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Re: [Phys-L] proportional reasoning, scaling laws, et cetera



That sort of thing just happened today. The sophs and juniors are taking algebra 2 and doing these complex matrices and problems with equations, but when I asked about some simple proportions of titrations in chemistry they couldn't do the simple algebra-one to calculate an unknown molarity. The math teacher is good, but they are only doing the examples from the book on that specific chapter. They do those well and can discuss it, but can't relate anything about demos or labs of titrations when it's not directly from a book. I asked one very bright student about the algebra 2 compared to the chemistry and he said he did the math work but didn't have any idea what it all meant. He "just did it" because the teacher had explained it in that context at the time. He had no clue how to figure out the simple proportion in the chemistry either because it was removed from math he had done in prior years in the same way they all do math... one chapter then another with specific examples in the chapter they are working on at the time. He can't transfer the math into the science. To him, math is one subject and science is another completely different thing and the one thing (the algebra) doesn't mean anything in the context of practical application in the science.

On May 16, 2012, at 7:04 PM, John Clement wrote:

Here is where looking at the research needs to be applied. Students often
have no trouble with questions like what happens when something doubles, but
the real test of proportional reasoning is when the two items are in an odd
ratio such as 2 to 3. Also when asking questions you need to supply
extraneous information with numbers. So you could put in that one car is
20% longer than the other but the masses are 2000kg and 3000kg.

There are also problem with understanding English language construction. My
favorite example there is the statement "A small car hits a parked moving
van. Which exerts the greater force on the other?". Students will ask "Is
the van parked or moving?" This reveals thay can't read English or
understand Newton's third law.

John M. Clement
Houston, TX


However the way these real world things are treated take
the problems way,
way from reality. The momentum of the bowling ball doubles
(how?); the
kinetic energy of the ball doubles (how?); the radius of
the track doubles
(how?); the rain immediately halves the
coefficient of friction (how?); the mass of the car doubles (how?).
All these "hows" are non-trivial. Certainly they all
convey to students the
message that the physics they are being taught and being
examined about
has little (nothing?) to do with the real world.

I agree that we could word the situations more carefully.
Instead of "the mass of the car doubles" we could say 2 cars,
one with twice the mass of the other, etc. Overall, the
student who is distracted by the "how" questions when we
speak of changes in the setup hasn't learned to discern
what's important and what is not in solving a problem. I was
discussing with a colleague the silliness that is seen on
final exams, and he was lamenting his students trying to find
a "use" for every number given in a problem.



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