Mr. Owens

This was recently on the math-learn list (you can go there to see the author’s name as I’m not sure if proper netiquette would have me include or exclude his name):

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. If you can get them to explore concrete situations where adding negative numbers is involved, they can in a sense be hit in the face with the fact that their answer does not predict the actual outcome. 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.

I don’t really know much about the author except that most of his posts make a lot of sense to me and he seems to really like the work of Shayer & Adey, Feuerstein, and Lawson. From what I gather some of their research is about teaching students how to think and/or reflect on their own teaching.

I know for myself that this one of the my biggest struggles. Trying to setup class in such a way that student errors are caught early, the student has a chance to figure out how/why they made a mistake, someone leads the student to the correct answer (directly or indirectly), and then the student has the chance to practice and have their work monitored over an extended period of time.  Meaning the next couple days or weeks.

If anyone has the answer as to how to do this with easily distracted middle school students … (actually maybe a set of clickers from Holt, Rhinehart, Winston or some similar technology that provides instant feedback and then break the students up into groups!!)