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• Task reformulation as a practical tool for formation of electronic digest of tasks

  1-27

  Ingrid Minďáková

  Dušan Šveda

  Views:

  29

  Creative thinking as well as thinking itself is being developed at active learning-cognitive activity of students. To make mathematic matter a subject of interest and work of students at classes, it is efficacious to submit it in a form of tasks. The tasks may be set up in a purposeful system of tasks by means of which reaching the teaching goals in the sense of quality and durability of gained knowledge may be more effective. A suitable means for presentation of tasks with their characteristics (as e.g. didactic function and cognitive level) as well as task systems themselves is an electronic digest of tasks as a database. The analysis of textbooks and digests of tasks commonly used at schools in Slovakia shows that they do not include all the types of tasks necessary for setting up complete (in the sense of didactic functions) task systems. One of the most important methods used for formation of the missing tasks is reformulation of tasks. The individual strategies of task reformulation are explained in details on examples in this article.

• Information System’s experiences of EGERFOOD project making use of it in the education of the database management

  197-210

  Tibor Radványi

  Emőd Kovács

  János Kormos

  Views:

  27

  We present in this article the background of a developed food safety tracking system searched and formed in the Regional Knowledge Centre of Eszterházy Károly College, the requirements following from this, and by way of the requirements towards the information system appearing expectations. The development of the consumer centre system is a complex task which provides fast and cost-effective information for consumers, food producers and concerned authorities. It accomplishes severe expectations of the tracking system in connection with data security and encryption beside all this. We demonstrate in this article that forming of database model why we chose the general model. We also demonstrate what kind of SQL server we chose for buffer servers and central data warehouse. We wish to support our choosing with the result of done efficiency examinations. It is important viewpoint what kind of database planning principles we base these examinations on and how we match them to the requirements of the system. As software engineers took part in the development effectively from the first minute of the planning of the system, we can examine with what this project work was able to raise students' qualification and knowledge in addition to the general curricular substance.

• Fehleranalyse beim Lösen von offenen Aufgaben Ergebnisse einer empirischen Studie in der Grundschule

  83-113

  Gabriella Ambrus

  Kinga Szűcs

  Views:

  9

  Open problems play a key role in mathematics education, also in primary school. However, children in primary school work in many relations in a different way from learner in secondary school. Therefore, the (possibly) first confrontation with an open task could be problematical. Within the framework of an international paper and pencil test it was examined how far children of primary school notice the openness of a task and which mistakes they do during working on that task. In particularly are meant by openness different interpretations of the task, which all lead to a set of numbers with more than one element as a result. For evaluation, a common classification system was adapted by slightly modification of the original system.

• Teaching reliability theory with the Computer Algebra System Maxima

  45-75

  Attila Csenki

  Views:

  23

  The use of the Computer Algebra System Maxima as a teaching aid in an MSc module in Reliability Theory is described here. Extracts from student handouts are used to show how the ideas in Reliability Theory are developed and how they are intertwined with their applications implemented in Maxima. Three themes from the lectures are used to illustrate this: (1) Normal Approximations, (2) Markov Modelling, (3) Laplace Transform Techniques.
  It is argued that Maxima is a good tool for the task, since: it is fairly easy to learn & use; it is well documented; it has extensive facilities; it is available for any operating system; and, finally, it can be freely downloaded from the Web. Maxima proves to be a useful tool even for Reliability research for certain tasks. This latter feature provides a seamless link from teaching to research – an important feature in postgraduate education.

• Learning and teaching combinatorics with Sage

  389-398

  István Vajda

  Views:

  36

  Learning Mathematics is not an easy task, since this subject works with especially abstract concepts and sophisticated deductions. Many students lose their interest in the subject due to lack of success. Computer algebra systems (CAS) provide new ways of learning and teaching Mathematics. Numerous teachers use them to demonstrate concepts, deductions and algorithms and to make learning process more interesting especially in higher education. It is an even more efficient way to improve the learning process, if students can use the system themselves, which helps them to practice the curriculum.
  Sage is a free, open-source math software system that supports research and teaching algebra, analysis, geometry, number theory, cryptography, numerical computation, and related areas. I have been using it for several years to aid the instruction of Discrete Mathematics at Óbuda University. In this article I show some examples how representations provided by this system can help in teaching combinatorics.

• Proof step analysis for proof tutoring - a learning approach to granularity

  325-343

  Marvin Schiller

  Dominik Dietrich

  Christoph Benzmüller

  Views:

  26

  We present a proof step diagnosis module based on the mathematical assistant system Ωmega. The task of this module is to evaluate proof steps as typically uttered by students in tutoring sessions on mathematical proofs. In particular, we categorise the step size of proof steps performed by the student, in order to recognise if they are appropriate with respect to the student model. We propose an approach which builds on reconstructions of the proof in question via automated proof search using a cognitively motivated proof calculus. Our approach employs learning techniques and incorporates a student model, and our diagnosis module can be adjusted to different domains and users. We present a first evaluation based on empirical data.