This paper presents some features of competencies, the structure of competencies, proposes a teaching process to contribute for developing students’ mathematical problem-solving ability in teaching Numbers and calculations, and illustrates some examples for the proposed process. At the same time, the paper also proposes levels of assessment of the expression of mathematical problem-solving capacity based on the expression of capacity for the elementary level that is specified in the program. The paper will contribute to supporting teachers in teaching Mathematics for pupil by developing students’ mathematical problem-solving capacity.