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A deep understanding of factor label, to me, is simply the
understanding that you are multiplying a quantity by the number 1,
somewhat disguised, and thus ending up with an equivalent quantity.
[At least that's one version of what one calls factor labeling;
dimensional analysis is another.] It's basic, but easily bypassed. In
HS chemistry, my friend and I used to joke about converting units
because we decidedly did *not* understand what we were doing. We made
up "problems" where you, for example, multiplied by (five kids)/(1
toy) and (three boys)/(five kids) and ended up with 3 boy/toys. That's
about as much sense as the process made for us. I do not recall the
teacher ever explaining the process as multiplying by the number 1.
Instead, he just did it on the board, really fast.
Bill
On Apr 18, 2011, at 5:56 PM, John Clement wrote:
I am not sure what is meant by deep
understanding of proportional reasoning.
John M. Clement
Houston, TX
a) Alas, some folks think the factor label method is a bad thing as
a matter of principle, because it allows students to solve certain
problems without necessarily having a deep understanding of
proportional reasoning and scaling laws.
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_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l