Alejandro S. González-Martín -
How is calculus content used in engineering? The case of integrals in the study of bending moments and first moments of an area
Abstract. Research about the mathematical needs (and their use of mathematics) of both engineering students and engineers in the working place is one of the areas of research in university mathematics education that has attracted increasing interest in the last ten years. Research has reported on the difficulties engineering students face in relating the content of their mathematics courses to what is taught in their professional courses. One way to address these difficulties is by better understanding how mathematical notions are used in professional engineering courses. Using tools from the anthropological theory of the didactic (ATD), we examine two topics from engineering programs that are defined using integrals: the drawing of bending-moment diagrams, and the use of first moments of an area. Our analyses of classic engineering textbooks show that, although the notion of integral is used to define these notions, the techniques used rely mostly on geometrical considerations (and not on integral techniques or theorems), and the justifications provided are a mix of (incomplete) mathematical discourse and professional justifications, with implications for students’ learning.
Biography. Alejandro S. González-Martín graduated with honors in mathematics in 2000 in Spain, completing his Masters (2002) and PhD (2005) in mathematics education, with a focus on the teaching and learning of improper integrals. He started working at University of Montreal in 2006, where we got tenure in 2010 and the highest academic rank in 2017.
Regarding teaching, he gave calculus courses for engineers during his PhD and, at present, he gives courses of mathematics education for pre- and in- service teachers, as well as courses of research in education. He has been awarded two prizes for excellence in teaching from University of Montreal in 2009 and 2016.
His research interests concern postsecondary mathematics education, with a special interest in calculus, textbook analysis, teachers’ practices, and the use of mathematics by engineers. His main research projects have been funded by the Québec and the Canada funds for research in social sciences. He has also been involved in the coordination of the university mathematics education working groups in the European conference (CERME) since 2011 and in the French-speaking conference (EMF) since 2015.
Finally, he has been involved in several projects in different countries to introduce university mathematics teachers to research in mathematics education (Brazil, Cameroun, Chili, Ecuador, Ivory Coast, Tanzania), in projects to restructure courses and training programs (Chili, Ecuador), and has collaborated in master programs in mathematics education (Brazil, Tunisia).