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

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.