Struggling with the Idea of Critical Thinking

I came across an excellent article (pdf) in Psychological Science by Daniel T. Willingham entitled "Critical Thinking" and subtitled Why Is It So Hard to Teach? The author first presents a case for the teaching of critical thinking as an integral part of the nation's educational product. This skill is defined "in layperson's terms" as

[S]eeing both sides of an issue, being open to new evidence that disconfirms your ideas, reasoning dispassionately, demanding that claims be backed by evidence, deducing and inferring conclusions from available facts, solving problems, and so forth.

It is also noted that there are particular kinds of critical thinking linked to academic pursuits, such as history or science. Here's an example of literary criticism (a review, in fact, so it's meta-criticism), chosen at random from Critical Inquiry (Spring 2003, pg 463):

[The author] demonstrates a thorough historical awareness of the obscene cruelty of the Stalinist and Fascist regimes and, in fact, suggests that the profoundly stupid cruelty of the totalitarian regimes is more theoretically pertinent than theory itself in the dark illumination it casts on the institutions of the West, where the term totalitarian is often used, in a way that to [the author] suggests gross complacency, emplifies the illusion of freedom and agency in contemporary democracy, illusions unavailable in non-democratic societies, where the truth is confronted more directly in the from of a short circuit between authority and brutality.

There are many other examples from a variety of disciplines that we could choose, and they will look different from one another. What is this "critical thinking" stuff that unites them? By the way, I'm not sure "emplifies" is really a word, but that's part of the fun.

Defining the process of critical thinking takes up a good bit of Willingham's piece. He presents the idea that there is a difference between superficial and deep structure, and that humans naturally cling to surface structure. Through training we can see through the surface structure and generalize problem solving. An interesting example is given.

A treasure hunter is going to explore a cave up on a hill near a beach. He suspected there might be many paths inside the cave so he was afraid he might get lost. Obviously, he did not have a map of the cave; all he had with him were some common items such as a flashlight and a bag. What could he do to make sure he did not get lost trying to get back out of the cave later?

The "correct" solution is to put some sand in the bag to use as markers within the cave, to be used to retrace the route back. What's interesting is that when this problem was posed to American and Chinese college students, 75% of the former latched onto the solution, but only 25% of the latter. The hypothesis is that this problem has the same deep structure as that of the story of Hansel and Gretel, which is common to American culture but not Chinese. That is, because of prior exposure, American students could see through the distracting surface structure (beach, cave, etc.) to see the underlying problem (the need to leave a trail behind oneself).

Even if one has been trained in deep structure, like mathematical methods of solving problems that may all look the same, but are really the same logically, one must also be trained to use this knowledge, argues the author--we have to know when to look for deep structure. The reverse is true also--even if one knows to look for deep structure, one must know how to do it. Knowledge of content and methods of inquiry are both prerequisites. But are they sufficient?

Critical thinking is not a skill at all is the hypothesis advanced later in the article, after a summary and discussion of the difficulties and general failure to prove that teaching critical thinking per se has been successful.

Critical thinking does not have certain characteristics normally associated
with skills—in particular, being able to use that skill at any time. If I told you that I learned to read music, for example, you would expect, correctly, that I could use my new skill (i.e., read music) whenever I wanted. But critical thinking is very different. [...] [P]eople can engage in some types of critical thinking without training, but even with extensive training, they will sometimes fail to think critically.

Here I will take my departure from the article and offer my own thoughts. I think the idea presented in the quote above is absolutely on the money. To illuminate, consider the following example. An employee works on a project for his supervisor, and presents the results. The latter reviews the work carefully and pronounces "you did a good job." This is obviously a desired outcome for the employee. Is it something we can teach our students: to do a "good job"? No. The reason is that this is a description of the outcome, and is not directly related to the process of attaining it. Note also that agreeing that the description is accurate does not give us license to assume that we can measure the accomplishment with some metric. This assumption is, unfortunately, blithely made very often in academic assessment circles.

We can understand this problem better by looking at its deep structure. Some abstract problems have very difficult solutions, which are nevertheless easily confirmed once found. Suppose I set up a row of cups numbered 1-1000 and secretely put a pea under one of them. Your job is to figure out where the pea is by turning over cups and looking. Generally speaking, you'll have to turn over 500 cups on average to find it. There are no shortcuts. But once it's found, verification is obvious. You'll know instantly that you did a "good job" if you find the legume on the second try. In computer science this phenomenon is well known, and even famous. An outstanding example is the P=NP problem.

Hard to construct, easy to verify describes many of the outcomes we observe in our professional lives. That's why experience and learned judgment are invaluable in most, if not all, professions. If we accept that critical thinking should not be thought of as a skill that can be taught but rather a judgment about efforts made, then how can we proceed? What can be taught?

I've argued before that critical thinking is a fuzzy concept, so maybe my reading of this article is just confirmation bias on my part, but that won't stop me from presenting my argument anew, framed in the current context.

The idea that knowledge and skills are both required to develop cognitive skills was a point mentioned earlier. But we can be more specific without becoming pedantic or falling into a mereological fallacy. Knowledge and algorithmic skills can be lumped together into a basket called analytical thinking, or if you prefer, deductive reasoning. Knowing facts is the simplest kind of deductive reasoning, but it also includes analyzing chemical processes according to given rules, solving all kinds of math problems, checking grammar, and so on. We spend a lot of time in education trying to convey this kind of knowledge.

Underappreciated, I believe is the complementary cognitive skill of inductive reasoning. During a college curriculum, this type of thinking sneaks up on a student, and he or she may fail simply because of the lack of warning. I think instructors mostly aren't aware themselves when they cross the threshold from analytical/deductive to what I'll call creative/inductive.

Creativity and induction are both generalizing operations: the creation of new knowledge for the learner. When I was in grade school, working with decimals and fractions for the first time, I remember creating the following hypothesis after working enough problems: the reciprocal of an integer n near 10 is about .10 - (n - 10)/100. This looks complicated, but in practice, if I wanted to remember what 1/13 was, I'd take the '3' from 13, turn it into .03 and subtract from one tenth to get .07. The actual reciprocal is .077, so it's not a bad approximation. On the whole, this is a lousy way to get the reciprocals, though, because it only works in a narrow range. My brain is just wired to remember processes rather than facts, so it stuck.

The point of this numerical digression is to illustrate the creative/inductive thought process. It's messy, often inaccurate, and a lot of work to get right. Unlike the step-by-step process of teaching an analytical/deductive skill, there are false starts and inevitable setbacks. There's not even a guarantee that there is a solution. This takes a whole different outlook on the part of the problem-solver. Students who are used to the analytical process, and who suddenly encounter the trial-and-error necessities of a creative process are often stymied. But I think it can be taught, and the first step is to recognize the problem and address it.

Unlike the fuzzy label "critical thinking," which arguably is not a skill at all, but an outcome of skills and knowledge, both analytical/deductive and creative/inductive skills can be taught and assessed. We just have to do so intentionally. Critical thinking as a skill to be taught and assessed is a meme that needs to go away... The sooner the better.