Students´ language in computer-assisted tutoring of mathematical proofs

Truth and proof are central to mathematics. Proving (or disproving) seemingly simple statements often turns out to be one of the hardest mathematical tasks. Yet, doing proofs is rarely taught in the classroom. Studies on cognitive difficulties in learning to do proofs have shown that pupils and students not only often do not understand or cannot apply basic formal reasoning techniques and do not know how to use formal mathematical language, but, at a far more fundamental level, they also do not understand what it means to prove a statement or even do not see the purpose of proof at all. Since insight into the importance of proof and doing proofs as such cannot be learnt other than by practice, learning support through individualised tutoring is in demand. This volume presents a part of an interdisciplinary project, set at the intersection of pedagogical science, artificial intelligence, and (computational) linguistics, which investigated issues involved in provisioning computer-based tutoring of mathematical proofs through dialogue in natural language. The ultimate goal in this context, addressing the above-mentioned need for learning support, is to build intelligent automated tutoring systems for mathematical proofs. The research presented here has been focused on the language that students use while interacting with such a system: its linguistic propeties and computational modelling. Contribution is made at three levels: first, an analysis of language phenomena found in students´ input to a (simulated) proof tutoring system is conducted and the variety of students´ verbalisations is quantitatively assessed, second, a general computational processing strategy for informal mathematical language and methods of modelling prominent language phenomena are proposed, and third, the prospects for natural language as an input modality for proof tutoring systems is evaluated based on collected corpora

Concept of a Robust & Training-free Probabilistic System for Real-time Intention Analysis in Teams

Die Arbeit beschäftigt sich mit der Analyse von Teamintentionen in Smart Environments (SE). Die fundamentale Aussage der Arbeit ist, dass die Entwicklung und Integration expliziter Modelle von Nutzeraufgaben einen wichtigen Beitrag zur Entwicklung mobiler und ubiquitärer Softwaresysteme liefern können. Die Arbeit sammelt Beschreibungen von menschlichem Verhalten sowohl in Gruppensituationen als auch Problemlösungssituationen. Sie untersucht, wie SE-Projekte die Aktivitäten eines Nutzers modellieren, und liefert ein Teamintentionsmodell zur Ableitung und Auswahl geplanten Teamaktivitäten mittels der Beobachtung mehrerer Nutzer durch verrauschte und heterogene Sensoren. Dazu wird ein auf hierarchischen dynamischen Bayes’schen Netzen basierender Ansatz gewählt

Multimodal design : the semiotic resources of children's graphic representation

In asking how children's graphic representation can be understood as multimodal design, I argue that meaning-making is a complex process of semiotic interweaving. My definition of graphic representation for this thesis embraces the full range of marks made on any graphic surface. Multimodal design is the socioculturally shaped process of transformation where existing semiotic (meaning-making) resources are chosen, shaped and combined according to the individual's interest and his or her perception of the particular representational or communicational need. I propose that graphic representation might be thought about as multimodal compounds (co-present writing and image) and multimodal composites (an integration of the modes that make up the self-contained entities of writing and image). I explore how texts can be understood multimodally by examining what the semiotic resources of children's graphic representation are, how they carry meaning and how they interrelate. Through in-depth analysis of writing and drawing both discretely and appearing together in the same graphic text, I analyse paper-based and electronic texts produced at home and school for different purposes. I take my interpretations of the signs children have made and my theorization always to be hypotheses. Language-as-writing and drawing-as-image offer potentialities for different ways of making meaning but common and particularized semiotic modes such as presentation, layout and punctuation operate across graphic representation. These modes work together in a semiotic partnership. I suggest that semiotic principles across modes of communication including and going beyond the graphic might include criteriality, connectivity and salience. This implies the notion of a multimodal disposition. The multimodality of children's graphic representational design has implications for pedagogy, curriculum policy, professional development and the research community.

A Tale of Two Approaches: Comparing Top-Down and Bottom-Up Strategies for Analyzing and Visualizing High-Dimensional Data

The proliferation of high-throughput and sensory technologies in various fields has led to a considerable increase in data volume, complexity, and diversity. Traditional data storage, analysis, and visualization methods are struggling to keep pace with the growth of modern data sets, necessitating innovative approaches to overcome the challenges of managing, analyzing, and visualizing data across various disciplines. One such approach is utilizing novel storage media, such as deoxyribonucleic acid~(DNA), which presents efficient, stable, compact, and energy-saving storage option. Researchers are exploring the potential use of DNA as a storage medium for long-term storage of significant cultural and scientific materials. In addition to novel storage media, scientists are also focussing on developing new techniques that can integrate multiple data modalities and leverage machine learning algorithms to identify complex relationships and patterns in vast data sets. These newly-developed data management and analysis approaches have the potential to unlock previously unknown insights into various phenomena and to facilitate more effective translation of basic research findings to practical and clinical applications. Addressing these challenges necessitates different problem-solving approaches. Researchers are developing novel tools and techniques that require different viewpoints. Top-down and bottom-up approaches are essential techniques that offer valuable perspectives for managing, analyzing, and visualizing complex high-dimensional multi-modal data sets. This cumulative dissertation explores the challenges associated with handling such data and highlights top-down, bottom-up, and integrated approaches that are being developed to manage, analyze, and visualize this data. The work is conceptualized in two parts, each reflecting the two problem-solving approaches and their uses in published studies. The proposed work showcases the importance of understanding both approaches, the steps of reasoning about the problem within them, and their concretization and application in various domains

Programming Languages and Systems

This open access book constitutes the proceedings of the 30th European Symposium on Programming, ESOP 2021, which was held during March 27 until April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The 24 papers included in this volume were carefully reviewed and selected from 79 submissions. They deal with fundamental issues in the specification, design, analysis, and implementation of programming languages and systems

Semiotics and Symbiosis – “Gap-Closing”: How Signs, Symbols, and Structure Impact the Teaching and Learning of Mathematics for Middle School African American Students

The purpose of this theory-building project was to generate a scientific platform through which society might stop using the data from standardized mathematics assessments to evaluate and scrutinize students and instead evaluate, scrutinize, and improve the processes and activities through which students engage in mathematics learning (Hilliard, 1994: Kozol, 2005; Ladson-Billings, 1997; Martin, 2000; Steele, 1992). In particular, this project focused on the syntax, semantics, and pragmatics (Peirce, 1902; Saussure, 1908/1998) of mathematics situations and the activities through which students might leverage these tools to construct their own mathematics knowledge in an effort to achieve mathematics proficiency (Kilpatrick, Swafford, & Findell, 2001). The participants of this project were self-identified African American male and female middle school students located in the southeastern region of the Unite States. This theory-building project used a re-engineered teaching experiment methodology (Steffe, 1991) located within a sociocultural and radical constructivist ideological frame (von Glasersfeld, 1983; Vygotsky, 1930/1978). More specifically, the students were mentored through a cycle of exploration, introduction, application, and inquiry when given mathematical situations. Data from observations and Socratic inquiries were collected and analyzed using cultural-historical activity theory (CHAT; Vygotsky, 1930/1978) and a newly developed coding protocol in order to seek aspects of metacognition, cognition, and mathematics proficiency (Saldaña, 2016). The reporting and analysis of the data revealed that the students could demonstrate progressive acts in their pursuit of mathematics proficiency. How the students were able to make such achievements were to be found, in part, in how they understood the semiotic aspects of any given mathematical situation––its syntax, semantics, and problem-solving elements. In addition, the students gave deeper and intentional attention to the metacognitive knowledge and metacognitive skills necessary to emphasize these semiotic aspects (Veenman & Spaan, 2005). Consistently, the responses from and the observations of each student were unique representations of their experiential selves. In the end, the aim of this theory-building project was to capture these unique representations and determine the specifics that might serve as components of a preliminary mathematics learning model

Artificial general intelligence: Proceedings of the Second Conference on Artificial General Intelligence, AGI 2009, Arlington, Virginia, USA, March 6-9, 2009

Artificial General Intelligence (AGI) research focuses on the original and ultimate goal of AI – to create broad human-like and transhuman intelligence, by exploring all available paths, including theoretical and experimental computer science, cognitive science, neuroscience, and innovative interdisciplinary methodologies. Due to the difficulty of this task, for the last few decades the majority of AI researchers have focused on what has been called narrow AI – the production of AI systems displaying intelligence regarding specific, highly constrained tasks. In recent years, however, more and more researchers have recognized the necessity – and feasibility – of returning to the original goals of the field. Increasingly, there is a call for a transition back to confronting the more difficult issues of human level intelligence and more broadly artificial general intelligence

The Road to General Intelligence

Humans have always dreamed of automating laborious physical and intellectual tasks, but the latter has proved more elusive than naively suspected. Seven decades of systematic study of Artificial Intelligence have witnessed cycles of hubris and despair. The successful realization of General Intelligence (evidenced by the kind of cross-domain flexibility enjoyed by humans) will spawn an industry worth billions and transform the range of viable automation tasks.The recent notable successes of Machine Learning has lead to conjecture that it might be the appropriate technology for delivering General Intelligence. In this book, we argue that the framework of machine learning is fundamentally at odds with any reasonable notion of intelligence and that essential insights from previous decades of AI research are being forgotten. We claim that a fundamental change in perspective is required, mirroring that which took place in the philosophy of science in the mid 20th century. We propose a framework for General Intelligence, together with a reference architecture that emphasizes the need for anytime bounded rationality and a situated denotational semantics. We given necessary emphasis to compositional reasoning, with the required compositionality being provided via principled symbolic-numeric inference mechanisms based on universal constructions from category theory. • Details the pragmatic requirements for real-world General Intelligence. • Describes how machine learning fails to meet these requirements. • Provides a philosophical basis for the proposed approach. • Provides mathematical detail for a reference architecture. • Describes a research program intended to address issues of concern in contemporary AI. The book includes an extensive bibliography, with ~400 entries covering the history of AI and many related areas of computer science and mathematics.The target audience is the entire gamut of Artificial Intelligence/Machine Learning researchers and industrial practitioners. There are a mixture of descriptive and rigorous sections, according to the nature of the topic. Undergraduate mathematics is in general sufficient. Familiarity with category theory is advantageous for a complete understanding of the more advanced sections, but these may be skipped by the reader who desires an overall picture of the essential concepts This is an open access book

Cyber Security and Critical Infrastructures

This book contains the manuscripts that were accepted for publication in the MDPI Special Topic "Cyber Security and Critical Infrastructure" after a rigorous peer-review process. Authors from academia, government and industry contributed their innovative solutions, consistent with the interdisciplinary nature of cybersecurity. The book contains 16 articles: an editorial explaining current challenges, innovative solutions, real-world experiences including critical infrastructure, 15 original papers that present state-of-the-art innovative solutions to attacks on critical systems, and a review of cloud, edge computing, and fog's security and privacy issues