June 15, 2014
June 15, 2014
June 18, 2014
Division Experimentation & Lab-Oriented Studies
NSF Grantees Poster Session
24.260.1 - 24.260.14
CAREER: Mathematics as a Gatekeeper to Engineering: The Interplay between Mathematical Thinking and Design Thinking – Using Video DataThis paper will focus on the analysis of video data to identify critical incidences of the transitionbetween divergent thinking and convergent thinking and the moments that lead to and followthese events. Video data allows the researcher to review and re-immerse him or herself back in tothe original context and explore points of interest that could not be captured fully in the fieldnotes, observations and existing artifacts (Powell et al., 2003). It encompasses all the dataavailable to the researcher and allows for exploration of data that cannot be fully represented byother means.In this study we explore the cognitive discord which can occur when engineering students, whohave been previously taught convergent mathematical thinking strategies, are exposed to thedivergent manner in which design problems are solved in educational engineering environmentsand in the real world. First-year engineers and senior design, engineering and mathematicsstudents are recruited to work, in isolation, on a common design task. This study uses the thinkaloud 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).A freshman engineering student (yet undecided about a specific engineering major) and a collegesenior in aerospace engineering will serve as case representations for our use of the criticalincident video analysis method. The analysis of the participants’ video data will reveal criticalmoments of transition between convergent and divergent thinking and will yield insight intosimilarities and differences in these students’ approaches to design problems. The entire threehour study is a design experience for the students and there are many opportunities for theparticipant to exhibit mathematical thinking. The use of video data to observe mathematical anddesign thinking in traditional education environments is not novel but there appear to be greatopportunities for deeper understanding of students’ thinking processes, when video data isanalyzed.Powell, A. B., Francisco, J. M., & Maher, C. A. (2003). An analytical model for studying the development of learners' mathematical ideas for reasoning using videotaope data. Journal of Mathematical Behavior, 22, 405-435.
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