After the longest week ever and the most emotional, it's finally break time. And by break I mean that now I have time to catch up on my engineering curriculum, so that I have something to teach when I return in 2 weeks. But by break I also mean sleeping past 5am and not being stressed out and in a hurry all day long to make sure I do everything and do it well.

I made 3 finals up from (mostly) scratch, and I like some of the questions I came up with or adjusted from other sources. They also spawned ideas for future lessons.

algebra:

Let s=the amount of suger you ingest (in mg)

Let c=the number of cavities you have

the independent variable is ___________

the dependent variable is ____________

_____ is a function of _______

The correct function notation is s(c) or c(s) (circle one).

This got me to thinking that the next time I am at the first day of teaching functions, after we go through some like this, I'm going to have the students each come up with a scenario and work it through and then we'll share out. That way they'll spend more time processing the concept and figure out what it takes to be dependent and independent and how things relate to each other and what functions are.

In engineering, part of the test was on statistics, so one question I adjusted from something I found on line was:

In a certain neighborhood, the following are household incomes:

$40000, $46000,$54000, ... (and 4 more like this), then $250000000

Find the mean______

Find the median_____

Your engineering firm wants a good sense of the income level for marketing purposes. Which number better represents the neighborhood income and why?

The median came out as something like $51000, and the mean came out roughly $230000000. It was interesting to me that not everyone got it right. More discussion in class next time.

These types of questions use to frustrate me endlessly when I was in school. I understand mean and median. I understand the point the question is making. But, in the real world, there is no situation in which someone says "$x represents the neighborhood income" because that wording is ambiguous and wouldn't explain the relationship between that number and the broader dataset. If you were reporting this data, you would give the mean or median labeled as such, and possibly explain that other than one extreme outlier, everyone was within a small range.

ReplyDeleteIt used to drive me crazy knowing that I completely understood all the concepts involved but would probably get this question wrong because the person writing the test interpreted "represent" differently and anticipated a different context in which the data would be reported and used.

Just my two cents, though, as someone who apparently never really got past my frustration with these questions. :) I may need to find a math therapist to talk to...

I see your point about presupposing the answer. I actually took any answer if the students had a good reason for their choice. I guess in my mind, a company wants to know what the majority of the people are roughly making as a salary. If you use the large mean number in this case ($230000000), then you may set your price too high for your product, and then most people couldn't afford it. If you use the median ($51000) then your price might more aptly reflect what the majority of people can afford to spend.

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