The properties of real numbers and the "mystery" of algebraic structures

Abstract

Teaching Algebraic Structures might represent some learning and understanding difficulties for the freshmen students of Industrial Processes Engineering at Universidad Autónoma de Sinaloa. In order to investigate the cause or causes of this situation, a diagnostic instrument (test) consisting of several questions was developed and was applied to a 40 engineering students’ group, about algebraic structures previous knowledge, mostly related with the conception of the real numbers laws. Although the subject of the real numbers laws is addressed for the first time in junior high and then delves in high school, the students reach the university without domain and sometimes without any knowledge of the subject. It will be part of this paper to present and discuss the results found in the diagnosis. It also highlights the importance and benefits of using a diagnostic instrument in subjects that are known to be difficult for students. Among the results that have been obtained, it is highlighted that there has been confusion about some properties of real numbers among students, and they make mistakes when trying to put them into practice. In particular, they often make mistakes when combining the implementation of a property within a subset of real numbers.