Abstract:

In the last decade, the concept of competence has been developed and competence-based learning has become the dominant educational approach in Latvia. It poses new challenge also for mathematics studies - promote each individual's opportunities to acquire knowledge, values and skills needed for participation in decision-making as well as knowledge, skills and values to work and live in a rapidly changing world.

Critical thinking, problem-solving approach and analytical skills are the most important skills that are developed in the process of mathematics education and are also the cornerstones of sustainability. In 2016, the World Economic Forum identified these skills as some of the ten skills necessary for the future of jobs employment.

Problem solving has become a key component for workplace success in an economy that demands flexibility and innovation. It requires goal-directed thinking in situations where no explicit solution is available. A second, often discussed area of desirable analytical competency is critical thinking. Thinking critically requires students to acquire, process, interpret, rationalize, and critically analyse large volumes of often conflicting information to the point of making an informed decision and taking action in a timely fashion. Therefore, it is essential to prepare young specialists at university to have good knowledge of mathematics, to be able not only to solve classical tasks, but also more complex ones, to see mathematical problems in various situations of life and solve them.

This paper is the result of scientific analysis and assessment of scientific literature and a number of information sources taking into consideration the author's reflection experience and observations in connection with what the process of mathematics learning should be under the competency-based approach allowing the development of a university student’s analytical skills, problem-solving and critical thinking.

Currently, at universities in Latvia, teaching mathematics consists mainly of transmitting of main concepts to students and teaching the task-solving techniques, focusing on the reproduction of knowledge rather than on the creation new ones. For that reason, it is necessary to give preference to learning methods that require constructive answers - projects, summaries, multi-task tasks, all that can reveal conceptual understanding better than tests or short answer tasks, and the most important problem solving - methods based on the development of mathematical imagination, creativity, heuristic thinking, etc.

The empirical part of the research is based on the survey of teachers of mathematics in Latvia, in order to identify their experience in the implementation of different pedagogical approaches in the course of mathematics, and to assess to what extent these methods contribute to the development of analytical skills, problem-solving and critical thinking and how they are developed in a particular study program.

Summarizing the findings in this study, the leading teaching strategy at the universities in Latvia is a teacher-directed instruction. This strategy is the most widespread and the most effective in terms of time if you have to learn a large amount of study materials. However, the study shows that the more often this strategy is used, the lower the student achievements in mathematics. To encourage students' analytical skills, problem-solving and critical thinking, other teaching strategies must be chosen.

Keywords:

Analytical skills, competence, competence-based teaching, critical thinking, pedagogical approaches, problem-solving, teaching methods.