# Misapplied math

North Carolina football fans objected to a math question that asked seventh graders to calculate the average gain for a team on the game’s first six plays.

The team opened with a 6-yard loss, a 3-yard gain and a 2-yard loss, which would have made it fourth down with 15 yards to go for a first down. The team’s fourth play was just a 7-yard gain, yet it maintained possession for a 12-yard gain and a 4-yard gain on two additional plays.

. . . Mildred Bazemore, chief of the state Department of Public Instruction’s test development section, said the question makes sense mathematically and was reviewed thoroughly.

“It has nothing to do with football,” Bazemore said. “It has to do with the mathematical concepts that you’re studying.”

Just throw in a 15-yard penalty for stupidity and it all works out.

Via Best of the Web.

This won’t fly in Texas.

2. alison says:

I’m not even sure the question is fair. It would probably be confusing to students who didn’t know that ten yards are required in the first place, even with the throw away first sentence. It’s a poorly written question even without the mistake.

3. Sigivald says:

Is this question confusing if you know football, then?

And is there some reason they can’t just ask students to compute the average of -6, 3, -2, 7, 12, and 4?

4. John from OK says:

What is so confusing about North Carolina netting minus 5 yards on their first three plays? Happens all the time.

5. Ivory says:

So is this gender biased because it would confuse the boys who know that you need 10 yards to continue playing? Or is it gender bias because it talks about football (which presumably women know *nothing* about)?

This reminds me of a time one of my fellow instructors was criticized for using the analogy of knitting to explain how proteins are put together. She was accused of being sexist and excluding the men in the class who would have not experience with that craft and would not be able to “emotionally relate” to the analogy. Education is fun.

6. Chris says:

tempest in a teapot … or furor in a football

nothing says that these six plays were in the same set of downs for example, if the team missed their 4th down conversion, then the other team might have had the ball

Alternatively, play 3 or 4 might have resulted in a fumble, or may have been a penalty which reset the down count … or a penalty after a play which resulted the first down being awarded. (but not the offense getting credit)

it might have been a scrimmage where the offense got the ball back again

it might have been the A and B team playing each other (or even against a common defense)

the creative mind reels with possibilities (not unlike reading the old Encyclopoedia Brown books to construct a counter argument “what if those glasses he put down were reading glasses, and bing farsighted, the accused really COULD see the culprit fleeing:) A great chance to exercise a football group to construct all of the ways that this is still possible.

sounds like someone searching for a reason not to do the math. (and in doing so, actually did even more math)

7. markm says:

Ivory: I doubt very many of the girls know how to knit, either. OTOH, it’s unlikely that this analogy relied on anything that you would have to know the difference between knitting, macrame, and weaving to understand.

However, I’m having trouble thinking of any valid analogy between knitting and protein formation. Proteins are formed by chemically linking subunits (amino acids) together in a long chain, after which the chain folds itself into shape under the control of attractive and repulsive forces between the side branches of various amino acids. It doesn’t keep getting poked through holes in the already assembled material to form a knotted-together network like a knit sweater.

8. markm says:

As Sigivald said, they could have just asked for an average of a set of signed numbers. But someone had to make a story problem out of it. When you write a story problem, it’s no longer just mathematical; it’s now in a real-world domain, where there are limits on the numbers possible or allowed. Violate those limits, and it’s not a valid problem. Assuming that your students will be ignorant of the limits is no good – it penalizes those most knowledgeable.

9. Ivory says:

Chris: In truth I’m not sure how the knitting analogy was used – only that it was criticized. But several things come to mind.

The first is that the nascent protein chain is moved from site to site in the ribosome much the same way stitches are moved from needle to needle during knitting. If you imagine the mRNA as the first “row” of stitches, the second row or amino acid chain is built based on the first row and then transferred out of the reaction site.

Second, the hydrogen and disulfide bonds that hold various structures (beta sheets and alpha helices) look like interlocking or woven threads holding a fabric together. Without them, the whole thing unravels. (Thus salt can be used to denature proteins because it disrupts hydrogen bonds.)

Third (and this is a stretch), proteins are sometimes chaperoned into the correct conformation by other proteins in the cell – this process can be like cabling where a third needle is used to change the proximity of stitches in a knitted fabric while the rest of it is woven together. Chaperone proteins act to twist the protein chain back on itself and portions of the chain that would not usually interact spontaneously are allowed to bond. This process is crucial in maintaining correct protein confirmation. When proteins from eukaryotes are produced in prokaryotic cells the correct chaperones are not present and the proteins can end up mangled, smooshed and inactive even though the amino acid sequence is correct.

Yes, I’m a science nerd and yes, I knit. While I don’t think I’d use any of these analogies without a model to show the class I think talking about knitting is not “sexist” or “gender discrimination”.

10. elfcharm says:

go ivory!!!
Granted, I didn’t understand most of what you said…
but it was entertaining.

11. mollo says:

My initial thought is to solve the problem by focusing only on the gains and ignoring the losses, since it’s questioning the gains. I would have taken the average of 3, 7, 12, and 4 and divided it by 4 plays.

Or, just to tick the teacher off, I would add 0, 3, 0, 7, 12, & 4 and divide it by six plays because and net loss means gain=0.