OK, I¹m kind of slow sometimes, I¹d rather admit it and learn something, so...
Why is the $0.16 irrelevant?
I got $132.16, using proportion and would have responded with that answer. I understand about significant figures, and if applied to this problem strictly speaking, would produce an answer of $130.
Of course I agree that electric bills are not proportional to usage because of the fixed costs, but given the question posed, I would have included the $0.16.
Regardless of what I missed above, I consider proportion to be a very powerful tool that we do not give our students in sufficient doses.
As I have noted in the past, my universe of discussion is my developmental students in an open-door institution. Many cannot compute area, nor solve ³you drive at 50 mph for two hours, how far have you gone², nor compute miles per gallon... But I can probably teach most to make a table which will allow them to solve a proverbial two-trains problem, which is what will be in the text. So they can do two trains, without a clue about what¹s going on, but still can¹t do one train. :-)
As for function, I wouldn¹t apply it to mpg, mph, electric bills as stated. But I would if the electric bill question had a fixed cost also. I think (I dare say I know) we don¹t give these students enough use of y = mx + b so it¹s truly useful, and can be applied in other contexts, like economics, for example or electric bills.
On 4/5/12 5:04 PM, "Ed Laughbaum" <email@example.com> wrote:
> Guy, > > The $0.16 is irrelevant. But then if I overcharged 1,000,000 customers by > $0.16 (or whatever it is based on usage). $0.16 becomes significant. The point > was that they couldn't solve a really simple problem. BTW: I failed to give > you a second data point in the original posting. Also, my point was that all > these highly trained people could only use what they had learned in middle > school. > > This discussion may not be worth the effort because no one knows what is the > proper approach or course or etc. > > Ed > ============================= > On 4/5/2012 4:09 PM, Guy Brandenburg wrote: >> >> Electric bills aren't necessarily exactly proportional to the kwh used. And >> does 16 cents really matter anyway? >> >> Guy >> >> >> On Apr 5, 2012, at 1:27 PM, Ed Laughbaum <firstname.lastname@example.org> >> wrote: >> ... >>> >>> Relative to this post, I have observed that I often see the mathematical >>> literacy proponents argue for proportional reasoning as a mainstay outcome. >>> This in turn, reminded me (recall through neural associations) of an >>> informal survey I took on several colleagues who were not in any of the STEM >>> fields but all had a bachelors degree through a PhD. In the following >>> "problem" everyone used proportional reasoning. >>> >>> If you use 1205 kWh of electricity and your bill is $130, how much is your >>> monthly bill if you use 1225 kWh? Everyone got $132.16 for the answer when >>> it is $132. >>> >>> What I wonder is, if focusing on proportional reasoning will solve this very >>> simple problem (of thinking relationships are proportional), or whether we >>> should be focusing on function. Or something else? Of course, my opinion is >>> on function, but it is an opinion.