Step-by-step formation of students' skill in applying the algorithm for converting numbers between number systems with bases p and q, where q is the degree of p

Abstract

The formation of the skill of applying the algorithm for converting numbers between number systems, where the base of one number system is the degree of the base of another, assumes to use a set of tasks to convert mental action from a conscious, open, external state into an unconscious, surrogated, mental one. When developing such a set of tasks, it is necessary to rely on the basic provisions of the theory of phased formation of mental actions. At the first stage of learning the algorithm, it is reasonable to offer students a set of tasks and questions that will allow them to independently single out the orienting basis of an action in short form. Work with an open form of recording a number will correspond to the stage of materialized action, while a materialized form of mental action can be combined with speech; the result of students' work at this stage will be the formulation of the algorithm. At the stage of forming an action in external speech, you can offer students tasks to work with the wording of the algorithm; to do this, you can use tasks "with omissions" and errors in the description of the algorithm. The translation of the action into external speech "silently" will be facilitated by tasks for finding out an error in solving a problem, for applying one step of the algorithm. To automate the described mental action, it is necessary that students should perform a sufficient number of standard exercises to convert numbers between number systems, including tasks where the use of the studied algorithm is impossible. For further development of the skill of applying the algorithm, it is necessary to use tasks that may require recreating the original, open form of action. The authors' experience shows that six lessons are enough to form the skills of using this algorithm, three of the lessons are devoted to students' independent work.