The Use of Analogy to Simplify the Mathematical Description of the Didactical Process The article presents a new method of modelling the didactical process using a developed educational network and the microsystems simulator. The didactical process can be represented in the intuitive form of a network of connected elements in a similar way to the electrical circuits. The network represents the differential equations describing a dynamic system which models the information flows as well as learning and forgetting phenomena. The solutions of the equations are more adequate than the direct formulas used in modelling i.e. the learning and forgetting curves known from the literature. The network variables and their meaning are relative to generalized variables defined in the generalized environment. This enables using any of the microsystems simulators and gives access to many advanced simulation and optimization algorithms. The use of the microsystems simulator enables simulation of the didactical process in time and prediction of effects also after its completion in the longterm. Based on the simulation, you can design a teaching process, as well as draw conclusions about the process itself and the composition of groups. Selected examples with a brief description have been included. The issues discussed in the work may be of interest to those involved in the analysis and mathematical description of the didactic process. The paper can be interesting for those who deal with modelling of the systems which incorporates the learning and forgetting process, in particular, in production processes or learning platforms.

Learning electric circuit principles in a simulation environment with a single representation versus xe2x80x9cconcreteness fadingxe2x80x9d through multiple representations Abstract   This study explored how learning in a simulation environment with a single representation compares to learning with concreteness fading in the domain of electric circuits in secondary school. Concreteness fading, an instructional technique where representations change from concrete to more abstract during a learning sequence, has been proposed as an approach to combine the strengths of each representation and to promote transfer, but the empirical evidence is not unequivocal. One reason may be that defining xe2x80x9cconcretexe2x80x9d and xe2x80x9cabstractxe2x80x9d for the purpose of concreteness fading is less straightforward in practice than in theory, as illustrated in the conceptualization of concreteness fading in this study. The results showed no differences in content coverage and total learning time between conditions, but the transition between representations temporarily increased learning time in the fading condition. An analysis of the learning revealed no differences between conditions on circuits similar in appearance to the simulation environment, but the single representation resulted in better application of the learned knowledge to realistic circuits. The discussion explores the results from the perspective of concreteness fading and alternative conceptualizations of the learning environment. One of these, resulting from the difficulty in positioning computer simulations within concretexe2x80x93abstract dimensions, is that computer simulations can include concrete and abstract in a single representation, which may be easier (and more effective) in classroom settings than multiple representations. This suggests that a welldesigned simulation can be a reckoned alternative to concreteness fading and to multiple representations in general in science education.