Solving equations: within graphical representations and algebraic symbols

Abstract

In this paper we propose a reflection on the importance of designing didactic paths to create a connection between graphic representations and algebraic language for the solution of equations. In particular, studies on the role of visualization in learning mathematics and on Early Algebra will open up a reflection on the use of graphical representations for solving first and second degree equations. Furthermore, referring to the technique of "costruzioni in linee" by Rafael Bombelli in which geometric representations are used for the construction of the solution formula of particular third degree equations, it will be presented an example of a mathematical situation in which the solving techniques will be supported by the geometric constructions proposed by the Bolognese mathematician. The mathematical situations presented will not be intended as a didactic proposal, the hope is that the examples shown and the research studies taken into consideration can be useful to the reader-teacher for the construction of inclusive and effective didactic paths, in which the algebraic and the visual-geometrical registers are more and more in communication with each other.