Visualization of the Chaos Game for non-hyperbolic iterated function system

The chaos game is a random algorithm generally applied to contracting (hyperbolic) iterated function system (IFS) which makes it possible to obtain the unique attractor of the dynamic system. However, when applied to non-contractive IFS extremely interesting results can be obtained that are not only important from a theoretical and application point of view, but can also be part of a mathematical didactics that seeks to modernize teaching. In this sense, this research present some results related to the application of the chaos game to non-contracting IFS are presented.

A NEW TEACHING METHOD AIMED AT ELIMINATING THE CAUSES OF STUDENTS’ UNSUCCESSFUL ALGORITHMIC PROBLEM SOLVING WITH PARAMETER

The new method of teaching the problems with a parameter was designed based on the identification of the reasons for the low success rate of the kids in solving the problems. In order to identify these causes and to find ways of their elimination, pedagogical research was carried out in two phases at selected universities of Slovakia (126 students) in 2016-2017. In the first stage the validity of the research hypothesis was confirmed, that the cause of the kids´ poor success in solving problems with the parameter is an algorithmic approach to their solution, a misunderstanding of the concept of a parameter and a formal determination of solvability conditions. Based on this, a new method of teaching the tasks with a parameter was developed. Its main idea is focusing on understanding the term parameter and showing its creative use in solving multiple tasks. In the second stage of the research, the success of the new teaching method was also verified experimentally. The results of the experiment confirmed the success of the students in solving the problems with the parameter, confirming that the basis of the success in solving the problems is the understanding of the term parameter and the ability to find their own solution to the task. It has turned out that the transition from the method of solving equations with a parameter by algorithms to the solution method by understanding the basic concepts and possibilities of their use is one of the methods to improve the teaching of mathematics. Keywords: algorithmic solution, formal conditions, mathematical didactics, problems with the parameter, understanding of the concept.

Mathematical Cognition in Metaphors Expressed Through Photography / Matematyczne Poznanie Poprzez Metafory Wyrażone Fotografią

The paper signals the foundations of the new method of teaching mathematics that is currently emerging from the concept of human cognition and the constructivist paradigm. The presented examples of the hermeneutic research conducted for 17 years are concerned with an analysis of the formulated mathematical problems in the language of photographic metaphors. Thoughts expressed through the photographic image and text consisting of the caption and the description (dual coding) reveal the structure of cognitive networks of authors of photographs, which has a special significance in creation of the new didactics that will fulfil the needs of the contemporary photosociety. Mathematical photoeducation free transition between art and mathematics lies on the student’s artistic sensitivity and on enlivening the student’s cognitive expression in a space distant from the classroom (at a lake, in the playground, on the skating ring or during a field excursion to a mineral museum). It utilizes the student’s natural interest in observable natural phenomena and in man-made objects. This kind of creativity, which relies on independent uncovering or constructing of knowledge with the help of a photographic camera, opens the gates to an entirely new space of mathematical didactics, as it brings to students’ awareness specific ways of association leading to accomplishment cognitive processes in relation to abstract mathematical objects.

Twenty articles in didactics of mathematics by Pranas Mašiotas

For many years, Pranas Mašiotas (1863–1940) was engaged as a teacher of mathematics, a director of gymnasium and a vice-minister of education. He compiled a number of mathematical manuals for Lithuanian primary and secondary schools. In twenty articles in mathematical didactics, published in the 30s of the 20th century, P. Mašiotas discussed upon the didactic issued that were most topical for teachers of mathematics in the said period.