Recursive function for solving a dynamic programming task: from knowledgeless form of competence towards knowledge and understanding

The recursive function for solving task 23 on dynamic programming of the Informatics Unified State Exam is used by examinees without a deep understanding of the principles of its operation: with the formed skill of its use, the necessary knowledge is missing, which is an knowledgeless form of competence. Understanding the principles of the program code and the transition from the knowledgeless form to full-fledged competencies (information, digital, mathematical, programming) will allow students to gain deeper knowledge of the theory of recursive functions, to form skills and attitudes in the field of solving dynamic programming problems at a higher level, which can lead to improved educational results, understanding of dynamic programming methods used, including Unified State Exam tasks and informatics Olympiads. To form the knowledge component of the competence, it is proposed to build, study and use call trees of the recursive function, created in the Observable programming environment, as well as study memorization as a key difference between the dynamic programming method and recursion.