True. At worst, unfairly inadequately taught. Predictable real-world complications can and should be taught, but are often not.
Some can make the leap beyond what’s minimalistically taught in lowest-common-denominator education and what real life requires. I wish the others didn’t have to.
Okay. I think I’ve said what I have to say on the subject.
Yeah, I agree.
I coach math team at our school, and even a lot of kids who are very bright and very good at math get tripped up by this kind of thing. Now, we do talk about it in practice, and by the end of the year I would expect that they would be able to do a problem like this without messing it up.
But how many kids in a typical school do math team? Probably… less than 4 percent 
While I wouldn’t exactly call this literacy in the way I usually think of the word, I do think that being able to catch and do unit conversions is actually an extremely useful skill in real life and one that is broadly useful, not just as an “asshole trick.” It’s true though that there haven’t been that many times in my life (not counting my job, where I do have to do this kind of thing on a fairly regular basis) that I’ve had to convert areas or volumes instead of linear quantities (and that’s mostly been for fun, like doing an order of magnitude calculation with my kids).
FWIW, I agree with (what I understand to be) your premise: the problem as presented isn’t very representative of mathematical literacy, given the state of mathematical education.
I think the only serious answer to that objection is that a basic pre-college education is clearly not enough to teach a functional level of real-life mathematical problem-solving skill. Probably why specific examples of problem-solving tend to fall to professionals. Like building tradespeople become skilled in length, area, and volume calculations, including unit conversion hitches.
It’s not even that, and that isn’t my premise. It’s that genres have genre expectations. This question violates genre expectations. It’s not an actual real-world situation: in the real world, most folks would solve this problem a different way (e.g., “Hey, carpet installer, what’s it gonna cost to carpet my living room?”)
If the question began by saying something like, “HEY THIS IS A DELIBERATELY TRICKY PROBLEM SO DON’T LET YOURSELF FALL FOR A DUMB TRICK,” then it’d set different genre expectations and would be a more valid test of folks’ ability to read for such situations.
The fact that mathematical teaching has degraded to the point that people expect it to be constrained to “genres” is a clear sign of its inadequacy.
I trust you’re an experienced math teacher, to say such things? Because I am a National Board Certified math teacher who teaches gifted math and who has worked with this sort of issue for many, many years.
If you don’t understand what a literary genre is, I’d be happy to help you.
I understand genres in principle.
I don’t think it applies in this context.
I’ve never understood why ‘word problems’ are so difficult for elementary students when they are made incredibly easy to work out in most cases. They would rarely rely on conversion of feet to yards unless part of a lesson converting units of measure.
That raises the question of whether this is a symptom or a cause. Do people fail at these problems because of innate limitations of their minds or from a lack of instruction and practice? We also have to consider the basis behind the structure of basic education. I don’t know how well students are instructed in reducing prosaically stated problems to well defined technical expressions at any level of education.
As a person that’s been teaching math for sixteen years and has studied how children learn, I disagree.
I see what you did there!!!
… and yes i do ignore the “~” … just you know what kind of person i am
Eh, as for the genre thing, I think by being a problem that some rando is saying will test “literacy” and even more so with the proviso that only 4% got it right (to be fair, the original people given the problem probably didn’t know that), it automatically triggers the genre expectation that there could be something about it that’s not the most extremely straighforward calculation possible. I know I was on guard just given the statement in the OP, and my middle schooler would be all over that too, even without the 4% remark. (Middle schooler, however, has been on math team for a while now, so she has a much stronger and more detailed grasp of genre expectations with regards to math problems than most kids. My other child, who is younger and hasn’t done math team, would not have those genre expectations triggered.)
But also! I feel that it’s wrong to say that a unit conversion is a “dumb trick.” (As opposed to, hey, be careful reading the problem!) If all kids got out of high school able to do this kind of unit conversion easily but not knowing a lick about factoring polynomials, I’d be much happier about the state of the world. That being said, it was chemistry and physics, not math, where I was taught about why unit conversions were important and why you should ALWAYS ALWAYS check for units! (But I think it should have been math and I should have gotten this knowledge before late high school!)
Wait, were my parents the only ones who would estimate the calculation on the side so that they knew they weren’t getting super overcharged by the carpet installer?
Exactly.
“Somebody else can do it” is not the answer.
The problem doesn’t ask for an estimate.
Which is kind of my point. We got the problem with that proviso, which told us to expect genre violations. It’d be impossible for folks to get that information during the study. I don’t see any sign that they were told to expect that.
Next week I’m going to give my students this problem, stolen from the Internet:
EVALUATE THIS EXPRESSION: 230 - 220 ÷ 2
THE ANSWER IS 5!
It’s a deliberate trick–but I’ll guide them through the trick, reminding them that I’d taught them factorials the previous week. Without that guidance, it’s not a fair test of mathematical abilities; it’s a riddle, a trick.
More nuanced – those who believe they can become good at almost anything if they work at it hard enough, and people who believe that if they aren’t already talented in that direction, it’s no use trying.
The truth is not as obvious as it looks.
Is your contention that if it did ask for an estimate, that it would be the genre of “hey, this is a bit more like real life” problem and then it would make more sense to check units? That’s… I don’t really get that, I guess.
Your 5! problem, I feel, is qualitatively different from “this problem has two sets of units in it.” There are lots of real-world applications, lots of applications in other academic subjects (see also my remark about physics and chemistry), and lots of jobs including my own, where you regularly need to deal with (at least) two sets of units and always be aware that you can’t assume what the underlying units are. Whereas I have never had a real-life problem that involves a trick with factorials, and when I’ve had problems with factorials in math contests, the nature of the factorial was made very clear in the problem itself.
The point of difference seems to me to be that you seem to think that using two different sets of units is a “gotcha,” while I think it’s… how things work in the world. I’ll also note that the OP didn’t say that it was testing mathematical abilities, it said it was testing “literacy.” I don’t think literacy is the right word either, but if we had another word for it – comprehension? competence? – I do think that it’s reasonable that someone’s definition of full comprehension of “explain what’s really going on here in a given situation” might include comprehending different units.
Someone commented this might say everything one needs to know about Great Courses. I couldn’t say, not having been exposed to very many.
The book The Neuroscience of Intelligence is actually excellent and summarizes difficult research in a complex area using unusually clear language. This single example is not a big part of the book or its thesis but stuck out for seeming unlikely to me, even if actually true.
People understand height in inches is not the same as in feet and this sort of thing may catch some people unawares but does not seem unfair, impractical or a new exposure. Many people must have done problems of equivalent or greater complexity many times, more so if they have taken even basic chemistry or physics.
Of course, in Canada we use metric with ample exposure to American units and so might (or might not) have a small advantage here. I didn’t look at the original problem but don’t think it involved metric. As for whether literacy means scientific literacy, it seems a pretty inclusive definition, not how I would personally use the term.
I think y’all are overlooking something very basic.
A square yard does not equal three square feet.
Unless you actually work with something that involves areas, that’s extremely easy to overlook…
