Conocimientos previos sobre propiedades de operaciones con números reales de ingresantes a la universidad. Su análisis usando análisis estadístico implicativo

Abstract

This work’s objective is to determine how knowledgeable new university students are regarding the properties of operations with real numbers (addition, multiplication, exponentiation and nth root) and what relations they establish between the knowledge that they have acquired in their pre-university education. In order to accomplish the planned objectives, in this work, via use of Statistical Implicative Analysis (SIA), the answers provided to a questionnaire found in a test of previous real numbers knowledge that was taken by new students of Facultad de Ciencias Exactas–UNNE (at the beginning of the academic year of 2017)were analyzed. SIA is a multivariate analysis technique that allows relations of type “if p, then, almost q” (quasi-implications or rules) between variables (the answers provided to the previously-mentioned question) to be established. These relations allow for exploration of the conceptual relations established by the analyzed subject and detect the cognitive difficulties that said concepts offer. The results are represented and visualized by use of an “implicative graph” and later bysimilarity and cohesitive trees that make possible the establishment of R-rules (quasi-implications that relate variables and rules or rules between each other). By observing the knowledge and conceptual relations established by the students, their lacking evolution from arithmetic thinking to algebraic is brought to light.