Overlap of Consciousness and the trouble with spot checks

One of the underlying assumptions in the "it's the student's fault" paradigm of education is that students are simply un, non, or irrational thinkers. They can not be trusted to proceed rationally from premises to conclusions. They cannot be trusted to behave predictably. They are taught perfectly reasonable methods for solving something, and yet they do something completely unexpected instead.

But this is false. Students, even poor students, are not un or non or irrational thinkers. They drawn perfectly reasonable, rational, and valid conclusion to problems. They managed to do so and get the wrong answer because their premises are wrong, and they draw perfectly reasonable conclusions given their initial premises. If you had their premises, you'd end up in the same place.

As a grad student, what I found so compelling about teaching was figuring out where students were going astray. I thought of it as a puzzle: to understand "Why in the world does the student think THAT?!?!!?"

Solving the problem meant creating of "an overlap of consciousness". That sounds silly, but fundamentally, you cannot understand what your student does or doesn't understand unless you are so well inside their head that you can see from their perspective.

You have to pay enough attention to them to understand what premises they actually hold, not the ones you think they hold.

Correcting an error by fixing the end point wasn't enough because unless I got to the root of the problem, I'd never fix the error that led them down the wrong path. Correcting their error required an overlap of consciousness, a willingness to let go of my own assumptions and listen to what they were saying about how to solve a problem. I had to let go of my own knowledge, and be where they were.

Here's an example: telling someone who tried to solve "what is 4% of 150" and gotten the wrong answer after they did 150 / .04 that "you take a percentage of something by multiplying, not dividing" will elicit "okay". IT WILL NOT STICK. Why? because they had SOME REASON for doing it that way--somewhere, somehow, someone told them something that made them think that made sense. If you just tell them "no, do it this way", that bad reason will still be in their heads, and when they next get confused or lost or frightened, they will default to the path in their neurons that they've already made: The Wrong One.

What needs correction is understanding why they made that mistake, and what premise they are following. And you need to get to the root of that before anything else will really come together.

(Why might someone divide by 4%? Because they are trying to take a part of a whole, right? And when you take 32 into 8 parts, you divide 32 by 8. Isn't this 4% just a part of a whole?)

As a lecturer, you're responsible for fixing these mistakes and doing everything possible to not create these mistakes in the first place. That's the real puzzle of teaching: how to bullet proof your lesson against misleading your own students. Because by and large, it's the teacher's fault. We don't pick good examples, or good counter examples. We don't realize what other assumptions we're working with. We get sloppy. We don't try to model the mind of someone who knows much less than we do about what we're presenting. But if we are going to improve, we are going to have to create an overlap of consciousness.

Herein lies the problem with spot checks of homework. From one perspective, homework is to provide the student enough practice to learn mastery of a subject. But from another perspective, it's the teacher's only possible opportunity to create an overlap of consciousness with the student.

In college, it's possible (though still not likely) to query students well enough to understand where they went wrong, where you, the teacher or the book, misled them. In 5th, 7th, or even high school, it's practically impossible to get at this by querying, because the students will simply shut down. Unless you ask in the most gentle and subtle way possible, they will hear you asking "Why did you do that? why did you think that?" and hear CRITICISM. And that will be the end of you knowing what they think.

So the only way to create the overlap of consciousness if by a thorough investigation of their work, and a very problem-solving model in our minds. Why would a student make that mistake? What assumptions in their mind could have led them there? Is that consistent with other assumptions they are making, even on correct problems? How could what I said/left unsaid/assumed led to this?

You must do their homework with them, in your own mind. You must go through their homework from their perspective, and you won't do that in a 10 second spot check.

A spot check only allows you to see the mistakes---to see that correction is necessary. It doesn't provide fertile enough ground for you to figure out why they made those mistakes, or where they were misled. Reteaching isn't enough, either, because in all likelihood, you'll reteach them the same error, albeit unknowingly, or you'll just add layers of confusion onto the underlying error. Unless you can get to the point where you know why they made the mistake, where you can say "no, THIS IS NOT TRUE, I MISLED YOU" you really aren't fixing their problems.

Teachers must get creative to create an overlap of consciousness with their student. They must stop assuming they know what their students think, let alone why their students think the way they do. From there, they can build lessons that treat the source of confusion.