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An Alternative Methodical Approach and Its Effectiveness to Learn Change of Basis Matrices in an Engineering Linear Algebra Class

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Conference

2024 ASEE Annual Conference & Exposition

Location

Portland, Oregon

Publication Date

June 23, 2024

Start Date

June 23, 2024

End Date

June 26, 2024

Conference Session

Mathematics Division (MATH) Technical Session 1

Tagged Division

Mathematics Division (MATH)

Page Count

18

DOI

10.18260/1-2--46543

Permanent URL

https://peer.asee.org/46543

Download Count

96

Paper Authors

biography

Meiqin Li University of Virginia

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Dr. Li is an Assistant Professor at the University of Virginia. She obtained her Ph.D. in Applied Mathematics from Texas A&M University-College Station in 2017. Dr. Li holds a strong interest in STEM education. For example, she is interest in integrating technologies into classrooms to bolster student success, creating an inclusive and diverse learning environment, and fostering student confidence by redeveloping course curricula and assessment methods, etc. Beyond this, her research intertwines numerical computation, optimization, nonlinear analysis, and data science.

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Abstract

Over the years, students have relied on textbook approaches to learn change of basis matrices. These methodologies often stem from complex abstract concepts, making them difficult for students to comprehend, especially for engineering students who do not have sufficient training for proofs. As a result, lots of students frequently resort to rote memorization of formulas without truly understanding the concepts behind them. Due to the intricacy of these formulas, it's not uncommon for students to make mistakes, leading to poorly solved problems. In response to this issue, this paper introduces an alternative approach that diverges from traditional textbook methods and investigates students’ perceptions on the effectiveness of this alternative approach. This alternative approach builds on foundational linear algebra skills, making it considerably more accessible and easier to understand for students. Furthermore, it eliminates the need for students to memorize complex formulas, promoting sustainable, long-term learning instead.

Li, M. (2024, June), An Alternative Methodical Approach and Its Effectiveness to Learn Change of Basis Matrices in an Engineering Linear Algebra Class Paper presented at 2024 ASEE Annual Conference & Exposition, Portland, Oregon. 10.18260/1-2--46543

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