Una propuesta metodológica para el aprendizaje de congruencia y semejanza de triángulos a través del método de Van Hiele

Abstract

Demonstrations play a significant role in geometry by fostering critical thinking and the ability to construct solid arguments; however, their formality can occasionally pose challenges for several students. Therefore, mastering demonstrations is essential, as it facilitates understanding and development of other branches of mathematics. The purpose of this research work was to create a reference document for students in the early semesters of the Mathematics Program at ESPOCH. The methodology used was a qualitative approach with a descriptive scope and a documentary nature, which allowed the collection of the most relevant information from various bibliographic sources, including web pages, articles, and books, among others. This information was vital for understanding the different theoretical concepts of triangle congruence and similarity and for applying Van Hiele’s method for demonstrations. As a result, a comprehensive reference document was developed. detailing the five phases of learning demonstrations: visualization, analysis, abstraction, formal deduction, and rigor. Additionally, several problems related to triangle congruence and similarity were provided, in which the five phases proposed for learning were applied. In conclusion, this reference document serves as an alternative and complementary resource for learning geometric demonstrations, supported by problem-solving. Consequently, it will enhance the development of cognitive skills in students.