The Art of Thinking

Another in our ongoing series of guest faculty blog posts; this one by Professor of Mathematics (and Associate Dean) Michael Lachance:



The single greatest export from a mathematics department is not mathematicians, but clear thinkers. Under the guidance of an instructor, students in mathematics classes, at every level, practice thinking. These days words like creative and critical adorn the main activity of thinking, but those words distract from what is really important: practicing thinking.

Mathematics does not have a lock on thinking. In every classroom around campus students are engaged in the practice of thinking, guided by teachers whom themselves are skilled in the art of thinking. At a university there is a path, a practice, for nearly every interest. It is tempting to distinguish among the paths—disciplines, minors, majors, and degrees—attributing a cloak of purity, perhaps exclusivity, to some over others. To do so is unfair to the student who pursues a passion or a dream, in either case a path, who chooses a form of practice with a distinct focus, under the guidance of a host of teachers who possess that passion.

Professors at a university are at once teachers and students. Their role in guiding and developing students is profoundly important, but the reason that they are given that opportunity is because of their past and ongoing commitment to their discipline, to their own thinking. Their effectiveness as a model is a function of their practice, their discipline, and this they deepen with each investigation, experiment, article, or book.

Young men and women who do not attend a university think no less than those who do. But the former are in effect responsible for developing their own thinking skills, sometimes missing the directed instruction that teachers provide. They have teachers to be sure—family and friends, workplace associates, structured religions, and media outlets. Even so, these students are less likely to be aware that these are their teachers. Students at a university, by virtue of their exposure to different thinkers and ideas, thoughts and models, are more likely to see themselves as engaged in a practice, to be reflective, self-aware, to see themselves in a context.

There is a phrase in some Buddhist traditions that is germane: “which must be cultivated to be known fully.” Cultivation is the key, whatever one’s pursuits or talents. And practicing thinking, for students and teachers alike, is how we come to know more fully.