kitchen table math, the sequel: two-fifths

## Wednesday, August 22, 2012

### two-fifths

re: oops

Here's the original image from Smarter Balanced Assessment Corporation:

And here is the Education Week adaptation of the original:

Presumably at least two people vetted this image: the person who created it and the editor who signed off on it.

Apparently neither one noticed that Figures A and C changed significantly from the first version to the second.

In the Smarter Balanced Assessment Corporation image, only Figure B. represents 2/5.

In the Ed Week image, A, B, and C all represent 2/5. (At least, Figure A. now looks as if it does to me.) As a result, the question Which model best represents 2/5? has become nonsensical.

I'm guessing this is a case of humanities-trained people -- people who 'don't use math' in real life -- knowing so little about fractions that they didn't 'see' the difference between the original image and the adaptation.

Allison said...

Yes, I'd surmise your reasoning is correct. Remember the op/ed arguing against algebra? In it, the author referred to "fermat's dilemma" as something he'd forgotten or never needed to know. Presumably an editor at NYT approved that, without catching that no one has ever called anything that, nor what format is famous for.

I guess it isn't surprising that someone can't tell the difference between 2/5 and 2/7 even if college educated.

Anonymous said...

"I guess it isn't surprising that someone can't tell the difference between 2/5 and 2/7..."

Well ...

5 = prime
7 = prime

therefore ...

5 = 7.

Right?

-Mark Roulo

kcab said...

Well, the person who signed off on it was probably misled by the change in c between the two versions in the original. That is, what is drawn for c in both figures in the Education Week article matches what is drawn for c in the second figure of the original.

powers math said...

Operations with powers. Multiplication and division of powers.
Power of product of some factors. Power of a quotient (fraction).
Raising of power to a power. Operations with roots. Arithmetical
root. Root of product of some factors.

Anonymous said...

Indeed, it must be a truly ignorant person who would mix descriptive text with the wrong illustrations. We should by all means hope such people don't prepare our test materials.

FedUpMom said...

To me, A looks like 2/5 in both the first and second versions.

Anybody else?

Independent George said...

To me, A looks like 2/5 in both the first and second versions.

You beat me to it. On questions like these, the drawings are not meant to be to scale - each rectangle is supposed to be the same size, meaning 'A' is just as much 2/5 as any of the other choices.

Allison said...

but remember, the original question was not "is this a model for two fifths?", it was which model best represents that fraction. so the ambiguity may have been intentional to distinguish it from the other model in B: b is unambiguous, and therefore better, than an ambiguous picture. you may not like the question, but it's plausible.

Anonymous said...

I looked at the link in the Smarter Balanced Assessment publication. I'll call the top figure in your post Figure 1 and the bottom Figure 2. Figure 2 from page five of the publication is described as the old-fashioned assessment where B is the right answer. Figure one is the new "deeper" assessment where the right answer is A yes, B no, C yes, D no. Partial Credit for YNNN, YYNN, YYYN. It makes no sense to me because without a ruler one is clearly led to estimate that B might be 2/5.