STEM Educational Guide for Integrating Mathematical and Statistical Concepts in Uncertainty Propagation Calculation
摘要
Many students in STEM struggle to understand error propagation and apply it effectively during experimental work. They often underestimate the importance of conducting thorough analysis and tracking errors throughout their experiments. Understanding the mathematical foundations of error propagation is challenging, often leading to difficulties in applying suitable statistical methods. This paper presents a practical guide supported by custom software that simulates errors in direct measurements using the Monte Carlo method. The aim is to enhance students’ understanding of error propagation by allowing them to visualize how uncertainties accumulate and influence results, thus making abstract theoretical concepts more accessible. The guide was implemented in a second-year physical chemistry laboratory session at a public university in Spain. By challenging the deterministic perspective common in traditional mathematical and statistical education, this approach encourages students to grasp the probabilistic nature of real experimental data. To support the guide, an intuitive software tool was developed to handle complex calculations and improve student interaction. The usefulness of this approach and its impact on students’ competence in error analysis were assessed with 57 students over one semester. Results showed improved understanding of statistical concepts and strengthened analytical skills. This work contributes valuable insights for enhancing pedagogical strategies in error analysis, focusing on improving educational tools and learning outcomes. It emphasizes the importance of visual and interactive resources in teaching complex scientific concepts and provides a reproducible model for other STEM disciplines.