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Re: [Phys-L] effective teaching of scaling/ratio use




Remember the Anna Karenina principle: Every successful
student understands the material more-or-less the same,
whereas each unsuccessful student is confused in his own way.
Not true. Everyone makes their own understanding, and successful students
do the same. So success does NOT indicate each student understands in the
same way. So both types of students have different ways of understanding.
Many successful students have actually learned to play the game, without
understanding. Teachers are actually easily fooled, and I include all of us
in that.


If a student can't handle proportional reasoning, in all
likelihood there isn't a problem with the proportionality;
there's a problem with the reasoning. Directly teaching
"ratios" per se is generally a waste of time. For further
discussion, see below.
Yes. Students have been taught ratios, but they don't recognize when things
are proportional. They don't use proportional reasoning. So they have to
begin to realize that their methods of reasoning are insufficient and they
have to begin to try to recognize when this is happening. That is what
"Thinking Science" does. It motivates the use of proportional reasoning.

As to teaching dimensional analysis, that is only helpful when students are
at higher levels of thinking. If they don't have proportional reasoning,
they don't understand algebra, and they can't understand that dimensional
analysis is actually a form of algebra. So proportional reasoning is the
vital component needed.

There has been research that shows that students who are forced to do
certain things such as dimensional analysis in a class tend not to do it
spontaneously outside of the class. If students can be put into a situation
where they see the answer is wrong, and dimensional analysis gives
information about how to get it right, then they will tend to use it.
Essentially things like this need to be motivated first, and then formal
teaching can be used to help the students.

John M. Clement
Houston, TX