These days the true nature of mathematics is often hidden from the average student. Too often it is imagined that mathematics involves memorizing an algorithm to be applied to a particular sort of problem, in order to use it to produce the right answer when one is set such a problem. Granted, that is one use of mathematics, and it is important for most people to learn in this way some basic skills, such as adding, multiplying, and carrying out the arithmetic of fractions. However, the practice of mathematics is much more like writing an essay comparing and contrasting the plot structures of Jane Austen and William Shakespeare: a mathematician is always making judgments about complex situations.  He or she handles the complexity by  finding elegant perspectives from which the situation appears crystal-clear.

My hunch is that most mathematicians will agree with my claim mathematics in its purest form is a creative activity. So why do I write? It is because the situation illustrates a problem with the way higher education is currently conceived.  Though I don’t necessarily agree with the whole of the article, Jeffrey J. Selingo hits the nail on the head in his “Rebuilding the Bachelor’s Degree,” in the April 22, 2016 edition of the Chronicle Review: “The problem right now is that the traditional college curriculum waits too long “to put students in over their heads,” as Alan Snyder, associate provost at Lehigh University, told me. So too many recent graduates approach their job descriptions the way they did a syllabus in college: They want concrete, well-defined tasks (page B9).”

“The problem right now is that the traditional college curriculum waits too long “to put students in over their heads,” as Alan Snyder, associate provost at Lehigh University, told me. So too many recent graduates approach their job descriptions the way they did a syllabus in college: They want concrete, well-defined tasks (page B9).”

Learning is an exciting drama that is our encounter with truth, beauty, and goodness. It is not about boring outcomes achieved in a process analogous to a factory assembly-line. Moreover, no one really wants an education dominated by the straightforward and boring accumlulation of well-defined skills and outcomes — not future employers, not professors, not students. Anyway, one learns much more when engrossed in the exhilarating joy of discovering a wonderful new world.

Why, then, the vocabulary of instrumentalism gain ground? Partly it has to do with accountability, partly with the principle that it is easier to take the mediocre route than to take the risks involved in searching for a better route.

Let’s take first the goal of accountability. If students are not ready for jobs and life when they graduate, we tear our hair out and ask what more we could do? We try to make it simple: what should they know and be able to do? Make that the goal, then decree that the classroom should consist of appropriate means for achieving the goals. Then test to make sure it is achieved and when it is not, either give professors seminars in better pedagogy, or hire ones that will yield better test scores. It sounds logical and it is well-intentioned.

Indeed, in some situations the focus on accountability is the right approach. If X absolutely needs to be learned, we should focus on ensuring X happens. One imagines especially in technical and vocational schools this would be important; however, even there, learning is easiest when it is fun.

In the setting of a higher-education, especially one in the tradition of the liberal arts, there is also a realization that the learning experience cannot be encapsulated in a finite set of outcomes. What would be the outcome of course on Shakespeare’s Histories? Or a course on the spirituality of Teresa of Avila? The only acceptable answers are not revealing, things like “An appreciation for Shakespeare’s genius and the depth and diversity of themes addressed in his plays.” Well, duh, something like that should happen, but it doesn’t come close to capturing the experience of entering deeply in Shakespeare.

The other option is to set, say, 5 very specific outcomes. One might be something like, “Being able to articulate with examples the ways in which Shakespeare drew on earlier source materials to craft his own unique plays.” The problem is that a course focused on meeting 5 such outcomes would very easily end up as something teaching to only those standards, and thereby become somewhat boring. Many students wouldn’t enter into the profundity of Shakespeare’s plays, but rather just find a way to cover their 5 bases. Interesting explorations not related to those five goals would tend to be minimized. Students would thank God they had managed to get through the heavy workload and feel satisfied they had fulfilled their duty as hard-workers in the boring but seemingly fair meritocracy that is the system for getting the stamps required to get a good job in a difficult economy.

Actually, this ineffability holds for technical education, too. The IT-specialist who is excited about the technology he works with and knows it inside and out because it is all interesting to him will be a much more valuable employee in the long run than one who merely shows proficiency in the particular skills currently needed, but has no deeper knowledge.

The second problem mentioned above is that mediocrity can be seen as better than striving for greatness and falling on one’s face. F0r teachers this pressure is real. If we have outcomes and everything is directly pointed at outcomes, we can always say we were doing logical things and doing what everyone thinks is reasonable. However, if we try something new, some new way to give students the correct intuition or help them fall in love with what is studied, it might fail miserably. Actually, to be fair, there is general recognition in higher education that it is good practice to try out new ideas and learn from the experience if they don’t work. Still, it takes courage: everyone wants to see good student evaluations, and now, rather than later.

Even if we recognize it is acceptable to try something new and fail at times, there is the problem of time. Developing a new approach is incredibly time-consuming. It is worthwhile, but there are only 24 hours in a day. I have seen this especially in connection with the flipped classroom, which in some contexts may be a great idea. But it is not if there isn’t enough time for it to be implemented without endangering the professor’s sanity.

In a way, this criticism of “outcomes” is a straw man. No one is against creativity in higher education, or students enjoying what they study. Indeed one can have all of these at the same time. The process of writing down outcomes may be helpful to a professor’s self-awareness and lead to fruitful adjustments to a course. (What am I trying to accomplish? Why am I doing X, which perhaps in the final analysis is irrelevant to the course?) What must be avoided is the temptation to think that writing down outcomes is more than just a nice idea that is more or less helpful depending on the context. We are always looking for the next silver bullet. It doesn’t exist, but if it did it would look less like thinking borrowed from corporate processes and more like encouraging students to lose themselves in a love-affair with the truth.