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Re: MLCS Webinar on April 24: Registration Open
Posted:
Apr 6, 2012 9:39 AM
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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
========================================
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> 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
> <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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