Abstract:

Our initiative targets second-semester engineering students, who have foundational knowledge in algebra and calculus, with the goal of elucidating the complexities of laboratory measurements and the propagation of error or uncertainty. Through two meticulously designed experimental challenges, we aim to merge theoretical insights with practical experience, fostering a culture of analytical precision and critical thinking—fundamental skills in the STEM disciplines.

The first challenge engages students with the principles of buoyancy, free body diagrams, and Newton's laws. Participants are required to indirectly determine the volume of helium balloons, which amusingly were in abundance on campus during February, characterized by their unique shapes (such as hearts or superheroes), through the measurement of a string’s length that holds the balloon in buoyant equilibrium. This task highlights the critical nature of understanding measurement uncertainty and the propagation of errors, serving as a cornerstone for scientific investigation.

The second challenge escalates the complexity by incorporating the Bernoulli equation and 2D kinematics, along with first-order differential equations. Students are tasked with calculating the range (distance) of a water jet issuing from a small aperture at the base of a cylindrical container as a function of time. This exercise not only reinforces the application of theoretical concepts but also introduces students to solving first-order ordinary differential equations using the graphical method of slope fields, facilitated through the use of MATLAB and Python. This hands-on approach not only reinforces their theoretical knowledge but also enhances their computational skills, mirroring real-world engineering applications.

A fundamental component of both challenges is the emphasis on determining the optimal number of measurements to reduce statistical uncertainty, thereby honing the students' experimental methodology.

By adopting the principles of Problem-Based Learning and Spaced Learning, these activities have been shown to be exceptionally effective in advancing STEM education. Feedback from a 5-item Likert scale survey conducted after the completion of the project reflected the students' proactive engagement and their satisfaction with this practical approach to understanding complex concepts.

This pedagogical method deepens students' grasp of scientific and mathematical principles and sharpens their critical thinking and problem-solving abilities, which are indispensable in the engineering field. Additionally, the inclusion of computational tools like MATLAB and Python not only enriches the educational experience but also prepares students for the challenges they will face in their future careers. This project presents a comprehensive approach to engineering education, designed to enhance understanding of measurement and uncertainty and develop a proactive, analytically skilled student cohort ready for the professional world.

Keywords:

Experimental Learning, Measurement Uncertainty, Engineering Education, Problem-Based Learning, Computational Tools in STEM, First-Year Undergraduate Engineering, Higher Education.