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

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2014 ASEE Annual Conference & Exposition


Indianapolis, Indiana

Publication Date

June 15, 2014

Start Date

June 15, 2014

End Date

June 18, 2014



Conference Session

NSF Grantees’ Poster Session

Tagged Division

Division Experimentation & Lab-Oriented Studies

Tagged Topic

NSF Grantees Poster Session

Page Count


Page Numbers

24.260.1 - 24.260.14



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Paper Authors


DeLean Tolbert Purdue University, West Lafayette Orcid 16x16

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DeLean Tolbert is a doctoral student of Engineering Education at Purdue University. She earned a Electrical Engineering from the University of Michigan–Dearborn and a M.S. in Industrial Engineering from the University of Michigan. Her research interests include: informal engineering learning and teaching, K-12 engineering education, and engineering thinking and learning within ethnic minority communities.

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Monica E. Cardella Purdue University, West Lafayette Orcid 16x16

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Monica Cardella is an Associate Professor of Engineering Education at Purdue University and is the Director of the MEDLEE (Mathematics and Engineering Design Learning Environments and Experiences) Research Group. She has a BSc in Mathematics from the University of Puget Sound and an MS and PhD in Industrial Engineering from the University of Washington. She teaches design to first-year engineering students at Purdue as well as an upper-level design course for seniors and graduate students. Her research focuses on the development of engineering thinking skills (operationalized as design thinking, mathematical thinking, and the interplay between the two) in children as young as 4 years old as well as older "children" (i.e. undergraduate students).

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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.  

Tolbert, D., & Cardella, M. E. (2014, June), CAREER: Mathematics as a Gatekeeper to Engineering: The Interplay between Mathematical Thinking and Design Thinking – Using Video Data Paper presented at 2014 ASEE Annual Conference & Exposition, Indianapolis, Indiana. 10.18260/1-2--20151

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