Representations in an integrated physics and mathematics course based on models

This study took place in an integrated Physics and Mathematics course for first-year engineering students at a private university in northern Mexico. The integrated course is taught based on Modeling Instruction as well as models and modeling perspective in an active learning environment. This innovative approach, combined with a classroom setting that incorporates the use of technology, promotes the connection and application of the contents from both courses. During the semester, students engage in solving problems (individually and collaboratively), present their models on whiteboards, and have discussions in teams and with the rest of the group. The objective of this study is to analyze how the models and representations shown in students' work evolve throughout the semester. Fifty-four first-year engineering students enrolled in the Physics I and Mathematics I integrated course. When students worked collaboratively in groups of three, they took pictures of their whiteboards, and all pictures were stored in a repository for all (students, instructors and researchers) to review. When students worked individually, instructors assessed their learning based on their written solutions. The analysis of the whiteboards confirmed that at the beginning of the semester students used few representations, whereas by the end of it they were incorporating congruently more than ten different representations, making their models more robust.