How well do you know yourself? How accurate is your perception of what you know? To what extent do you understand how you learn? Whether you are a student or instructor, these are among the most pressing questions that you need to consider. I want to give you a handle on how to do so.

Defining the essence of  knowledge is a tangled, murky, and worthwhile endeavor that has busied philosophers for many centuries. In the context of modern education, though, it is as much a tactical question as a philosophical one. Teachers and learners need to disaggregate different types of knowledge. The famous (infamous?) Bloom's Taxonomy makes one suggestion for how to do so through its identification of different domains of learning.

I am a bigger fan of Anderson & Krathwohl's taxonomy, which is a revision of Bloom's. In a later post, I will discuss this taxonomy and how to use it, but for now, suffice it to say that an important process that it highlights is metacognition, essentially thinking about thinking. For those of you who are fans of such self-referential ideas, you may also appreciate this:

Metacognition is a crucial aspect of learning, and in my experience, one that we frequently neglect. Metacognition has several aspects, but two important ones are

• Metacognitive knowledge, which is what a learner knows about her/himself, and
• Metacognitive regulation, which refer's to a learner's ability to react to metacognitive knowledge by making alternations to control her/his own learning.

What does weak metacognition look like? Suppose that I assign calculus students to read a textbook chapter on derivatives. I ask my students to write a brief response to the reading in which they explain what they found challenging. A response like "I don't understand derivatives" or "derivatives are confusing" signals a student with weak metacognitive knowledge who cannot identify particular points of difficulty. A response like "I don't see why one of the correct geometric interpretations of the derivative is as the slope of a tangent line" signals a student with stronger metacognitive knowledge who can articulate specific challenges. Hopefully, this metacognitive knowledge serves as the gateway to metacognitive regulation, which would address the subject matter. For instance, the student could then decide to re-read the specific paragraph explaining the concept, try a practice problem involving the geometric interpretation of derivatives, ask somebody for help with the idea, or take one of dozens of other possible concrete steps.

If you are a student, I encourage you to work hard to be clear and specific with yourself about what you find challenging. If you are an instructor, I encourage you to discuss metacognition with your students and to structure activities and assignments that require it. For the sake of concreteness, here are two examples of how I do this:

1. As I mentioned above, I ask my students to respond to reading assignments (in writing) and to articulate their difficulties. I give them feedback on whether they have expressed their difficulties with sufficient specificity.
2. I give students the opportunity to partially regain missed points on quizzes by turning in corrected solutions. But as part of these corrected solutions, they must also include an explicit discussion of what they did wrong the first time through, and what their original challenges/misunderstandings with the question were. I only restore points if the new solution is correct, and if the metacognitive explanation is well-developed.

Good metacognition take practice. We can all learn to be better metacognitive thinkers. I wish you luck in your quest to know yourself.