Given any topic, you (or students) basically fit into one of three categories.
- You really understand the idea (and can probably explain it so well to someone else that he or she now understands).
- You don’t understand the idea at all…because you don’t care to know (I don’t care about understanding how to hot-wire a car) or you have tried and just can’t quite get it (for me, this would be how to make really good ice cream, I don’t know how they do it, and I’ve tried).
- The last category is the most dangerous to be in…You think you know, but, in fact, you don’t know at all.
The third category is dangerous because you won’t actually know that you are in that category until you are tested in some way. For our students, this is probably too late. Because for the most part, the next opportunity (if they have another opportunity) for them to prove that they understand, is a final.
This is also a scary place to be in as a person in general. For example, what if I thought I really did know how to pilot a plane, or swim, or something else that may cause me to get hurt.
But, when I say dangerous, I don’t mean that students are in danger, I more mean it is a bad place to be because of the consequences of thinking they know, when in fact they really don’t. They will not ask a question…why would they? They already understand. Or learn what they are doing wrong, so then they can do it right…again, because they are already doing it right, they wouldn’t look to learn what they are doing wrong…deceptive, isn’t it?
It is more likely for someone to move from the second category (where they know they don’t know) to the first category (where they really know) than it is for someone to move out of the “dangerous” category. If you didn’t know how to do something, like make a chocolate cake, you could learn how by looking up a recipe, watching a cooking show, watch someone else,…there are so many options. Once you learned, you move from the second category up to the first.
One of my greatest fears is that I am (for some areas and topics) living in the “dangerous” category without even knowing. Maybe my pride, or something. I guess one of the ways I try to do a self check is by learning more (about whatever), and admitting when I really don’t know (again, dumb pride).
What are you doing to make sure you are not in the dangerous category? In terms of teaching? Or anything for that matter?
Math M Addicts 