Teaching logic is always tricky.... Every semester, about this time, I begin teaching logical proofs. Every semester varying numbers of the class understand how to complete one and then move on to learn more of the rules of induction and substitution rules ----
and a few of them "don't get it".
This semester I've started doing practice quizzes with my evening class. The concept is simple -- they do one problem, complete it and I grade it when they turn it in. I tell them if they have made a mistake (but not what the mistake is or what it should be... because the others would hear...). They are pass/fail and they need to pass 3 of 4 of them to be exempt from the final exam.
The catch is that if they don't pass the first time, they can come back after break to correct their error and work on more problems. If they pass, they get to go home early. As a motivator to work earlier than they normally would, this seems to be working out!!!
Last night my Uber-Tutor led a small group practice problem session in the classroom and I took the two who 'don't get it' into the hall to work on the basics. This was a smart move on my part... UT had a few more people, but they all got the basic process and could make progress on their own, so she'd help them along but didn't have to start over from scratch teaching them how to do proofs.
I took the hard two for some one-on-one time.... which is something I haven't had the chance to do before. Both of them failed the quiz and had received that quiz back last night -- and they were motivated to learn. After spending over an hour working with them, I've come to some conclusions....
First of all, they aren't dumb. I've had students who were just unable to complete the course because they didn't have the cognitive ability. These two seem to be averageish students, clearly not the intellectual shining stars (they were at home watching NCIS), but not at all the ones who shouldn't be in college.
I also don't think they are really lazy -- or they wouldn't have stayed. I'm not so sure they've both really tried as hard as they can, but I also don't think they know how hard they can try. That is often something my course teaches students -- and it it surely is what taking logic taught me -- exactly how hard I could work my brain to accomplish something way outside my comfort zone. And --in many ways they are lucky to come across a class that does this for them now, rather than in grad school when it happened to me....
I do think they haven't really absorbed the techniques I've been discussing in class to overcome the learning challenges involved with doing proofs. I don't think they thought they needed to do these things until they failed a quiz. I'm sure they haven't actually tried to do those things -- as when I explained them again, they acted as if the techniques were new...
I think they are easily frustrated. These are students for whom frustration leads to quitting.... So, when they can't make progress on a problem, they stop working problems all together -- instead of moving to the next one to see what they end up with.
They also seem to be unwilling or wary of taking intellectual risks. So, they don't write down something they think could be wrong, even if it is correct... These are the same students who may have a creative thought for a paper and take the safe path instead. They may have something unusual or provocative to say in class and not say it.
I'm sure these students are typical of the students who 'don't get it'.
I hope they learned something from me last night -- because I'm sure I've learned something from and about them.