Problems of Cascade Type and Their Use for Assessment of Students’ Academic Achievements in Mathematics

Mathematical problems that contain a common condition and an ordered list of tasks are traditionally called cascade problems. Problems of this type are extremely popular during teaching of mathematics. At the same time, they can be used both in the formation of knowledge, skills and abilities (competencies) of students, and to assess their academic achievements. In the paper we give a thorough theoretical analysis of possible types of cascade problems, describe methodology and provide examples of their applications on different stages of studying mathematics at school, in particular, during the final attestation of graduates. According to our statistical survey of mathematics teachers in Ukraine and Republic of Moldova, we clarify their attitude to problems of cascade type, as well as the advantages and disadvantages of using such problems. It is shown that the use of cascading problems in the school course of mathematics contributes to the adequate formation of important competencies of students in their learning process.