average…

Posted on July 1, 2011

1


So, there’s been more commentary about the khan academy… I was compelled to add my own, to wit:

I just started looking at the video for figuring out averages, since I have a student looking for resources to review that.
It starts out with a black screen and a guy doin’ the lecture thing… I’m thinking “okay, this is new and different?” Then he’s telling me that hey, I might use the word average non-mathematically, saying “the average voter wants…” or “the average student would like to leave early.” He doesn’t go into what the words mean there, perhaps because he really should have said “typical,” not average… that meaning has nothing to do with the concept of “average.” (Do “C” students want to leave early? And the “A” and “F” students don’t?)
How does he explain what average means?
He doesn’t.
He does mention once, in passing, that the average is “between those numbers.” (Not between the highest and the lowest, just ‘between the numbers,” even though it’s *not* between most of the pairs of numbers.)The numbers he chooses are four small numbers and a much bigger “outlier,” and they’re just stuck out there. There is no context whatsoever. Then he says that we can “kind of” use 7.25 to *represent* that set of numbers.
Huh?
What does that mean?
Next (without review or practice or scaffolding), he presents what he calls a harder problem — you’ve got four test scores, you figured out the average, now what do you have to do get to have a higher average (get that A)? IN his explanation he says “you know that that the sum of the first four scores is 4 x 84″ — I do? And just how do I know that?
He demonstrates it — by multiplying. He could have said “the sum of the first four scores is 336 — because you just added them!” … or, perhaps, given that missing explanation of what average means, but instead he says “You sum up the first four exams here” pointing at… multiplication. He assumes that I will understand that if the average of four numbers is 83, then the four of them will add up to 83 x 4. Since I’ve just done one whole lesson in averages, I think that is expecting a lot. I *know* that a good number of students who are already confused and frustrated with math will simply consider this One More Time when we’re changing rules and definitions.

Then, he figures out what the missing test score has to be by solving for x by doing algebra with fractions, and multiplying by five… I’m afraid my students haven’t gotten there yet.

I hear all kinds of *talk* about the value of math that means something — but theory and practice seem to be worlds apart. Lip service to “they need to know the concepts!” when it really boils down to “if you can’t figure it out yourself, you’re not good enough.”

I hear people saying they lurrrv Khan Academy — oh, and they’ve got graduate degrees. If you’re already imbued with academic culture and just need to review the procedure again, perhaps you’ll love this. Learn math? I don’t see how.
 

(*… so I went to http://www.virtualnerd.com/algebra-2/probability-statistics/average-definition.php to see what the virtual nerds had to say about it.

She didn’t mangle terms — but do I have any idea why I’d want to know what an average is?    No, it’s all “elements” and n sub this and n sub that.  Welp, don’t criticize others if you can’t do better, right? I’m going to try, this 2012.

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Posted in: math, numeracy, rant