively yet were less confident when formal notation was required. Across all participants, shifts between representations occurred rarely, and emotional responses—such as hesitation or relief—often accompanied these moments. Conclusion: The findings indicate that students’ understanding of convergence is shaped strongly by the representational mode they depend on. This limited flexibility suggests the need for instructional approaches that actively support transitions between symbolic, visual, and verbal representations so students can develop a more connected and meaningful understanding of convergent sequences

Incorporating visual representations, rather than strictly relying on symbolic representations, is a research-based strategy for supporting fraction learning. However, students must also make transitions between visual and symbolic fraction representations to apply the conceptual understanding they gained from visual representations to symbolic fraction computation. Virtual manipulatives (VMs) offer opportunities for supporting students in making these transitions, as many fraction VMs integrate visual and symbolic representations into one manipulative. Some VMs also dynamically link the representations, so learners can observe how changes to one representation impact the other. For these features to support students in transitioning among representations, teachers must orchestrate opportunities for students to use and reflect on their use of the features. This study examined how six fourth- and fifth-grade teachers orchestrated opportunities in lesson plans for students to make transitions among the visual and symbolic representations within and beyond fraction VMs. Results showed that teachers used two strategies for orchestrating these transitions: VM choice and direct teacher intervention. Implications of teachers’ uses of these strategies are discussed in terms of what kinds of transition opportunities were made available to students and what professional learning experiences could be needed to support teachers in orchestrating transitions.

POLITICAL myths are an integral part of political life in all twentiethcentury mass societies. The unfailing idealism of the founding fathers, the infallibility of Lenin, the inevitably glorious destiny of France-all of these familiar affirmations are examples of political myths; they constitute generalizations that oversimplify or distort objective reality for the conscious or unconscious purpose of increasing emotional mass support for a particular leader or party. While both totalitarian and democratic politicians create and use myths, they employ them for quite different purposes. For a democratic political figure myths are not weapons with which to, destroy the political framework of the society. Since there exists widespread agreement on the rules of the political game, myths are integrated into the discussion of issues, not of the system itself. The situation is tragically different when a faction of the politically articulate members in a mass society uses political myths as part of its effort to destroy a democratic framework. In this context political myths have the function of perverting and distorting reality, rather than merely increasing the political impact of substantive issues. The supporters of an antidemocratic party willingly accept the group's myths as reality, even empirically verifiable reality.' The myths structure all experience and beliefs so that the myths' supporters can become effective and obedient followers of a totalitarian party, but never members of a politically mature electorate. In small numbers they are objects of ridicule; in large masses they undermine and finally destroy any system of parliamentary democracy. German society after World War I was an ideal incubator for a wide variety of totalitarian myths. The successive internal and external shocks that eventually destroyed the Wilhelmian Reich left a society that was in

Multiple representations have been widely used as a reasoning tool for understanding complex scientific concepts. Thus this study attempted to investigate the current practice of using multiple representations on Year 4 science classrooms in terms of modes and levels which appear in curriculum documents, teaching plans, tasks and assessments, teaching practices, and students' behaviors. Indeed, documentary analysis, classroom observation, and interview were used as the data collection methods. First of all, Year 4 science documents were analyzed. Then classroom observation was used as a collecting method to seek what actually happen in the classroom. Finally, in-depth interviews were used to gather more information and obtain meaningful data. The finding reveals that many modes of verbal, visual, and tactile representations within three levels of representations are posed in Year 4 documents. Moreover, according to classroom observations and interviews, there are three main points of applying multiple representations into classrooms. First of all, various modes of representations were used, however, a huge number of them did not come together with the levels. The levels of representations, secondly, macroscopic and cellular levels were introduced into all classrooms while symbolic level was provided only in some classrooms. Finally, the connection of modes and levels pointed out that modes of representations were used without the considerations on the levels of them. So, it seems to be that teaching practice did not meet the aims of curriculum. Therefore, these issues were being considered in order to organize and design the further science lessons.

There are three steps of cognitive processes, that is: 1) acquire new information, 2) transform information; and 3) test the relevance and accuracy of knowledge or evaluation. This study aims to describe the students the cognitive process of junior high school to solve mathematical problems based on Bruner's three modes of representation. The research is qualitative descriptive. The subjects were three students of junior high school; each of them is with high, medium, and low abilities. The results showed that the cognitive processes of high and medium abilities were able to acquire information and transform it to solve the problems in the enactive, iconic, and symbolic representation. For the testing relevance and accuracy, high-ability subject only works in the enactive representation. Middle-ability does in the enactive and symbolic representation. The low-ability subject was able to do all three cognitive processes on questions the enactive representation, but other questions in the iconic and symbolic representation cannot be solved.

This research intended to describe the mathematical representation of students in solving statistical problems based on the Krulik anf Rdunick steps. This research is a qualitative descriptive study. The subjects of this study were students of the second semester mathematic education study program. The procedure of subjects using purposive sampling techniques. Data collection techniques in this study were observation, interviews and documentation. Data validity used triangulation. Data analysis techniques using the Mile and Huberman step, namely data reduction, data presentations, drawing conclusions and verifyingconclusions. The results The results of this study are as follows: (1) subjects with high ability in the read and think and exploration and plan stages, using verbal and symbolic representations. The stage of select a strategy, using symbolic representation. The find and answer stage, uses symbolic and visual representations. In the reflect and extend step, the subject uses verbal representations. For students with moderate ability in the stage of read and think and explore and plan using verbal representation. The stage of finding an answer and select a strategy using verbal and symbolic representation. The reflect and extend stage of the subject uses symbolic representations. In students with low ability to read and think and explore and plan using verbal representation. Stage select a strategy subject using symbolic representation.

Critics and philosophers have occasionally been troubled by the question whether the cinema is an independent art form-independent, that is, of the theatre, from which it borrows so many conventions.' This question can be traced back to a more basic one, the question whether photography is capable of representing anything. I shall argue that it is not and that, insofar as there is representation in film, its origin is not photographic. A film is a photograph of a dramatic representation; it is not, because it cannot be, a photographic representation. It follows that if there is such a thing as a cinematic masterpiece it will be so becauselike Wild Strawberries and La Rigle dujeu-it is in the first place a dramatic masterpiece. It seems odd to say that photography is not a mode of representation. For a photograph has in common with a painting the property by which the painting represents the world, the property of sharing, in some sense, the appearance of its subject. Indeed, it is sometimes thought that since a photograph more effectively shares the appearance of its subject than a typical painting, photography is a better mode of representation. Photography might even be thought of as having replaced painting as a mode of visual representation. Painters have felt that if the

How can cognitive load in visual displays of computer simulations be optimized? Middle-school chemistry students (N = 257) learned with a simulation of the ideal gas law. Visual complexity was manipulated by separating the display of the simulations in 2 screens (low complexity) or presenting all information on 1 screen (high complexity). The mode of visual representation in the simulation was manipulated by presenting important information in symbolic form only (symbolic representations) or by adding iconic information to the display (iconic + symbolic representations), locating the sliders controlling the simulation separated from the simulation or integrating them, and graphing either only the most recent simulation result or showing all results taken. Separated screen displays and the use of optimized visual displays each promoted comprehension and transfer, especially for low prior-knowledge learners. An expertise reversal effect was found for learners' prior general science knowledge. Results indicate that intrinsic and extraneous cognitive load in visual displays can be manipulated and that learners' prior knowledge moderates the effectiveness of these load manipulations.

Part 1 Defining thinking: thinking as association of ideas, response to biological demands, adaption to the environment, cognitive restructuring of situations, resolving discrepancies. Part 2 Reasoning: insight learning - a chimpanzee insight cognitive style - uses for a brick human reasoning - processing negative statements, probabilistic reasoning. Part 3 Representation: concept formation schemas scripts cognitive maps. Part 4 The development of representation: modes of representation - enactive representation, iconic representation, symbolic representation, representation and revision strategies the development of schemata, the body schema, assimilation, accommodation. Part 5 Problem-solving: trial and error learning learning sets mental sets lateral thinking brainstorming. Part 6 Computer modelling: computer simulation artificial intelligence - expert systems.

Due to growing interest in twenty-first-century skills, and critical thinking as a key element, logical reasoning is gaining increasing attention in mathematics curricula in secondary education. In this study, we report on an analysis of video recordings of student discussions in one class of seven students who were taught with a specially designed course in logical reasoning for non-science students (12th graders). During the course of 10 lessons, students worked on a diversity of logical reasoning tasks: both closed tasks where all premises were provided and everyday reasoning tasks with implicit premises. The structure of the course focused on linking different modes of representation (enactive, iconic, and symbolic), based on the model of concreteness fading (Fyfe et al., 2014). Results show that students easily link concrete situations to certain iconic referents, such as formal (letter) symbols, but need more practice for others, such as Venn and Euler diagrams. We also show that the link with the symbolic mode, i.e. an interpretation with more general and abstract models, is not that strong. This might be due to the limited time spent on further practice. However, in the transition from concrete to symbolic via the iconic mode, students may take a step back to a visual representation, which shows that working on such links is useful for all students. Overall, we conclude that the model of concreteness fading can support education in logical reasoning. One recommendation is to devote sufficient time to establishing links between different types of referents and representations.

Creative thinking is the cognitive activities that process the received information to produce new representations. Therefore, it is necessary to develop creative thinking and represent a problem. This study aims to investigate the students' creative thinking processes based on representation in solving mathematical problems reviewed from cognitive style. Qualitative research was used as a procedure of the study. The data was collected through MFFT questionnaires, mathematics problem tests, and interviews. This research involved 31 eighth-grade students at one of junior high school in Kendal regency, Central Java. Those two subjects represented the reflective and impulsive cognitive styles that have been selected based on their mathematical abilities. The data was analyzed through iterative method. The results of the study showed that both subjects demonstrated a different performance in solving problem. In term of fluency, both subjects used visual representations in interpreting information. On the originality, the reflective subject used symbolic representations. while the impulsive one used symbolic and verbal representations in constructing the mathematical expressions. However, both of them have not yet created new ideas in solving problems. Moreover, on the flexibility, these both subjects used visual and symbolic representations that could solve the problems by utilizing the environment objects towards the interpret problems into mathematical expressions. However, the reflective subject made a mistake in elaborating the formula as well as the impulsive subject can do it. These results indicated that both subjects have used the representation of each indicator of creative thinking in solving problems.

This study looks at illustrated popular literature as a tool for shaping its readers–viewers’ perceptions of national histories. The author explores this issue through the example of Rudolf Herzog’s book for German school students «History of Prussia» ("Preußens Geschichte'', 1913) illustrated by Arthur Kampf and Georg Belwe. Despite the book’s popularity in the 1910s, this paper offers its first academic examination. The study combines terminology and methods coming from the fields of history of representations, political mythologies’ and visual cultures studies as well as art history. The author also adheres to methodological recommendations formulated by researchers in illustrated literature. The paper demonstrates that «Preussens Geschichte» exemplifies personality- and event-centred «official-nationalist» approach to history writing. The book’s contents reflect the current political situation and seek to promote the imperial government’s agendas as well as certain moral values. The author argues that the specific purpose of Kampf and Belwe’s illustrations consisted in stressing and simplifying the book’s key subject matter and facilitating its memorisation. The ballads performed the same function. The author maintains that the stylistic unity and repetition of similar subject-matter in Belwe and Kampf’s work contribute to the book’s overall representation of Prussia’s history as a coherent narrative. Belwe’s pictures encapsulate the book’s main ideas through the use of generalised images rather than directly translating Herzog’s prose and poetry into pictures. Kampf’s illustrations further stress the role of monarchy and army as the key actors of Prussian history through the artist’s selection of subject-matter and employment of artistic devices. Together with Herzog’s text, his pictures promote determination, courage, and self-sacrifice for the sake of the country. Two other themes that dominate Kampf’s illustrations are the bond between the monarchy, the nation, and the church (an element of The Second Reich’s official nationalism) as well as Prussia’s technological advancement as an epitome of its political power.