On the door of her office, Alison Campbell has a sign that says "the biggest factor in learning is what the learner already knows". Or something like that. In other words, students build upon an existing foundation when they make sense of the world. This can be very helpful, or very unhelpful, depending on whether that foundation is correctly laid. One of the roles of a teacher (I would say one of the hardest roles of a teacher) is to identify where there are cracks in those foundations before the student starts building too much upon it. If that doesn't happen, the student is likely to run into something that just doesn't fit with what he or she already knows, or thinks she already knows, and it's going to cause them problems.
It's not what you don't know that hurts you, it's what you know that ain't so
as the saying goes. (I haven't been able to track down the origin of this quote - some attribute it to Mark Twain but I think others disagree. Can anyone help?)
I ran into an example of this while marking some third year assignments this week. Students were tackling a problem in which a mechanism was rotating. Now, to the large majority of the class, it is clearly evident that something of mass m moving in a circle of radius r at speed v has a force on it of m times v squared divided by r. They did it till they were sick of it at school, and it has stuck. The problem is, that they are WRONG. What!, you cry, but that's correct isn't it? F=mv2/r for circular motion. Yes, but ONLY when the speed v is CONSTANT. If it isn't, there's another term to consider.
Now, the interesting thing from my point of view is that I though that the students were over this misconception. I'd talked about it in class, and even done a couple of formative multiple choice questions with them in lecture time that showed me (so I thought) that they appreciated this subtlety. But, when the pressure was on with an assignment, a great many students abandoned what we'd talked about in class and reverted back to what they perceived as their foundation knowledge.
So what went wrong with my formative assessment? Did it come too early after the discussions on the subject? Were my multiple choice questions just poorly written. I need to go back and have a rethink on this. At least I've identified that a problem still remains, via the assignment, which is a good thing as it gives some time to talk about the issue again before the exam (and before the students leave and try applying F=mv2/r inappropriately in the design of some safety-critical piece of machinery.)