Abstract:

In this document, the design of a proposal to enhance the comprehension of the concepts stated in the field of Applied Calculus, is reported. This proposal presents the development of a learning environment that adapts to the profiles of students in the course of Applied Calculus for engineering level. The profiles were defined by a diagnostic study which identified the necessity to link the application problems for the derivative and integral concepts with aspects of Algebra, Geometry, Trigonometry and Analytic Geometry. This diagnostic study was the first phase of this research, for which a questionnaire was designed taking into account points raised in the literature, and it was applied to all students who were studying Applied Calculus on the first semester of March to August 2015, in the morning shift of one of the Academic Units of the National Polytechnic Institute (IPN), in addition for conducting interviews with 10 teachers who teach the subjects of Basic Sciences at pre-engineering level and 8 teachers who have taught Applied Calculus at higher levels.

The theoretical framework underlying this research was Learning Based on Problems for the Calculus content and Artificial Intelligence for developing the learning environment.

The second part of this research was to review the statistics of approval, disapproval and understanding of the subject Applied Calculus at IPN Academic Units, during the two semesters covered from August 2014 to August 2015. It was found that 55% disapprove Applied Calculus after taking the course, and of that percentage, only 2% approve this Learning Unit by Title Proficiency Examination (ETS), which corresponds to the students who had studied the subject and have taken at least one course of strengthening Calculus whose duration is one month before submitting the ETS evaluation.

By statistical analysis, is concluded that taking the reinforcement courses is an option to approve very few students. On the understanding of the required concepts to solve problems in Calculus it was found that only 1% of students who failed the subject had reached an average understanding of them.
As noted, it was decided to design and implement an Adaptive Learning Environment to the students profiles. Placing this research in a third phase.

The profiles were defined as follows. Profile One: Students who have difficulty to model algebraic expressions. Profile Two: Students who have difficulty using Geometry concepts. Profile Three: Students who do not remember aspects of Trigonometry, and Profile Four: Students with difficulties in using Analytical Geometry.

The learning environment designed allowed to place the students in one of the four profiles and provided necessary information to one or more of the mentioned branches of Mathematics, as well as, the formulated questions that led students to the given problems solutions. The difficulty level of the problems was growing according to the students evolution in order to solve the problems in the ETS.

For the design of the learning environment, conscious agents were used. Now, is starting the fourth phase of this research, which involves testing of the Learning Environment, and it will be reported in the extended document.

Keywords:

Learning environment, Calculus, profiles.