Special Issue on Mathability (Guest Editor: Attila Gilányi)
Abstract: Data Analyst or Data Scientist is one of the most sought-after professions. In tertiary education, the most common way for someone to become a Data Analyst is to learn Business and, later, if someone has some computational skills they can learn Computer Science as well. With the two degrees, they can solve real-life problems in their job. But there are a lot of necessary things they had never studied before because the basic conceptual methodology and the mindset were not based on any of the two curricula. Our aim is to develop a method in introductory business education to lay down the bases of the right-thinking towards data sciences for undergraduate students in Economics. If they are interested in the topic, they can orient themselves towards data sciences during their further studies. In this paper, we present a methodology to help Economics and Business Students to understand the main business questions, formalize the questions correctly, find computer-based solutions, and discuss/debug the results. Furthermore, students must learn basic data transformations and data enrichment methods as well, which is the primary feature of high-mathability problem-solving approaches. The tool we use is Microsoft Excel which contains OLAP (On-Line Analytical Processes) elements.
Keywords: OLAP; data science; formalization; management questions; computer problem-solving; high-mathability teaching approaches; knowledge transfer; spreadsheets
Abstract: Each term in the title is relatively new, but all of them emerge more and more frequently in various contexts. News regularly introduces some interesting events from the world of 3D printing (that is strongly related to 3D modeling) and Mathability also has an impact on many scientific research projects. This paper makes an attempt to explore how Mathability applies in the field of 3D modeling, by examining the features of Tinkercad. The investigation is completed by analyzing assignments submitted by students. My objective was to get some impression of the extent, of the students use, of their algorithmic skills, in 3D modeling and to explore whether a non-typical programming interface encourages or discourages the application of their programming skills. The results show that the students who majored in the Computer Science Bachelor Program, had a weak affinity, to demonstrate how they could apply tools of higher Mathability, in Tinkercad and thus, the unusual framework and the task did not sufficiently motivate them.
Keywords: 3D printing; 3D modeling; Tinkercad; Mathability
Abstract: It is known that the sum of the squares of the reciprocals, of positive integer numbers, is finite. It can be asked... What is the smallest area rectangle into which all the squares of sides of length the reciprocals of the positive integers can be packed? In connection with the investigations related to mathability and to applications of computer assisted methods, for considering mathematical problems, an improvement for the best known ε is presented, herein. The GNU program, Octave, was used for the calculations.
Keywords: Mathability; Cognitive Infocommunications; Computer Assisted Methods; Packing; Square
Abstract: Mathability refers to a branch of cognitive infocommunications that investigates any combination of artificial and natural cognitive capabilities relevant to mathematics, including a wide spectrum of areas ranging from low-level arithmetic operations to high-level symbolic reasoning. In connection with investigations related to mathability and to applications of computer-assisted methods for studying mathematical problems, in this paper, animation of the planar hyperconvex sets of radius r is presented. This animation helps us understand some properties of hyperconvex sets and to see the differences between convexity and hyperconvexity.
Keywords: Mathability; Cognitive Infocommunications; Computer Assisted Methods; Animation; Convex set; Hyperconves set of raduis r; Spindle convex set; Ball polyhedron
Abstract: In the teaching/training of programmers, the development of mathematical skills is given as much priority as that of IT skills. A complex IT problem solution is inconceivable without adequate mathematical background knowledge. In our research, we would like to show this connection through the analysis of programming tasks, for which we use the automatic solution evaluation system developed by the Faculty of Informatics of the University of Debrecen almost a decade ago and the data accumulated during its use. We examine the effectiveness of users in solving programming tasks that require mathematical and IT knowledge, compare performance in different programming languages, and look for topics where improvement is needed. The results show that, contrary to our expectations, students perform better on tasks that require both mathematics and informatics skills.
Keywords: ProgCont system; automated evaluation; programming; mathability; computer problem solving
Abstract: In spite of the fact that teaching programming is obligatory in Hungarian public ICT education, the low number of lessons accompanied by the lack of students’ knowledge and interest marginalizes the topic. Research and experience show that even when working with experienced teachers, students have a hard time mastering imperative and object-oriented programming languages. These languages usually approach problem-solving from a mathematical perspective, with a minimal design IDE (Integrated Development Environment) and output screen. As an alternative solution, schools and courses apply various visual programming environments that make it possible to create colorful motivating games and animations even in one lesson. In our research, we compared two visual programming environments: Scratch (control group), developed for education, and Construct 3 (experimental group), developed for game and software development. We conducted measurement of the efficacy of the two environments for teaching programming in two grade-8 groups. The students learned the topic by solving traditional algorithmic tasks but taking advantage of the visual interfaces. The results, in accordance with previous findings, show that in developing the students’ algorithmic skills there is no difference between these visual programming languages. Furthermore, we found proof that the selected teaching methods play a crucial role in the development of said skills of the students.
Keywords: visual programming; algorithmic skills; Bebras; ICT education; programming education; Construct 3; Scratch
Abstract: The dissemination of research results might be as crucial as the research itself. The widely accepted two major forms of dissemination are written papers and live presentations. On the surface, if we see the problem in hyper attention mode, these documents are different in nature. However, their preparation requires the same problem-solving approach, and beyond that, they share the fundamental rules of design since both are extended text documents, with varying proportions of text and/or non-text contents and static and/or dynamic media types. Closely related to this problem is the phenomenon of different types of attention (hyper and deep attention), thinking (fast and slow) modes, and problem-solving approaches (high- and low-mathability). In the world of immense and various forms of data and information, the role of so-called hyper attention is fundamental and inevitable, but the presence of deep attention is essential as well. In the present paper the knowledge items involved and shared in the design and the preparation of text-based documents are detailed from the view of concept-based problem-solving, the perspective of attention and thinking modes, along with samples originated from various sources and subject matters. The aims are to discuss the theoretical background of effective and efficient document design and preparation and to call attention to the consequences of ignoring, neglecting the proper use of attention types and thinking modes.
Keywords: end-user computing; attention modes; thinking modes; deep and surface computer problem-solving approaches; low- and high-mathability
Abstract: In this study, we present the items and the results of a complex task in which the data management knowledge of students was measured in the 2018 academic year. Our results obtained from statistical analyses are in line with previous studies that analyzed informatics/computer science coursebooks and concluded that current books favour surface-based approaches and consequently, are unsuitable for developing students' computional thinking skills. Furthermore, our study found evidence that contrary to Prensky's unproven claim, digital children also need teachers’ support in spreadsheet environments to learn effective computer problem-solving strategies, avoid common spreadsheet errors, and acquire basic algorithmic and programming skills. Our results, clearly show that the widely accepted low-mathability approaches should be excluded from the teaching-learning process due to their ineffectiveness, and should be replaced by high-mathability approaches, which support knowledge-transfer, effective end-user computing, and introductory studies to “serious” informatics/computer sciences.
Keywords: Informatics; algorithmic skills; computational thinking; computer problem-solving; knowledge-transfer
Abstract: Discussion, evaluation and error recognition, in natural language digital texts, is one of the most neglected areas in the digital world, despite the fact that text management is the most prevalent computer related activity. Millions of erroneous text-based documents of different types are in circulation, without us being aware of how fragile, damaged and harmful they are. It is well accepted in programming and even in other end-user activities, that error recognition plays a crucial role in teaching, learning and in real-world problem-solving processes. In the present paper, we introduce the High-mathability Error Recognition Model, which consists of the processes used in discussion and concept-based problem-solving and we also provide examples of the utilization of the model. We argue that error recognition and correction, and the assessment of problems in text management are as important as in other fields of informatics and computer sciences. In our study experimental groups studying with the Error Recognition Model and control groups studying with low-mathability tool-centered approaches were compared. It was found that the Error Recognition Model is more effective in digital text management, than for the tool-centered methodologies, in two error types: the typographic and layout-breaking error categories and a strong compensation effect was found in the syntax error category.
Keywords: teaching/learning strategies; lifelong learning; improving classroom teaching; data science applications in education; information literacy
Abstract: Mathability in its definition, refers to cognitive infocommunication and combines machine and the human cognitive capabilities that are essential for mathematics. Through the years, the notion evolved and its methods turned to be applicable for self-education and constructive learning. In this paper, we would like to investigate how some of the methods can be practiced to meet requirements of the contemporary labor market, especially if we consider as an aid of ICT.
Keywords: Mathability; Education; Constructive Learning; Learning of Adults; Soft Skills; Activating Methods; Edu-coaching; Activating Educational Method; Life Long Learning; Self-improvement