07-07-2012, 10:32 PM
(This post was last modified: 07-08-2012, 11:59 AM by MongoJerry.)
It's amazing how difficult these kinds of unit conversion problems can be for many people. I taught an Introduction to Astronomy laboratory course where as a project we built a scale model of the solar system to fit inside the large grass quad in the middle of the campus. One of the first concepts I had to go over was metric unit conversions, and I always started off by using money as a starting point. It was amazing to me how many people could convert dollars into cents and back in seconds and yet couldn't convert meters into centimeters or back, even though it was the exact same problem. There's such a disconnect at the stage where you take a problem that you can solve and then abstract it to a general case.
There's also the ability to estimate or check for "reasonableness" that eluded so many of my students. For example, in the same project where we were trying to scale the solar system down to fit inside the campus's quad, a student might after some multiplications find that a model planet should be 10,000 km away from our model Sun and think they were done with the problem. This would be after we had already talked about a km being about 6/10ths of a mile and about the length of the entire campus.
There's also the ability to estimate or check for "reasonableness" that eluded so many of my students. For example, in the same project where we were trying to scale the solar system down to fit inside the campus's quad, a student might after some multiplications find that a model planet should be 10,000 km away from our model Sun and think they were done with the problem. This would be after we had already talked about a km being about 6/10ths of a mile and about the length of the entire campus.