The core of engineering includes both mathematical thinking and design thinking. Previous work has focused on design thinking skills and behaviors exhibited by novices, experts, first-year engineering students, and senior engineering students. In this NSF-funded study, we sought to explore the interplay between mathematics and design by observing students from diverse disciplinary backgrounds engage in mathematical and design thinking as they solve a design task. Students in engineering majors (n=17) and mathematics majors (n=13) were recruited to work independently on a design task. In this paper, we present analysis methods, data, and findings from two seniors: one undergraduate engineering major and one undergraduate mathematics major. Ultimately the research team anticipates making comparisons between final design quality and using narrative analysis to explore design and mathematics processes. The findings from the complete data set will support deepened understanding of the role mathematics and design thinking in solving engineering design tasks and will create a baseline for comparing engineering student's mathematics and design behaviors in future analysis.