Alternative Conceptions

One of the basic facts of science and mathematical education is that you have to deal with Alternative Conceptions in your students.
Basically humans are very good at finding patterns in the world, but we're very reluctant to give up on discovered patterns, even with plenty of evidence that they don't work. We also have a weird tendency to only seek evidence that confirms our theory, and discount or dismiss evidence that rules our theory out.
The following link lists a series of common Alternative Conceptions.


The only way that you can correct these are through the use of negative examples (examples that show a particular idea just doesn't work), compelling presentation of alternative explanations (demonstration and experimentation) and relentless checking of student understanding (quizes and assessment).

You have to do this a lot. In my experience, to guarantee the supplantation of an alternative conception in a class of High School students typically requires exposure to ten different negative examples, for each exposure the students have had to a positive example (Even if the different positive exposures are of the same example). And if a student hits that positive example again, there's a chance they'll revert. *sigh*