CAREER: Mathematics as a Gatekeeper to Engineering: The Interplay between Mathematical Thinking and Design Thinking – Using Video Data

There is a need to better understand how students gain accurate engineering conceptual understandings and how they apply them in practice. There are varied approaches to study the development of engineering knowledge and thinking skills. This paper focuses on the use of video data to uncover and document students’ thinking and development and presents lessons our team has learned as we use video data to support our investigation. Video data allows the researcher to review and re-immerse him or herself back in to the original context and explore points of interest that could not be captured fully in the field notes, observations and existing artifacts . In this study we explore the cognitive discord, which can occur when engineering students, who have been previously taught convergent mathematical thinking strategies, are exposed to the divergent manner in which design problems are solved in educational engineering environments and in the real world. First-year engineers and senior design, engineering and mathematics students are recruited to work, in isolation, on a common design task. This study uses the think aloud protocol to capture student thinking processes. The data includes a collection of artifacts (e.g. drawings, audio transcriptions, screen capture, interview transcriptions, and video data). We anticipate that using video as data will help us to identify critical incidences of transition between divergent thinking and convergent thinking and the moments that lead to and follow these events. A freshman engineering student (yet undecided about a specific engineering major) and a college senior majoring in fashion design will serve as examples of using video data to observe mathematical and design thinking. The analysis of the participants’ video data will reveal critical moments of transition between convergent and divergent thinking and will yield insight into similarities and differences in these students’ approaches to design problems. Although the use of video to record and observe mathematical and design thinking in traditional education environments is not novel, using video as a primary data may create great opportunities for deeper understanding of students’ thinking processes in engineering education.