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

This paper presents the results of a pilot study of the impact of Personal Need for Structure of the selected mathematical competence. We were interested whether there is a relationship between cognitive-personal variable (Personal Need for Structure) and the mathematical knowledge about fractions of freshmen. We realized the experiment with 113 students of the Constantine the Philosopher University in Nitra, Slovakia. We examined statistically significant dependencies between the cognitive-personality variable of the Personal Need for Structure and its subfactors F1 (the wish of the structure) and F2 (the reaction to the lack of the structure) and the success rate of solving tasks and word problems with fractions. We used statistical Cochrane Q test to detect dependencies between factors of the Personal Need for Structure scale and the Mathematical knowledge. We proved that the success rate of solving word problems with fractions is inversely proportional to the need for the structure. This means that the higher the overall score on the Personal Need for Structure scale and its subfactors is, the lower is the success rate of solving the word problems.

The research was aimed at finding relations between mathematical knowledge and cognitive individual variable. We realized the experiment with 162 students of the Constantine the Philosopher University in Nitra, Slovakia. We had two variables—the personal need for structure (PNS) as a cognitive-individual variable and knowledge of the fraction as a mathematical variable. The relationships between the factors of the personal need for structure scale and the knowledge of fractions were determined by the IRT model. We have proven a negative correlation between the successful solving of fraction test and score in the PNS scale. This means that the higher the success rate of solving the fraction tasks, the lower the overall score on the personal need for structure scale and its subfactors.

Educational activities aimed at improvement of conceptions in first class at the elementary schools embody mainly in the process of assigning the numerical information to different number conceptions. We realized teacher experiment with the 6 and 7 years old children attending the first class at the elementary school. We explored the level of their number conceptions and the ability to use them. For the realization of the experiment we chose number 3, because it is the number from the numerical scope 1-10 and as it is freely distributed in fairy tales, advertisements and other areas of ordinary life. Children were asked to draw what they imagine, when we say number “three”. We pursued the ability of children to assign the specific model to a given number. Children were asked to arrange the pictures into groups according to some similarity and to explain their choice. Thus the mental maps of children concerning their images of number three were created. Children created the fairytale with number 3 from their models

In this research, we set two main goals: to provide empirical data that point to the knowledge of fractions among fifth-grade primary school pupils on a national scale; and to determine the level of knowledge about fractions among university students, including future primary school teachers. We used two tests—the national-wide test T5 for the fifth-graders (a research sample of approximately 45,000 pupils), and the modified fraction test based on Sfard’s theory of reification, for the university students (162 students). At the end of the study, we focused on a content analysis of the university students’ solutions. We identified persistent difficulties with concepts of fractions not only by fifth graders but also by future primary school teachers.