Abstract:

Recently, artificial intelligence (AI) has emerged as a complementary alternative in the educational field. Its application in mathematics courses, in particular, has shown promising results in supporting student learning. This paper presents a specific experience using AI tools such as ChatGPT and Mathematica in the teaching of differential equations (DE). The methodology employed in this research consists of three distinct phases, each designed to maximize students' understanding and application of differential equations concepts.

In the first phase, students are asked to complete a questionnaire covering basic concepts of differential equations outside the classroom. Additionally, they are required to solve some simple exercises using a specialized differential equations GPT model, named GPT-DE, developed by the authors. This model is designed to provide detailed explanations and guide students through solving basic DE problems. This phase aims to assess the students' prior knowledge and familiarize them with using AI tools in a mathematical context.

In the second phase, the instructor reviews and discusses the concepts evaluated in the questionnaire in class. During these sessions, topics are further explored by solving additional exercises, providing students with a more solid and contextualized understanding of differential equations concepts. This phase facilitates an interactive environment where students can clarify doubts and consolidate their learning through direct interaction with the instructor and peers.

The third phase involves students solving more complex problems and exercises, which have practical applications. Once the students have developed their solutions, these are compared using GPT-DE and the AI tools of Mathematica. Mathematica is a powerful platform for performing symbolic and numerical calculations, and its integration into the course allows students to verify their solutions and explore different methods for solving DEs. This phase not only reinforces autonomous learning but also encourages the critical use of technology for solving complex mathematical problems.

The implemented educational strategy covered a variety of fundamental topics in the study of differential equations, including: linear differential equations of the first and second order, applications of differential equations, Laplace transform and numerical methods for solving differential equations. The study was conducted with engineering students at the Instituto Tecnológico y de Estudios Superiores de Monterrey, Estado de México Campus (ITESM-CEM). The paper discusses in detail the three phases, providing specific examples and analysis of the interactions between students and AI tools. Learning outcomes were evaluated through exams and projects, and analyzed both quantitatively and qualitatively to determine the effectiveness of the educational strategy. Data indicate that students who used AI tools showed a better understanding of differential equations concepts compared to those who followed traditional teaching methods.

In conclusion, the integration of artificial intelligence in the teaching of differential equations not only supports students' autonomous learning but also enriches the educational process by providing new forms of interaction and exploration of complex mathematical concepts. This study offers a solid foundation for future research and applications of AI in mathematics education and other scientific disciplines.

Keywords:

Technology, Educational Innovation, Higher Education, Mathematica, ChatGPT.