Over the last four or five years, I've noticed that an increasing proportion of students demonstrate an increasingly difficult time understanding how conditionals work. To the point where a huge proportion of them now seem incapable of understanding sentences of the form "if P, then Q". They act as though it means the same thing as plain old "P and Q".
This causes problems. For one thing, it makes it hard for them to understand, in a general way, what in the hell is going on with things. It's as though they see the world as a series of fundamentally unconnected, independent occurrences. They see two facts sitting there by themselves, and it doesn't occur to them that they might have anything to do with each other—that they might be somehow connected. (And I find it very hard to believe that this accurately reflects how they see the world. It can't be that they don't see a connection between the drinking and the drunkenness, for example. They can't see the drunkenness as unconnected with the drinking. Can they? They can't.)
For another thing—and this is where the confusion really makes itself known—it causes problems when they try to explain how the philosophers we study defend arguments in which they employ conditional premises. Which is almost all of them. And it causes real trouble when they try to defend a conditional that comes up in the context of an argument in the form of modus tollens. In that case, they're trying to explain why some person thinks that "P and Q" is true, when they know that the very next thing is to explain why the same person thinks Q if false. They tie themselves into highly confused, contradictory knots.
Relatedly, students often find it hard to explain how to defend a premise when the student him- or herself believes that the premise is false. That is, they find it hard to explain why someone would think that P is true when they think (or maybe they even know) that P is false. I think this is closely related to the conditionals thing. They don't realize that you can use P even if you don't believe that P. Maybe there are interesting hypotheticals involving P; maybe Socrates believed that P; maybe reasonable people disagree about P. But they can't see it, or at least they act like they don't. If they believe that P is false, they find it impossible to consider what things would be like if it were true, or why someone else might disagree with them.
I think this is pretty strange. Right? I don't really remember when I learned that if/then sentences don't just mean that P is true and so is Q; that they assert some kind of connection between P and Q. But I think I don't remember because it's so obvious that this is what it means that I didn't find it noteworthy (or else it happened so long ago that I forgot about it). So, I guess the question is, how can these students be so oblivious to something that's at once so obvious and so crucial to understanding how the world works?