In the modern mathematics learning process in school, the skill of creating examples and counterexamples in both familiar and new situations is emphasized. In the context of critical thinking, the construction of examples and counterexamples is an effective technique for evaluating statements and justifying arguments. This technique is suitable for students before other methods of proving general statements in mathematics are introduced.The aim of the study is to highlight the topics of the study course "Elements of Mathematical Logic and Set Theory" for the Professional Bachelor's degree in Teacher Education, which are relevant for constructing examples and counterexamples. In the study, the qualitative and quantitative analysis of the answers of the students in teacher programs to the questions of the questionnaire about the student experience related to the ability to formulate examples and counterexamples was carried out. The research shows that the creation of examples and counterexamples to the given statements does not cause great difficulties. It is much more difficult to create statements with mathematical content for grades 1-6, the truth verification of which, using the technique of constructing examples and counterexamples, would activate the formation of understanding of mathematical concepts and relationships. In order to connect the topics of the "Elements of Mathematical Logic and Set Theory" course with the planned results of primary education, a qualitative content analysis of the Latvian primary education standard and the primary education program was carried out. Based on the results obtained in the study, the authors identified several topics that are relevant in the course "Elements of Mathematical Logic and Set Theory".

From September 2020 schools in Latvia gradually started introducing mathematics curricula and approaches in accordance with the new standards of primary education. The changes aim to prepare a competent student who is ready for self-directed learning, who is able and willing to study and solve real problems of the changing world. A competent teacher is needed to manage this individualized learning process. The research aims to find out the typical mistakes and their causes in the results of the 9th grade students' mathematics exam in Latvia, to provide support to teachers for the improvement of methodic competence of self-directed learning. To clarify the situation about mathematics studies, researchers of Daugavpils University carried out an analysis of the results of the mathematics exam in the 9th grade in the years 2015-2019 (the exam did not take place in 2020). After assessing the quality of pupils' knowledge, we can judge for which mathematics topics teachers need methodic help in the self-directed learning process in primary school. In a survey of teachers in 2018 and 2020, we sought their views on the causes of 9th grade students' mathematics exam outcomes, problems in distance learning and suggestions for methodic assistance to teachers in implementing self-directed learning. In this article we give solutions in which directions the methodic competence of primary school mathematics teachers in studies and further education should be improved.