RECURSION AS A BRIDGE BETWEEN MATHEMATICS AND COMPUTER SCIENCE

Abstract

Recursion is a technique in which a function calls itself during the process of solving a problem, thereby reducing complex tasks to simpler, selfsimilar instances until a base case is reached. This approach to problem-solving plays a significant role in both mathematics and computer science, particularly in algorithmic modeling and the mathematical formalization of problems. The aim of this paper is to demonstrate how recursive models can be methodically adapted for teaching purposes, with particular emphasis on building a connection between algorithmic and mathematical ways of thinking. The paper begins from a computer science perspective, through an analysis of the execution of recursive functions in the Python programming language, after which a mathematical formalization in the form of recurrence relations is gradually introduced. Special attention is given to the educational context, where recursion is made accessible to secondary school students, especially those in specialized IT programs, as well as to university students, through intuitive and visually recognizable examples. Among these, the Fibonacci sequence stands out, as its appearance can be observed in nature, such as in the arrangement of leaves and the spiral structures of shells, contributes to a more intuitive understanding of recursive definition and the gradual construction of more complex structures from simpler ones. In this way, recursion presents itself as an effective didactic tool that enables bridging the gap between mathematics and computer science teaching, and fosters deeper understanding among students.