John Clement on student misconceptions:
When students have a misconception, it can be deeply rooted, so that telling them or grading them has no effect. Remember that once brain connections are established they do not go away or unconnect. So it is not a matter of just refusal, but rather often a misconception.
The students have to buy into the ideas by discussing it. Written answers explaining why and how you do things can also be useful…
Experiencing a physical situation involving the math is a much more
powerful stimulus than just being graded with a red pencil.
But when doing physical examples, the students must always predict the
answer before it is revealed by the experiment or demonstration.
Otherwise they can not be faced with the fact that their thought
process is not in line with reality.
Getting students to use a method is really a matter of convincing them
that it works better than an alternative. So they have to be put into
situations repeatedly where the wrong result is predicted by the
method they are currently using. But again, grading is usually a poor
reward for motivation. It is more effective if it is instantaneous,
and extremely ineffective when delayed. When students get their papers
back the next day they do not reflect on that they were thinking about
to get the wrong answer, but rather on what is the right answer. The
result is that the wrong method often lies dormant and is not affected
by the grade.
One technique that has been shown to be effective is having students
vote on answers, and then if enough get it right discuss the problem and convince each other. Notice that it provides immediate feedback.