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Cliff Mass of the University of Washington surveyed his Atmospheric Science 101 class at the University of Washington and found the following:
Consider these embarrassing statistics from the exam: The overall grade was 58%
43% did not know the formula for the area of a circle
86% could not do a simple algebra problem (problem 4b)
75% could not do a simple scientific notation problem (1e)
52% could not deal with a negative exponent (2 to the -2)
43% could not do simple long division problem with no remainder!
47% did not know what a cosine was.
Shocking does not begin to describe it. I recommend everyone go over the Seattle's "Where's the Math" website and take a look at the great stuff they've accumulated there as they have been involved in the lawsuit.
Cliff Mass: full post
Cliff Mass: the test (pdf file)
with answers (pdf file)
I'm taking the test now.
Unfortunately, I find I have forgotten what a rational exponent means - and I didn't manage to figure it out just by mulling it over briefly. Which is annoying.
update
I got everything right, and I believe I would have figured out the meaning of a rational exponent if I'd thought about it instead of Googling it.
The reason I got everything right is Saxon Math. I've worked my way through Saxon Math 6/5, 8/7, Algebra 1, and most of Algebra 2.
did they not know the formula for the area of a circle, or did they not know how to use the formula for the area of the circle?
ReplyDeleteI mean, I actually used their website for my atmosphere and weather class at UVA so they must have a decent department.
I mean, I suspect that there was a pi*r^2 somewhere in the formula for some parameter of a cyclonic (or anticyclonic) system and they just simply had not mastered it.
Not being able to do an algebra problem would be more like being unable to translate a word problem (now using scientific concepts) into algebra.
Worrying, but not like utterly shocking.
Well, I now have proof that I will need to outsource teaching my DD anything beyond simple algebra. I vaguely remembered something about "soh cah toa" but for the life of me couldn't think of what the phrase actually *meant*.
ReplyDeleteI also made a really boneheaded mistake on 1(c) and divided by 2 rather than taking the square root. As soon as I saw the answer, I felt like a complete idiot.
In my defense, I'm 15 years out of high school vs. 1-3 years out like the students in the class.
For a university class that has the word "science" in it, frankly this is beyond shocking. I'll give this quiz to my 8th grader and see how she does. She won't know the cos(alpha) but everything else she's been exposed to. Since she's doing geometry this year she may be a little rusty on the algebra stuff. I'll report back.
ReplyDeleteAs a person who re-taught herself scientific notation, I can tell you that that is a topic that has to be taught explicitly and practiced.
ReplyDeleteIt's the Wayne Wickelgren issue, I think: "it all looks the same." (Wickelgren, who was a cognitive scientist, talked about this as a problem for students trying to memorize math facts.)
Just doing practice problems with scientific notation is enormously helpful to understanding place value & percent.
Take it from me --- !
btw, one thing kids absolutely need to be taught: how to figure things out when you can't remember how to do something.
ReplyDeleteI hadn't used negative exponents for quite awhile, and I was able to figure out the principles by fooling around with simple cases.
ALL kids need to know how to do this - but I don't think people teach them.
I used to bug C. about it -- will have to bug him again for PSAT prep.
Speaking of figuring things out, I've changed my mind: I wasn't going to figure out the meaning of a rational exponent left to my own devices.
ReplyDeleteSpeaking of which, why does anyone ever teach the formula for circumference of a circle as 2piR? Doesn't that only serve to confuse it with the area formula, when C=piD would work just as well and be a more unique and concise mnemonic?
ReplyDeleteprolly because the area formula uses radius...
ReplyDeleteit's a little easier putting everything in terms of r.
When you integrate 2pi*r dr you get pi*r^2. Again with respect to r and you get 1/4 of a volume of a sphere...