Knowing and Understanding

by Matthew Koslowski on August 12, 2009
in Essays

“A hunter left his cabin and hiked two miles south, turned and hiked two miles west, shot a bear, and hiked two miles north back to his cabin. What color was the bear?”

If you answered, “White,” you gave the right answer. But how did you arrive at the answer?

Educators need to concern themselves as much with how their students arrived at the answer as they concern themselves whether the answer was correct.

What a Trivia Night Can Teach Us about Teaching

While reading Never Work Harder Than Your Students, I came across the above question as part of an anecdote. At a trivia night, a very intense, competitive trivia night filled with teachers, the scores were neck and neck. This question, the final question stumped everyone except Justin, who was the only person at the party to answer, “White.”

Everyone wanted to know how Justin knew the answer.

“Well,” Justin began shyly, “I noticed that all of the numbers in the problem were the number two.”

“Go on,” we prodded.

“And, on a job application, when they ask you about your race, white is usually the second option. So, I figured the bear must be white.”

Of course that wasn’t the explanation the brain teaser game provided. The real explanation had something to do with the fact that the only place on earth where you could walk in that pattern and end up back where you started was on the north pole and the only bears on the north pole were polar bears. But, Justin hadn’t used any of that reasoning. He got the answer right, but he didn’t really understand the problem.
– From Never Work Harder Than Your Students, Dr. Robyn Jackson, page 112.

Without asking Justin how he arrived at the correct answer, the other contestants would never have figured out that Justin had won through false reasoning. Teachers need to engage their students and solicit this kind of feedback in their classrooms, as I discussed in my post Testing, Assessment, and Feedback, to insure their students aren’t winning through false reasoning.

If he had been asked, “Do you get why that’s the right answer?”, I hope that Justin would have said, “No, not really. I was kind of lucky.”

And we need to hope that our students will be able to say the same.

Do you understand me?

At any rate it seems that I am wiser than he is to this small extent, that I do not think I know what I do not know.
– Socrates in Plato’s Apologia, from The Complete Dialogues of Plato (Edith Hamilton and Huntington Cairns, eds.), pages 7-8.

What do we mean when we say, “I know it” or “I understand it” or “I got it”? And how can we be sure that we really do?

Cognitive scientist Dr. Daniel Willingham writes about how to improve teaching by employing applicable knowledge from the neuro- and cognitive sciences. In his essay, “Why Students Think They Understand–When They Don’t”, he discusses two heuristics that we employ that can trick us into believing we know something whether we actually do or not: “familiarity” and “partial access.”

Each of us is busy and each of us is dealing with a steady stream of information flowing at us and over us. We need to employ heuristics, methods of screening information to make sure we are assimilating everything we need to accomplish our tasks.

When we are familiar with something, when something has been primed for us (to use another cognitive science expression), we are more likely to discount the amount of attention that it needs and focus on what is new.

In high school and college, preparing for tests meant skimming through my notes. Often I would find myself seeing a familiar phrase or word and, in my head, check a little box, saying to myself, “Yep, I know that. And I know that. Hey, and that too!” If I came across something I had forgotten or that seemed unfamiliar, I would spend time on that. This probably was not the most effective studying method.

And, of course, there were times when I misread a question while taking the test because I was familiar with part of it in one context and did not read the whole question closely.

Perhaps familiarity really does breed contempt.

Partial Access
I have embarrassed myself, as I think we all have, by overstating my knowledge. I thought because I knew something about something related to what was being sought that I could drill down to the correct knowledge. The instances that I haven’t been able to remind me to laugh at myself.

Partial access is that feeling we get that the answer is right on the tip of our tongues. We may know things related to the right answer and as we toss about in our memories we may find we are unable to come to the right answer. Because we know things related to the right answer and have encountered the right answer in context related to those things we are able to recall, we can fool ourselves into thinking we know the right answer.

Now that we know this, what do we do with it?

Informally, when talking about knowing something, we often mean we are familiar with it, that in hearing someone else talk about it we comprehend and recognize it but often when asked to verbalize it we are unable to do so. Teachers need to be careful that they understand what students mean when they say they know something. The expectation that we need to set is that when we say, “I know it,” means, “I would be able to explain this to others and demonstrate this as necessary.”

While recall is foundational to knowledge, it is a function of memory. Knowledge is the ability to manipulate, to integrate, or to apply, or a combination of those operations, the facts and figures stored in your memory towards some end.

Teachers can provide students with assessments and self-tests that they can use to judge the depth of their own knowledge. An educator’s job is to help train the student how to effectively and efficiently learn the material and assess for themselves where the gaps are that they need to fill, to teach their students to be wise and not to think they know what they do not know.

When designing curricula and tests, teachers who are aware of the effects of familiarity and partial access will be able to design their classes in such a way as to insure that students understand why an answer is correct and explain how they know something. Then the teacher will know whether the students understood the lesson.


One Response to “Knowing and Understanding”
  1. Judy says:

    Matthew- I have just completed my first foray into your start-up blog and found it rewarding because I took something new and interesting from each entry. The magician’s formula is a unique approach to writing, but I recognize and like it. Our minds love to take a journey and be amazed, especially when there is a “Prestige” ending. I am looking forward to continuing this journey with you. -Judy