The aim of the study was to examine the effects of problem-based learning which was established on differentiation of content at three levels of complexity in the processing of the content of Analytical geometry in the plane. In this context, an experimental research was conducted, on a sample of secondary school students (N = 165) in order to examine whether methodical approach designed on the principles of problem-based learning based on differentiation of content gives better effects in learning compared to the traditional mode. The results of the final measurement shown that the experimental group achieved better overall success than control group. The results suggest that the proposed methodical approach contributes to better student performance in teaching geometry and that the most significant progress is achieved in the group of students who are average in terms of success and with ones below the average.

Authors of this paper draw attention to the importance of developing critical thinking in the process of education. For this purpose, we organized a research (an experiment with parallel groups) on a sample (N=246) of third-grade students of primary school, to examine if critical thinking can be developed by a better planned selection of content. The obtained results show that the selection of content can encourage and develop critical thinking of all students, and that there should be no restrictions regarding the classification of students by their overall performance at school.

An effective instructional approach in elementary mathematics education has a significant role in the understanding of mathematical concepts and overall student achievement. We point out the characteristics, significance and effects that may be achieved in mathematics education through the application of project-based learning. The aim of the study was to examine the effects of project-based learning on student achievement in lower elementary mathematics education and examine whether the project-based model was equally acceptable to students with different marks. We arranged quasi-experimental research instruction (experiment with parallel groups), on a sample (N = 147) in order to examine whether an instructional approach based on the principles of project-based work would achieve better effects of learning and student achievement compared to the usual way of learning implemented in mathematics education. Results of the final measurements show that students in the experimental group, who worked according to the model of project-based work, achieved better compared to students who worked in the usual way. With this study we have shown that project-based instruction has significant effects on student achievement in lower elementary mathematics education, and that it can undoubtedly contribute to the methodological empowerment of teachers in their teaching practice.

Given the fact that early mathematics education is important for further learning of mathematics, authors of this paper examine the effects that preschool mathematics education on development of geometry concepts in children. On a sample of 290 children, through a one-on-one interview, we studied the development of geometry concepts in children at the end of preschool education in Serbia. Research results show that the preschool mathematics education achieves significant effects developing geometry concepts in children. Preschool mathematics education does not achieve equal effects on the development of all geometry concepts covered by the curriculum of preschool education, that there are no differences in the development of these concepts depending on the location of the preparatory preschool institution and the gender of the child, but that the education level of the child's parents has great impact on the development of these concepts.

Correct understanding of the equals sign is the key to understanding arithme- tic, and a fundamental concept important for learning other areas of mathematics. Research around the world repeatedly mentions problems with correctly understanding the equals sign, emphasising the limited view of the equals sign as a command ”to calculate“ among students. The goal of the research was to identify the development of the concept of equality in line with the operationalised levels (operational, relational, and relational in the context of real-life prob- lem solving) and determine differences in understanding between students of the second (N = 190) and the fourth (N = 210) grade of primary school. The research was carried out using the testing technique. The research results show that students do not possess sufficiently developed relational understanding of the equals sign and that operational understanding prevails. Students of the fourth grade demonstrated better understanding of the equals sign at all levels of under- standing than the second graders.