Semiotic Aspects of Differential Equations: Analytical and Graphical Competency in the USA and Tunisia

Abstract

In this article we present the results of an investigation into semiotic aspects of an introductory differential equations class from two countries. In order to perform a comparative analysis, students in the USA and Tunisia were given common questions on their midterm exams that examined analytical and graphical competencies. Our results indicate that across both classes, the ability of the students to answer analytical questions was much higher than their ability to answer corresponding graphical questions, especially in the USA, and that it cannot be assumed that the graphical properties of basic functions have been retained by students when entering the course. We contend that this may need to be addressed at the beginning of the semester, with inquiry-oriented pedagogies and an appropriate use of computer algebra systems offering ways to enhance proficiency in converting between the different registers.