FROM THE QUADRATIC FORMULA TO THE CONCEPT: THE HISTORY OF MATHEMATICS IN THE STUDY OF SECOND-DEGREE EQUATIONS IN 9TH GRADE

Abstract

This text aims to reflect on an experience developed with a 9th-grade class in a public elementary school in the municipality of Sertaneja (PR), Brazil. The starting point was a simple question posed by the students themselves when the quadratic formula appeared in class — commonly referred to in school practice as the “Bhaskara formula”: where does this name come from and, above all, why does the procedure work? Motivated by this inquiry, the teacher organized a teaching sequence inspired by the historical development of quadratic equations. In the first part, ancient methods for solving quadratic equations were explored, and the main mathematicians involved in the construction of these ideas were introduced. Next, the geometric representation of the solution was analyzed through the strategy of completing the square, followed by the deduction of the quadratic formula. In the second part, students were invited to solve six historical problems from Babylon, India, the Islamic world, and Europe, engaging with different modes of algebraic reasoning. At the conclusion of the activities, it was observed that the students understood the foundations of the procedure and recognized Mathematics as a human, historical, and constantly evolving creation. The experience suggests that integrating the History of Mathematics into teaching can foster a more comprehensive approach to quadratic equations, preventing the topic from being reduced to the mechanical application of a formula.