The article focuses on the approaches to the teaching of the same subject matter, namely the theorems for congruent triangles. The approaches mainly differ in the pupils' participation on the creation of new knowledge and are ordered on the scale instructional teaching - constructivist teaching. Three of the approaches have been tested in real classrooms and the trials are described in the article.
Článek pojednává o matematických úlohách souvisejících se šachovnicí a šachovými figurami. Ze šachu však budeme potřebovat pouze pravidla pro pohyb figur po šachovnici. Postupně se zaměřujeme na jezdcovy procházky po obdélníkových šachovnicích a dále na tzv. nezávislost a dominanci figur a vztah mezi nimi na čtvercových šachovnicích. Ukážeme, že některé problémy lze řešit elegantněji, pokud je přeformulujeme v řeči teorie grafů.
Addition of curves yields an interesting possibility for geometric experiments at basic and secondary schools. Addition of curves and surfaces is a tool used in architecture. The article presents some problems with solutions which can be used at the primary and secondary schools and which allow for pupils' experimenting and making hypotheses.
Subadditivity is the key property which distinguishes the popular risk measures Value-at-Risk and Expected Shortfall (ES). In this paper we offer seven proofs of the subadditivity of ES, some found in the literature and some not. One of the main objectives of this paper is to provide a general guideline for instructors to teach the subadditivity of ES in a course. We discuss the merits and suggest appropriate contexts for each proof.With different proofs, different important properties of ES are...
We have developed a chemical kinetics simulation that can be used as both an educational and research tool. The simulator is designed as an accessible, open-source project that can be run on a laptop with a student-friendly interface. The application can potentially be scaled to run in parallel for large simulations. The simulation has been successfully used in a classroom setting for teaching basic electrochemical properties. We have shown that...
In this study, we introduce new methods for constructing t-norms and t-conorms on a bounded lattice based on a priori given t-norm acting on and t-conorm acting on for an arbitrary element . We provide an illustrative example to show that our construction methods differ from the known approaches and investigate the relationship between them. Furthermore, these methods are generalized by iteration to an ordinal sum construction for t-norms and t-conorms on a bounded lattice.
Za jednu z největších kontroverzí v historii statistiky je považován spor o správné provádění testů statistické významnosti. Počátky tohoto sporu lze zaznamenat již v první polovině 20. století. Na jedné straně zde stojí významný anglický statistik R. A. Fisher a proti němu polský matematik J. Neyman spolu s anglickým statistikem E. Pearsonem. Spojením těchto dvou přístupů nakonec vznikla metoda statistického testování nulové hypotézy (NHST), která je dnes běžně používána v empirickém výzkumu. Článek...