Formation of sign-symbolic structures in schoolchildren related to the description of recursive objects

Abstract

The Federal working program of basic and general secondary education in computer science at an advanced level involves introducing students to recursive algorithms: students should be able to analyze ready-made recursive subroutines and develop their own.

A condition for the meaningfulness of students' actions when solving a programming problem is the organization of their sign-symbolic activity at the stages of transition from solving a problem for specific input data to a visual and verbal description of the algorithm, and from the description of the algorithm to the commands of a programming language. When developing recursive algorithms, the intermediaries between the problem and the program for its solution are sign-symbolic structures that are unfamiliar to students: recurrence relations and tree-structured diagrams. The appropriation of these structures by students is facilitated by their performance of tasks on the verbal description of recurrent sequences, the determination of recurrence formulas and base cases for them, finding a specific term of a recurrent sequence given a formula and initial values, and constructing a recursion tree for a ready-made recursive subroutine. The article provides examples of tasks of these types and also describes an educational software environment developed by the authors that allows students to analyze the features of the operation of recursive subroutines.