Geometrical versus analytical approach in problem solving—an exploratory study

Magdalena Lemańska, Ingrid Semanišinová, Carlos Soneira Calvo, María José Souto Salorio, Ana Dorotea Tarrío Tobar

In this study we analyse the geometrical visualization as a part of the process of solution. In total 263 students in the first year of study at three different universities in three different countries (Poland, Slovakia and Spain) were asked to solve four mathematical problems. The analysis of the results of all students showed that geometrical visualization for problems where there is a possibility to choose different ways of solving is not as frequent as one would expect even if the problem is hardly solvable without it. Especially Spanish students prefer to solve the problem analytically. Visual reasoning is mostly regarded as an intuitive, preliminary stage in the reasoning processes and nothing needs to be done to develop it. On the basis of our results we consider it necessary to regain the use of geometry in the classroom and encourage visualization, the use of the figure, the physical and spatial intuition.