Abstract:

Each year an average of 1200 students enter university at the Faculty of Chemistry (UNAM). All of them must take the subject of Differential and Integral Calculus, which is one of the most difficult to understand from the student’s point of view. What could we do as Calculus teachers to improve this problem?

Searching for an answer, I have watched that students seldom asked: What is the importance of studying Calculus? What is the purpose of derivate if I could obtain the same results from Wolfram Alpha apps? How does it help in my vocational training as Chemistry professional the study of Calculus? Why is so hard to solve Calculus application problems?

All along my fifty years as Math teacher, these proper questions have brought me to build reflexive thoughts about the learning practice of Calculus. I am worried about our students finding sense to the big effort they made to understand this subject.

I have been observed that a significant number of our students are concerned about these difficulties. These questions have helped me to build some statements:
a) Mathematics in general, helped them to build well-ordered thought structures, essential for a chemical professional.
b) Learning of Differential Calculus could bring the basics skills that helped them to solve difficult problems as well as to elaborate dynamic models that describe processes related to Chemistry.
c) Elaborating models that give them “the full movie” of these processes, enable them to calculate what was happened instantaneously instead of a “fixed photo” of them.

This way of thinking made us to change old methods in Differential Calculus learning. We must insist on formation of well-ordered thought structures, rather than simple mechanization. In this paper I will show some proposals in order to reach this objective.

It was of the mainly importance for me to ask students to make teams and create a poster that showed their skills on Calculus application problems. The majority of them have reported it was very helpful. These works have been exhibited in the “researching week” promoted by our faculty.

Incorporating in classroom several Calculus apps will teach them to focus more and more on application problems. These ideas, from my point of view, are fundamental in their vocational training as chemical professional.

I will display some didactical strategies that I had applied in my classroom such as learning based on problems and collaborative learning in order to improve the assimilation of concepts and well-order thought structures. I will develop a rubric that will be used for an evaluation of learning based in this approach. At the same time, I will expose the way some apps have helped students to elaborate dynamical models and the resolution of application problems, which is essential on their vocational training.

References:
[1] M.A. Flores, E. Fautsch, Cálculo Básico: Diferencial e Integral. México: Progreso 1986
[2] D. Zill, W.Wright, Cálculo de una variable. Trascendentes tempranas. México: Mc.Graw-Hill 2018
[3] E.Morin, La Mente Bien Ordenada. Repensar la Forma, Reformar el pensamiento. México: Siglo XXI Editores.2020

Keywords:

Differential Calculus, well-ordered thought structures, dynamic models.