Creativity is an essential feature of personality that is used in everyday life. It allows us to be flexible when dealing with real life situations. Mathematical education should be seen as one of opportunities for creativity development, although creativity is not traditionally associated with maths. One of the education goals at any school level should be to encourage pupils to think creatively, think logically and to be able to solve problems. We describe activities suitable for different school levels in this paper. We use brainstorming in mathematical education. When creating problems we cooperated with student in the age of 13 and 14. We asked them to look for “any geometry” and take photos of interesting objects as they walk at the playground. Next, students create ideas for geometrical tasks based on taken photos. Rich collection of collected photos represents the base for the creation of mathematical problems, without specific measures related to geometrical objects. These open problems could be completed and solved by students

Math trail is a type of outdoor activity conducted in groups. Group members work together, communicate, and find common and best strategies for solving problems. Thus, it combines the use of mathematics in real life with a pleasant walk. Pupils have the opportunity to explore mathematics linked to real objects, solving standard and non-standard problems. Teachers, in turn, can use mathematics in this way as a tool to connect it to other STEM disciplines. This article first describes the results of research aimed at assessing spatial ability and mental rotation in students at technical vocational schools in Slovakia. A stereometry test was solved by 455 students. We then created a mathematical walk aimed at developing students’ spatial ability. The experiences presented in the article may be helpful as other mathematics’ popularization stimuli. We believe that when students are engaged in problem-based learning activities that are related to STEM disciplines, in particular, by connecting with the subjects in the problem context of the real world, STEM disciplines may become more important for students. Interdisciplinary STEM learning imitates authentic real-world problem-solving.

School-age children and being outdoors are intrinsically linked. Education and the outdoors offer unique opportunities to extend the learning potential of children at this age in a more engaging way. From the point of view of mathematics, this way of learning is very suitable and certainly motivating for the pupils since mathematics, especially geometry, is not very popular among pupils. Therefore, in this article, we describe how we used an out-of-school learning experience for second-level primary school pupils (sixth to ninth grade) to link mathematics to outdoor learning. Activities that we solved with pupils in the outdoor environment were solved in the teaching process using only modeling. Practical applications were illustrated through interesting topographic fieldwork, which we analyzed for their appropriate integration into the teaching process by means of a priori analysis. The inclusion of these practical problems was preceded by research on 781 pupils of primary schools who solved application problems related to the circle and the square. It was clear from the research that pupils have a significant problem with the geometric interpretation of simple geometric concepts, which can be improved with the use of mathematical modeling and the linking of similar problems that can be carried out in a non-school environment.

The National Curriculum for Upper Secondary Education in Slovakia (ISCED 3A) specifies the mathematical standards and lesson quantity in Slovak schools. The major topic in ISCED 3A is stereometry, considered as one of the most problematic areas for students by a large majority of mathematics teachers. In general, the results of a large-scale opinion survey indicate that a high level of spatial imagination is necessary to solve stereometrical tasks. Slovak and Czech researchers in this field concur in the conviction that an appropriate level of spatial imagination can be systematically developed through selected types of tasks by using special methods, strategies and suitable forms of visualization. The results of several studies emphasize the need for the introduction of these types of tasks also with respect to the implementation of ICT in the educational process. In our paper, we analyze in detail the conclusions of Slovak and Czech mathematics experts and university teachers whose research field is focused on the development of spatial and geometric imagination. Based on the findings that the subject area is developed mainly through planar sections of solids, we propose a new inspirational type of tasks on sections of cube buildings of special solids constructed from multiple cubes. We discuss the results of pilot tests in the recommendations, where we analyse various aspects of the educational process in regard to the implementation of appropriate geometry software Cabri 3D in teaching support

In this paper, we introduce the notion of an elliptical segment as some analogy of the circular segment and we focus on the problem of calculation of its area. Based on the analytical method, we derive the formulas, which can be used for the numerical approximation of the area of the given segment.

Visual perception and visualization are crucial in mathematical thinking and, more importantly, in geometric thinking. Our research study aimed to follow the link of geometric transformations, mental rotation, spatial ability, and visualisation in geometric thinking. During a longitudinal study, we examined the spatial ability-related geometric competencies of 11–12-year-old students from three lower secondary schools. We analysed their test results from axial symmetry and its application in practical problems, orientation in spatial labyrinths, and building spatial constructions with three views. During a detailed analysis of the written results, a grounded theory hypothesis arose that there was a possible relationship between symmetry perception and spatial thinking. This hypothesis was tested with CHIC statistical analysis. The analysis, however, did not show any deeper connection between symmetry perception and spatial thinking from the given data. We can conclude that this connection occurs in individual cases but not in general.