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Learning to Integrate Mathematical and Design Thinking in Engineering

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2015 ASEE Annual Conference & Exposition


Seattle, Washington

Publication Date

June 14, 2015

Start Date

June 14, 2015

End Date

June 17, 2015





Conference Session

First-year Programs Division Technical Session 2: Design in the First Year: Challenges and Successes

Tagged Division

First-Year Programs

Page Count


Page Numbers

26.1079.1 - 26.1079.12



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Paper Authors

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DeLean Tolbert Engineering Education, Purdue University Orcid 16x16

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Monica E Cardella Purdue University, West Lafayette Orcid 16x16

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Learning to Integrate Mathematical and Design Thinking in EngineeringIn the engineering profession, engineers encounter a wide range of problems, ranging from well-defined to ill-defined, which require different combinations of mathematical and designapproaches and skills. Today’s future engineers enter college with pre-college experiences whichmay lead them to have misconceptions about the nature of engineering problems. Oftentimes,they perceive that engineering problems have linear problem solving processes, are well-defined,highly constrained and are quick to solve. To combat this misconception, it is necessary to firstinvestigate the ways that students currently use mathematical thinking and design thinking ashigh school students transitioning to undergraduate engineering students.The following research questions guide the investigation of students’ mathematical and designthinking: (1) How do students respond to open-ended, ambiguous design tasks? (2) How domathematical thinking activities impact design thinking activities? and (3) How do students’thinking processes differ based on mathematics, design and engineering backgrounds? At a large,research focused institution in the Midwestern region of the United States, students begin theirengineering careers as “first-year engineers” before applying to a specific engineering discipline,within the college. Most first-year engineering students complete two introductory engineeringcourses, which expose them to compound engineering problems. These problems developstudents’ problem solving skills as the problems increase in complexity, ill-definedness andcontext dependence, over the duration of the first course.From this institution, we are currently recruiting 30 first-year engineering students, 15 seniorscompleting an engineering degree, 15 seniors completing a degree focused in design (i.e.industrial) and 15 students completing a degree in mathematics. Students are recruited to spend 3hours designing a playground for a fictitious neighborhood. Students are asked to “think aloud”as they work in isolation solving this open-ended and ambiguous task. Verbal protocol analysisis the primary research approach and allows the researchers to uncover invisible thoughtprocesses. The thought processes are then analyzed using a coding scheme informed by: (1)Schoenfeld’s framework for mathematical thinking, (2) XXXXXX’s modified version of thatframework, (3) a framework for design thinking and (4) emergent themes from the dataset.In general, we anticipate observing how students experience design fixation, their specificmathematical thinking behaviors and use of diverse design processes. In this study, fixation isviewed as double edged, in that a student may become fixated on a example designs andunderlying principles. Additionally, they may exhibit fixation as an attachment to their own earlymathematical or design concepts, ideas or solutions. Schoenfeld’s and XXXXXX’s modifiedmathematical thinking framework will allow the researchers to investigate mathematical thinkingbehaviors beyond the use equations and language. Student’s mathematical thinking knowledgeand ability to apply said knowledge will also be explored. Finally, the design thinkingframework, will allow the researchers to create a summary of major activities and the overallstructure of each student’s design process.Preliminary findings suggest that students elicit different mathematical and design strategies,which vary based on previous design and mathematical experiences. Some students acknowledgethat they have a perceived weakness in these areas, while others exhibit confidence in their ownabilities. These varying levels of confidence are often observed by the facilitator during studyand validated during the follow-up interview. With respect to design strategies, studentsparticipate in this study at different points in the semester. Student who participate after learningnew design thinking skills articulate that there is a tension between the design process taughtbefore college and that being taught in their introductory engineering course. With respect tomathematical thinking, students often comment that they used very simple mathematics but failto recognize the diverse types of mathematical knowledge they are accessing and applying, todevelop a solution to this design task. Design fixation occurs in most of the participants’ data butit does not have the same characterization across the data.This paper will focus on the “ways of thinking” that freshmen students exhibit when solving theplayground design task. We anticipate that the findings from this portion of the study will informthe way that engineering courses are designed. If the focus of engineering problem solving is todevelop advanced mathematical and design skills in future engineering professionals, studentsshould be taught how to elicit mathematical and design “ways of thinking” to solve diverseproblems. This work may also have implications for pre-college engineering learningenvironments, which can help students to recognize the mathematical and design knowledge atplay in their everyday problem solving experiences.

Tolbert, D., & Cardella, M. E. (2015, June), Learning to Integrate Mathematical and Design Thinking in Engineering Paper presented at 2015 ASEE Annual Conference & Exposition, Seattle, Washington. 10.18260/p.24416

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