Erekjék

Cikkek

Lifelong learning and understanding the world around us...

I am to do more than arguing that informatics is a fascinating scientific discipline with interesting applications in almost all areas of everyday life. We pose the following questions: What are the educational requirements demanded from school subjects? Can we answer this question as satisfactory as we can do it, for instance, for mathematics, physics or chemistry? Does the teaching of informatics enrich education in ways other subjects cannot or do not sufficiently contribute? Answering the questions above can not only be helpful for the discussion with politicians about integrating proper informatics and not only ICT skills in the educational systems, but it can also help us as teachers to focus on the fundamentals and on sustainable knowledge. Follow-up Questions: How does A prepare the pupils for dealing with jobs and duties in society? Does the teaching A contribute to the understanding of our world and, if yes, in which way and the what extent? What is the contribution of teaching A to the development of the way of thinking and the ability to solve various kinds of tasks and problems? How important is the teaching of for the ability  successfully study at a school?  If one deals with the problem of teaching a subject A in schools, one has to beable to answer the following three fundamental questions: 1. Does the teaching of A contribute to the understanding of our world and if yes, in which way and to what extent? How does A prepare the pupils for dealing with jobs and duties in society? How important is the teaching of A for the ability to succeccfully study at a university? Do universities expect some fundamental knowledge of the discipline . What is the contribution of teaching A to the development of the way of thinking and the ability to solve various kinds of tasks and problems. In the following three sections, we aim to give at least partial answers to these questions regarding the subject of informatics. Before we deal with the three questions posed above, let us explain why we do not deal with imparting ICT skills in this article. Clearly, ICT skills have become important not only for studying, but also for future employments. Therefore, these skills need to be taught at school. However, in this article we focus on the unique, sustainable and lasting knowledge that informatics can provide. Mobile phones are becoming small, powerful computers. Do we consider introducing the subject of using mobile phones into school education? We hope that this will not be the case. We do not intend to answer these rhetorical questions; the only aim in posing them is to expose the extent of public misunderstanding about computer science. Let us only note that experience has shown that teaching the use of a computer does not necessarily justify a new, special subject in school. There are two main points in the relation between teaching core informatics and imparting ICT skills. First of all, none of our three principal questions posed above can be answered satisfactory if one reduces informatics to a computer driving licence. Secondly, reducing teaching of informatics to educating the usage of concrete software systems (word processor, spreadsheet, etc.) is the main reason for the current very bad image of informatics. Following our experience and some investigation in countries that replaced the teaching of informatics by imparting ICT skills, the pupils do not consider informatics as a science, they find it boring and not challenging enough to choose it as a subject for the study at a university. There is no other way out than to teach computer science in such a way that it is at least as attractive and deep as other natural sciences and mathematics.   The following two discoveries of computer science are of this kind. The limits of automation and the concept of algorithms All possible tasks (problems) can be partitioned into two classes, namely algorithmically solvable and algorithmically unsolvable tasks. Due to the introduction of the notion of the algorithm by A. Turing we got an instrument for classifying computing problems into those solvable by computers and others unsolvable by computers. We discovered the existence of a rigorously defined limit of automation. Quantitative laws of information processing and the concept of computational complexity To perform a computation or to process information in order to solve a concrete task requires some amount of work. There exist quantitative laws of information processing. For each task of information processing, one can investigate the amount of computer work sufficient and neces- sary in order to solve the task. We discovered that more computational resources help us to solve more tasks and that there are arbitrarily hard tasks with respect to the amount of work required. Thousands of prac- tical computing problems cannot be solved because the amount of work necessary is beyond the physical capabilities of our universe. The core scientific topic of informatics is to recognize how much information one can extract from the given data by a reasonable amount of work. Both fundamental concepts mentioned above do not only reveal us the existence of some natural laws of information processing. Similar to physics, these concepts are also crucial for many of today’s applications. For instance, the current e-commerce, based on public-key cryptography, would not exist without the fundamental concepts of algorithms and computational complexity. Examples of how to introduce these concepts in an appropriate way for secondary schools is presented in numerous books. Another important issue about computational complexity is the fact that many computing problems can be solved efficiently, but it is a challenge to discover an efficient algorithm for them and this subject of informatics is very fruitful. A classical problem from cryptology that is not practically solvable using a naive approach is for example the calculation of powers with very large exponents. But with an ingenious trick, the so-called fast exponentiation, this is efficiently doable. In Appendix A we present an approach we used in the textbook Ein- führung in die Kryptologie to introduce the fast modular exponentiation to secondary-school students. We conclude that informatics has a nontrivial scientific depth that is fascinating and can challenge young people with its goals and problems. Informatics expands science also by giving new dimensions to the fundamental categories of science such as determinism, nondeterminism, randomness, proof, simulation, correctness, efficiency etc. Many of its discoveries are surprising and attractive to young people. For instance,  xchanging a deterministic control by a randomized one, whose decisions are partially influenced by random bits, can essentially decrease the amount of work necessary to reach the intended goals. We only need to get more experience with teaching these topics understand ably in our schools. There is no doubt that, in our society based on knowledge which is extracted daily from a huge amount of data, one cannot understand the world around us without some fundamental knowledge of informatics. The same is true for the control of technical devices in the technical world created by man.  Because the amount of data is growing fast, one needs a well-structured way of saving it as well as efficient algorithms for searching, processing and communicating it. Many scientific disciplines, not only the natural sciences, generate knowledge from the data they collected by experiments, measurements, and assessments. To extract knowledge from the given data often requires a huge amount of computer work. This can only be done if one is able to develop specific efficient algorithms for these tasks or to ask computer scientists for their support. But this cannot be achieved without the ability to describe the problems exactly. Of a similar importance is the application of simulations. In order to forecast some development, we create models and run simulations on them. This originally basic research instrument of physics, chemistry and engineering became a fundamental tool in sciences like economics, sociology, psychology, etc., which avoided the use of exact mathematical methods for a long period of time. Without simulations, many research projects would be unthinkable. Nobody discusses whether mathematics has to be a part of school education or not. But informatics is the scientific discipline making  athematics to a technology. Due to this, mathematics is applied everywhere. Programming is a part of informatics with a growing importance. All technical systems are controlled by programs and therefore all students of technical sciences need to master programming. Slowly, but surely, this becomes true also for several areas of the natural sciences and even for humanities. Programming is not only the ability to implement given methods into programs. Much more important is the ability to use abstractions to describe problems, to analyse them and to find methods for solving them. Definitely, we conclude that teaching informatics in school is not only a contribution for the study of related topics at university. The knowledge about the capabilities and limits of computer science and the way of working in informatics is at least as useful for the study at a university as any other classical subject of high school curricula. To teach the discoveries of informatics, its methods, and ways of thinking and acting contributes to education at least in the same amount as teaching mathematics or other classical subjects. Additionally, teaching informatics brings new elements to the schools that we are missing already for a long time. Informatics contributes to science with new fundamental concepts and terms like algorithm, computational complexity, efficiency, verification, simulation, information security, etc., and gives a deeper insight on some fundamental notions of science such as determinism, nondeterminism, and randomness, to name a few. Teaching informatics has became important to successfully study at a university in many scientific disciplines. More and more scientific disciplines expect and will expect fundamental knowledge of informatics and especially the ability to apply it in their own discipline. The way of thinking and working in informatics enriches the human way of thinking and can essentially contribute to the success of young people in their life, whatever they will do in the future.