Rolling in the Deep: Explanatory Depth

Think about the following questions:

1. On average, how many pounds of coffee does Columbia export to the United States in a year? 
2. What is the formal procedure for filing a patent with the U.S. Patent Office?
3. How does a sewing machine work?

Instead of producing an answer for each question, rate each question on the following dimensions:

• How likely am I to know the answer?
• How confident am I that I know the answer? 
• How well could I explain the answer to a friend?

Getting Meta-cognitive About Question Types

In a previous post, we talked about two types of meta-cognition: the what (what we know) and the how (how we know what we know). The above questions all target the what, but can be further categorized into 3 different types of questions.

Declarative Questions: The first question is a simple, declarative fact that can be answered by going to a search engine and entering a query that will return a sensible answer. For declarative questions, figuring out if you know the answer or not is a relatively straightforward process. You look into long-term memory and search for an answer (or a close approximation). If you don't get any hits, then you know you don't know the answer.

Procedural Questions: The second question is procedural, in that you must know the steps of the process necessary to achieve an end goal. To learn how to file a patent, you could also interrogate your favorite search engine, ask an expert (e.g., a patent lawyer), or learn the process yourself by reading through the steps on the U.S. Patent website. Again, knowing if you know how to do this might be as simple as asking yourself, "Have I ever filed a patent?" If the answer is "no," then you know you don't know how to do it. 

Mental-model Questions: The third class of question has a definite declarative component. The facts, however, are not stated in isolation. Instead, they are linked together in some coherent way. For simplicity, I will call this type of question a "mental-model question" because it requires knowledge about causal connections between related facts. When asked if you know how a sewing machine works [1], what probably happens is that you think about a sewing machine and what it does. Then you think about the various components that are in a sewing machine and how they interconnect. Finally, you run a mental simulation and see how the various components interact. 

The interesting feature about mental-model questions is that you typically don't get a binary "yes/no" when you ask yourself if you know the answer. For example, when you ask yourself if you know how a sewing machine works, the answer is probably not "yes" or "no," but somewhere in between. The degree to which someone understands something is what I am calling explanatory depth. If a person has deep knowledge of a topic, then they are able to provide lots and lots of details. If they only have a cursory understanding, then they will give you a much shorter and more incomplete explanation.

The Deep End of the Spool

How might we cultivate the skill of assessing our own depth of understanding of a topic? One way to evaluate the depth of our knowledge is to try to provide an explanation and see how far you can get. For instance, if someone asks me, "Do you know how a sewing machine works?" I might be tempted to say "yes." To test whether my meta-cognitive awareness about my knowledge of the inner workings of a sewing machine is well-calibrated, however, I could attempt to provide an explanation. My explanation would go something like this: 

There are two primary parts of the upper portion of the sewing machine: the needle and a spool of thread. The thread is fed through a hole in the bottom of the needle, which moves up and down, piercing the fabric. Underneath the fabric is a hole that the needle descends into, where it meets another length of thread coming from something called a bobbin. Through some bit of magic, the thread from the needle combines with the thread from the bobbin to form a stitch. 

After actually trying to explain how a sewing machine works, I realize now that my meta-cognitive awareness of sewing machine mechanics was not well-calibrated. As you can plainly see, I do a fair bit of hand waving when it comes to the process by which the thread from the bobbin intertwines with the thread on the needle. Now that I am better calibrated, meta-cognitively speaking, I would have to say that I do not understand very well how a sewing machine works because the depth of my explanation is lacking precise details. [2]

The STEM Connection

Why is this important for learning? The concept of explanatory depth is important because it is often the case that we only have a partial understanding of many different topics. That partial understanding, however, makes us overconfident about what we know. As stated in a previous post, we want our students to be highly calibrated in judging how well they know something.

There are a couple of obvious ways to test and improve explanatory depth, and thereby increase meta-cognitive awareness. As is the case for any desired skill, practice always helps. To build meta-cognitive awareness about mental-model questions, we need to give our students as many opportunities to explain their reasoning as possible. This might be in the form of small groups so that students can explain to each other how things work. Working in small groups also exposes students to the ideas of their peers, which could be an added bonus in that students may better understand an explanation from a peer who has recently gone through the process of acquiring his or her own understanding. This is obviously in direct contrast to hearing an explanation from a teacher who has understood the topic for several years, and has thus forgotten why the topic is potentially confusing. It might also be beneficial to have whole-class discussions so students can model and test their reasoning in front of others.

Another, perhaps more controversial, recommendation would be to start using oral exams. It's likely that students will mutiny if they hear their next exam is going to be a face-to-face conversation with their teacher. But hearing a student talk about what they know is probably the best way to diagnose how deeply a student knows a topic. To prepare, the teacher would need to develop a robust scoring rubric so that it is obvious how deep a student's explanation is. 

The depth of an explanation is a pretty good proxy for how well you know something. I strongly recommend trying to explain things as much as possible because when you falter (as I did above), you uncover new opportunities to learn and refine your knowledge!


Share and Enjoy! 

Dr. Bob

For More Information

[1] Miyake, N. (1986). Constructive interaction and the iterative process of understanding. Cognitive science, 10(2), 151-177.

[2] For a great animated gif that demonstrates the sort of magic I couldn't explain, see the wikipedia entry on the sewing machine (hat tip: Mike Hasko).