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Teaching Mathematics and its Applications Advance Access originally published online on July 1, 2008
Teaching Mathematics and its Applications 2008 27(3):150-159; doi:10.1093/teamat/hrn008
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© The Author 2008. Published by Oxford University Press on behalf of The Institute of Mathematics and its Applications. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

Which mathematics should we teach engineering students? An empirically grounded case for a broad notion of mathematical thinking

Monica E. Cardella

Address for correspondence: Monica E. Cardella, School of Engineering Education, Purdue University, 701 West Stadium Avenue, West Lafayette, IN 47907-2045, USA. E-mail: mcardell{at}purdue.edu

Submitted May 2008; accepted June 2008

While many engineering educators have proposed changes to the way that mathematics is taught to engineers, the focus has often been on mathematical content knowledge. Work from the mathematics education community suggests that it may be beneficial to consider a broader notion of mathematics: mathematical thinking. Schoenfeld identifies five aspects of mathematical thinking: the mathematics content knowledge we want engineering students to learn as well as problem-solving strategies, use of resources, attitudes and practices. If we further consider the social and material resources available to students and the mathematical practices students engage in, we have a more complete understanding of the breadth of mathematics and mathematical thinking necessary for engineering practice. This article further discusses each of these aspects of mathematical thinking and offers examples of mathematical thinking practices based in the authors' previous empirical studies of engineering students' and practitioners' uses of mathematics. The article also offers insights to inform the teaching of mathematics to engineering students.

Monica Cardella is an Assistant Professor of Engineering Education at Purdue University. She received her PhD in Industrial Engineering at the University of Washington where she was a Graduate Research Associate at the Center for Engineering Learning and Teaching (CELT). Dr Cardella's research concentrates on characterizing engineers' mathematical thinking, engineering design thinking, assessing design process knowledge, and K-12 engineering education.


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