What is the object of the encapsulation of a process?

Several theories have been proposed to describe the transition from process to object in mathematical thinking. Yet, what is the nature of this ''object'' produced by the ''encapsulation'' of a process? Here, we outline the development of some of the theories (including Piaget, Dienes, Davis, Greeno, Dubinsky, Sfard, Gray, and Tall) and consider the nature of the mental objects (apparently) produced through encapsulation and their role in the wider development of mathematical thinking. Does the same developmental route occur in geometry as in arithmetic and algebra? Is the same development used in axiomatic mathematics? What is the role played by imagery

Introduction to Gestural Similarity in Music. An Application of Category Theory to the Orchestra

Mathematics, and more generally computational sciences, intervene in several aspects of music. Mathematics describes the acoustics of the sounds giving formal tools to physics, and the matter of music itself in terms of compositional structures and strategies. Mathematics can also be applied to the entire making of music, from the score to the performance, connecting compositional structures to acoustical reality of sounds. Moreover, the precise concept of gesture has a decisive role in understanding musical performance. In this paper, we apply some concepts of category theory to compare gestures of orchestral musicians, and to investigate the relationship between orchestra and conductor, as well as between listeners and conductor/orchestra. To this aim, we will introduce the concept of gestural similarity. The mathematical tools used can be applied to gesture classification, and to interdisciplinary comparisons between music and visual arts.Comment: The final version of this paper has been published by the Journal of Mathematics and Musi

The traces left by the information designer. Data visualization and enunciation

A common understanding considers information design to be a clear and immediate transfer of information, in which the author disappears to make the data emerge with utmost clarity. This idea of infographics as a transparent and objective medium is questioned by several scholars and practitioners who consider visualization not just as a representation of numbers, but as an interpretative device. In this essay, we will review these positions, with special regard to the use of the semiotic concept of enunciation, which is also beginning to be used in critical design theory and digital humanities. This concept allows us to detect the traces of the act of enunciation in the visual artefact. In particular, we will deal with the recognition of visualization as an act of interpretation, the visual calibration and distancing from one’s statement in journalism and scientific communication and the visual reference to the production process in graphic design

Development of the activity of gifted schoolchildren in mastering geometric con-cepts in figurative structures

Background: The relevance of developing mental activity for mastering geometric concepts relates to the change in paradigmatic foundations taking place in modern education. Such a change is associated with the recognition of a schoolchild as a subject of educational and cognitive activity, the initiator of own activity. Objective: The authors attempted to describe a model of a didactic system for developing active usage of geometric concepts in the process of teaching geometry to mathematically gifted schoolchildren in 10-11 grades. The authors also used the GeoGebra dynamic system as a component of the electronic educational environment (EEE). The objective is achieved by characterizing the architecture of the system model, which evokes active usage of geometric concepts within schoolchildren in learning situations; substantiating psychodidactic conditions for the effective development of this activity using the GeoGebra dynamic system; and defining levels, criteria, and indicators of development. Methods: A specially organized educational activity in EEE and a developed system of tasks within the framework of the elective course “Problems of solid geometry and computer graphics” for 10-11 graders represent a didactic means of developing the activities related to figurative-spatial methods of information coding. Findings: The authors described a didactic system model for mastering geometric concepts in figurative structures in the process of teaching geometry to 10-11 graders using the GeoGebra dynamic system. Conclusions: Fostering schoolchildren’ mastering geometric concepts in figurative structures occurs under the direct influence of teaching. However, this process is complex and internally contradictory. The structure of this kind of activity contains actions of different nature

Development of the activity of gifted schoolchildren in mastering geometric con-cepts in figurative structures

Background: The relevance of developing mental activity for mastering geometric concepts relates to the change in paradigmatic foundations taking place in modern education. Such a change is associated with the recognition of a schoolchild as a subject of educational and cognitive activity, the initiator of own activity. Objective: The authors attempted to describe a model of a didactic system for developing active usage of geometric concepts in the process of teaching geometry to mathematically gifted schoolchildren in 10-11 grades. The authors also used the GeoGebra dynamic system as a component of the electronic educational environment (EEE). The objective is achieved by characterizing the architecture of the system model, which evokes active usage of geometric concepts within schoolchildren in learning situations; substantiating psychodidactic conditions for the effective development of this activity using the GeoGebra dynamic system; and defining levels, criteria, and indicators of development. Methods: A specially organized educational activity in EEE and a developed system of tasks within the framework of the elective course “Problems of solid geometry and computer graphics” for 10-11 graders represent a didactic means of developing the activities related to figurative-spatial methods of information coding. Findings: The authors described a didactic system model for mastering geometric concepts in figurative structures in the process of teaching geometry to 10-11 graders using the GeoGebra dynamic system. Conclusions: Fostering schoolchildren’ mastering geometric concepts in figurative structures occurs under the direct influence of teaching. However, this process is complex and internally contradictory. The structure of this kind of activity contains actions of different nature

Development of the activity of gifted schoolchildren in mastering geometric con-cepts in figurative structures

Background: The relevance of developing mental activity for mastering geometric concepts relates to the change in paradigmatic foundations taking place in modern education. Such a change is associated with the recognition of a schoolchild as a subject of educational and cognitive activity, the initiator of own activity. Objective: The authors attempted to describe a model of a didactic system for developing active usage of geometric concepts in the process of teaching geometry to mathematically gifted schoolchildren in 10-11 grades. The authors also used the GeoGebra dynamic system as a component of the electronic educational environment (EEE). The objective is achieved by characterizing the architecture of the system model, which evokes active usage of geometric concepts within schoolchildren in learning situations; substantiating psychodidactic conditions for the effective development of this activity using the GeoGebra dynamic system; and defining levels, criteria, and indicators of development. Methods: A specially organized educational activity in EEE and a developed system of tasks within the framework of the elective course “Problems of solid geometry and computer graphics” for 10-11 graders represent a didactic means of developing the activities related to figurative-spatial methods of information coding. Findings: The authors described a didactic system model for mastering geometric concepts in figurative structures in the process of teaching geometry to 10-11 graders using the GeoGebra dynamic system. Conclusions: Fostering schoolchildren’ mastering geometric concepts in figurative structures occurs under the direct influence of teaching. However, this process is complex and internally contradictory. The structure of this kind of activity contains actions of different nature

The Reconcilability of Non-Euclidean Geometries with Kant's Philosophy of Mathematics

This thesis examines Kant’s philosophy of geometry, and the possibility of reconciling non-Euclidean geometries with Kant’s philosophy of geometry. Kant believed that the propositions of Euclidean geometry are necessary and universal. In addition to that, he embraced the view that the character of space is Euclidean and he did not give any credence to the possibility of determining the character of space by using another geometrical structure. He also propounded the view that experience plays no positive role in the acquisition of geometrical knowledge. In this thesis, the views of Helmholtz, Poincaré and Reichenbach as to the positive role experience plays in the genesis of geometry are elaborately discussed. In the light of their views, it is shown that different environmental conditions have the potency to compel sentient beings like us to adopt nonEuclidean geometries. These geometries, in turn, has a proper intuitive content in contradistinction to Kant’s claim that they are only possible logically, not intuitively. Under these considerations, this thesis shows that it is not possible to reconcile Kant’s theory of geometry with non-Euclidean geometries even if undergoes appropriate modifications offered by certain philosophers such as Strawson, who tried to reduce the scope of Kant’s theory of geometry to visual space by arguing that visual space cannot be non-Euclidean. For Strawson, the propositions of Euclidean geometry are necessary and universal as was propounded by Kant, but its validity its limited to our visual space. This thesis also shows the possibility of visualizing non-Euclidean geometries by considering the views of abovementioned philosophers in contradistinction to Strawson’s arguments in support of Kant’s theory of geometry.Bu tez genel hatları ile Kant’ın geometri felsefesini ve Öklid-dışı geometrilerin Kant’ın geometri felsefesi ile uzlaştırılabilirliğinin olanaklılığını araştırmaktadır. Kant Öklid geometrisinin önermelerinin zorunlu ve evrensel olduğunu savunmuştur. Buna ek olarak uzayın karakterinin Öklidyen olduğunu ve uzayın geometrik karakterinin farklı bir geometrik yapı kullanarak belirlenemeyeceği görüşünü benimsemiştir. Kant’ın ortaya attığı bir başka görüş ise geometrik bilgimizin kökeninde deneyimin asla bir payı olmadığıdır. Geometrik bilgimizin kökeninde deneyimin pozitif bir rolünün olduğuna ilişkin Helmholtz, Poincaré ve Reichenbach tarafından savunulan görüşler detaylı bir şekilde tartışılmıştır. Bu görüşler ışığında, farklı çevresel koşulların, bizim gibi canlıları farklı geometrik yapıları seçmeye itebileceği gösterilmiştir. Öklid-dışı geometrilerin bunun sonucunda duyumsal bir içeriğe sahip olabileceği Kant’ın bu tarz geometrik sistemlerin ancak mantıksal olarak mümkün olabileceği fakat duyumsal olarak mümkün olamayacağı görüşünün aksine gösterilmiştir. Bütün bunlar hesaba katıldığında, bu tez Kant’ın geometri kuramının Öklid-dışı geometriler ile uzlaştırılamayacağı gösterilmiştir. Strawson gibi Kant sonrası filozoflar, Kant’ın geometri kuramının geçerliliğini görsel uzayı kapsayacak şekilde modifiye etmeye çalışmışlardır. Strawson’a göre Öklidyen geometri Kant’ın savunduğu gibi zorunlu ve evrenseldir, fakat geçerliliği görsel uzay ile sınırlıdır. Fakat bu tezde görsel uzayımızın da Öklid-dışı bir içeriğe sahip olabileceği yine aynı filozofların görüşleri göz önünde tutularak tartışılmıştır.M.S. - Master of Scienc

Multimodal literacy in academic environments: PowerPoint as a motivational genre

his paper explores PowerPoint (PPT) as a leading genre in academic discourse, focussing on the implementation of student motivation boosting strategies. ICT nowadays plays an increasingly important role in pedagogy, by reinforcing the informative and persuasive impact of instructional materials through multimodal strategies including verbal and visual codes, as well as performative elements. A hybrid genre in academic oratory, PPT offers corporeality of knowledge, modularity and easily transmittable format, providing presentations with structure and facilitating ordering and summarizing operations. PPT can therefore be ranked among today’s epistemic machineries, whereby knowledge is construed by discourse. The paper analyses the semiotic and metadiscursive features of a corpus of presentations produced in various universities for both academic staff and students. Research questions explore how PPT can be used to motivate teachers and students, from both an ideational and interactional standpoint. An integrated analytical approach is employed, bridging multimodal and critical discourse analysis

Multisensor Data Fusion for Cultural Heritage Assets Monitoring and Preventive Conservation

This paper shows the first phase of an ongoing interdisciplinary research project aimed at codifying procedures for the control and non-destructive analysis of the conservation status of CH artefacts to guide preventive preservation actions. It specifically explains the results of an experiment aimed at defining the procedural phases of semantic-informative enrichment of a digital architectural model where the morpho-metric components acquired with instrumental survey techniques are linked with cognitive and technical aspects (microclimatic, material, and geometric deviation data), with the aim of making this model a support for the simulation of scenarios connected to preventive preservation programmes. The research was carried out on the church of San Michele Arcangelo in Padula, affected by plaster detachment from the frescoes on the intrados of the vaulted systems. The work was conceived to support a mainly qualitative assessment regarding a possible relationship between micro-environmental variations and visually perceived degradation phenomena to provide a first indication of the conservation status of the investigated surfaces. The analyses were conducted through algorithms that, as such, are repeatable and objective. In addition, these processes, as they were applied to the models derived from the architectural survey, made it possible to make the most of these outputs. Therefore, by combining the algorithmic manipulation of the digital representations with the necessary critical interpretation of the data by the specialist, it was possible to address some actions of direct intervention and guide the most appropriate choices for subsequent in-depth diagnostics, more targeted, reducing the damage to the historical heritage