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RE: MLCS Webinar on April 24: Registration Open
Posted:
Apr 9, 2012 8:55 PM
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usage charge functions are usually step functions, actually. They round up to the nearest full unit.
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From: owner-mathedcc@mathforum.org on behalf of Ed Laughbaum
Sent: Fri 4/6/2012 6:39 AM
To: Philip Mahler
Cc: mathedcc
Subject: Re: MLCS Webinar on April 24: Registration Open
Hi Phil.
The extra $0.16 was the outcome of the apparently sum total mathematical knowledge of college graduates -- all relationships are proportional. It is just like with developmental students coming straight from HS, who think everything relationship is linear and then after passage of time think all relationships are proportional. Yes, I have generalized when I probably should not have done so.
Sure, I do exaggerate to make a point. As several posters have mentioned, the usage-charge relationship is not a proportional relationship, but rather a linear function. So my point was that the method for solving the problem was more important than the answer. But of course, the answer told me how they solved the problem.
Best Regards,
Ed
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On 4/6/2012 7:01 AM, Philip Mahler wrote:
OK, I'm kind of slow sometimes, I'd 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 "you drive at 50 mph for two hours, how far have you gone", 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 what's going on, but still can't do one train. :-)
As for function, I wouldn't 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 don't give these students enough use of y = mx + b so it's truly useful, and can be applied in other contexts, like economics, for example - or electric bills.
Phil
On 4/5/12 5:04 PM, "Ed Laughbaum" <elaughba@math.ohio-state.edu> <mailto:elaughba@math.ohio-state.edu> 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
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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 <elaughba@math.ohio-state.edu> <mailto:elaughba@math.ohio-state.edu> 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.
--
Edward Laughbaum www.math.osu.edu/~laughbaum.6/
The Ohio State University
231 West 18th Avenue
Columbus, OH 43210
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