## Sunday, April 19, 2015

### All this playlet needs is a title. I'm thinking "No math skills and no calculator make Rosencrantz something something..."

Scene: A large examination hall.  Rows on rows of desks, each occupied by a student concentrating on an exam paper
A hand shoots up.

Rosencrantz Andor Guildenstern: Yes?

Panicky Pete: I don't have a calculator.

R/G: You probably don't really need one.

Cut to closeup of exam question.  We read

"If you have 100 rodents and 37 of them are hamsters, what proportion of your rodents are hamsters?"

PP: Is it OK if I write it as a fraction?

R/G: I'm sorry - what's the problem?

PP: I can't get the number - I don't have a calculator.

R/G: Errr...

PP: Is a fraction OK?

R/G: Ummm...

PP Looks anxiously at R/G

R/G [sadly]: Ok, yes, you can leave it as a fraction.

R/G walks away down the rows of desks slowly shaking his head and chuckling ruefully.  Camera pans slowly out until R/G is just a dot moving through a vast snowy landscape.

1. Our student handbook contains a general exam policy, which of course no student ever reads. However, the presence of such a policy liberates anyone proctoring an exam to respond cheerfully and without hesitation as below:

Panicky Pete: Is it OK if I write it as a fraction?

Proctor Hep: Just do your best.

PP: But . . . [exhibiting both righteous indignation and lip-quivering foreboding] I can't get the number -- I don't have a calculator.

PH: The question contains no typographical errors. Just do your best to answer it.

PP: But . . .

PH: That's all the help I can give you.

Camera cuts to view from front of room, over shoulder of Other Proctor. PH walks up aisle and joins OP. Dialog is whispered.

OP: What was the problem.

PH: No problem whatsoever. In a few days, you can probably read in my eval that Proctor Hep was unhelpful.

2. We here so appreciate you doing your own boldfacing and italicizing.

3. This strikes me as a close parallel to the problem I'm having with students and the construction of bibliography entries. I have no objection to the use of automatic citation generators, but students need to understand the basic principles of constructing bibliography entries, so they can check that an error or anomaly hasn't produced gobbledygook (which happens pretty frequently), and so that they can deal with situations that aren't quite covered by any of the standard formats (also a pretty common occurrence, especially when it comes to newer electronic formats). None of this should be hard; I'm pretty sure the year-long research project I produced in 5th grade had at least a rudimentary bibliography, constructed without the help of citation generators (or parents), and I know I was following models in the Warriner's and the Turabian handbooks by middle and high school, as were my classmates. I don't think any of us had difficulty with the concepts involved, though some of us brought more or less patience to the task.

But, even provided with very clearly laid-out examples from the online version of the Hacker handbook (which contains both multiple sample entries and bracketed explanations of each element of each entry), a significant number of my students seem completely flummoxed by constructing a bibliography entry. They've never done it by themselves, and they know it's important (and wrongly think that constructing an entry wrong could get them accused of plagiarism), and I think they just clutch.

And then there are others who look at the model, look at the information they have, and do something sensible and more or less correct, which is all I'm looking for. How to move students from the first group to the second, I'm not sure, but I don't think it's a matter of spending more time in class on constructing bibliography entries (which I really don't want to to do). It's more a matter of attitude, or knowing how to tackle an unfamiliar task, or (real) self-confidence, or something along those lines.

4. The question does sound confusing. The percentage is 37%. But what's the proportion? Saying that it is one third is inaccurate. It is more than that. But then, that's the kind of approximation one is using to estimate the "proportion". The student may be confused precisely because he knows that this is close enough to say one third, yes far enough from that to be penalized for the inaccuracy of such an approximation. Maybe it's really the percentage (37%) that he has to provide? Or is the proportion 0.37? What that is supposed to mean may have been clarified in the course, but it does sound confusing otherwise.

1. Not confusing at all. In my world, proportions are not limited to one significant digit. Therefore, 37% and 0.37 are acceptable responses, and I would probably (slightly grudgingly) accept 37/100 because I can imagine instances where 8/12 is no less correct than 2/3.

But FFS, someone who is confused by this question AND needs a calculator to resolve it should GTFO of college.

2. So basically, you just want the exact percentage. That's why it's confusing. Because a proportion is something like approximately one fifth, one third, one half, two thirds, three quarters, etc. The proportion here is slightly more than one third, but saying that would be deemed wrong.

3. Basically I want the proportion.

4. At first, I thought that the problem was completely clear. "Oh, he wants the proportion. The answer is 37/100." But then OPH said that they prefer 37% or 0.37 to 37/100, which I found greatly confusing.

A proportion (or more mathematically correctly, ratio*) is a comparison of two quantities by division. If one out of three ducks is white, then the ratio of white ducks to all ducks is 1:3 or 1/3. Or one could say that the proportion of ducks that is white is 1/3.

(*Side note: in mathematics, a proportion is technically a situation in which two ratios are equal, like 1/2 = 3/6; however, it seems like we're using "proportion" to mean "ratio" here, so let's just ignore that.)

Every time I've learned about ratios, or read about them in textbooks, or taught ratios, the definition is a comparison of two quantities by division. To me, 37/100 fits that definition much more precisely than 0.37 or 37%, as the two quantities being compared are 37 and 100. There are 37 hamsters for every 100 rodents, so the answer is 37:100 or 37/100. Of course, if the answer reduced, I would expect a simplified fraction. But whenever we deal with ratios, we generally use fractions.

So I think this problem is confusing in this instance, not because there should inherently be any ambiguity about what the answer is (it should be 37/100), but because the instructor expects the answer in a different form from what most logically fits the definition of ratio.

5. Oh, for CRYING OUT LOUD! The problem here ISN'T precision worthy of an actual mathematician. The problem is that this TWIT can't figure out that 37/100 = 0.37 = 37% without a calculator!

6. It seems to me from the context that definition 1 of "proportion" (in Oxford and M-W dictionaries) is the one being used. In many contexts, proportion, portion, fraction, and ratio could be used interchangably, but ratio does not carry as much of the connotation of "the size of one part in comparison to the whole", and is often used to compare the sizes of two or more of the whole's constituents.

7. Fer THE LOVE OF GOD read the original playlet - the student recognized that they needed to write the answer as a proportion (0.37); the problem arose not from "confusion" arising from how the question was worded (this word appears to have taken on mystical status, probably highlighted in student survival guides as a magic phrase that when uttered is supposed to wash away all sins and foibles in an academic setting), but because the student couldn't figure out how to "calculate" 37/100 as a proportion, and felt they needed a calculator to write the number as a proportion, not a fraction (which is what "37/100" is). The point of the playlet was to point out that a university-level student is a numerical moron who performs worse at math than my elementary school age children (and that's saying something, seeing as we get notes home from the teacher...), and its got NOTHING. TO. DO. WITH. THE. QUESTION. WORDING. It's got nothing to do with non-STEM either (RAOG, I haven't gotten the sense from your previous posts that you're a STEM prof); if you've got a functioning ATM, credit card, or phone and you can figure out how not to overdraw your account, go over your credit limit or exceed your monthly data usage, you've got the math skills to figure out 37/100 without a calculator. The kid's a tool. Stop making excuses for the kid.

8. I am not arguing that the student isn't a nitwit; that may or may not be true, and I don't care. What I'm arguing against is the notion that proportion = decimal and proportion ≠ fraction.

That is wrong. Just plain wrong. And if someone is teaching that to students, then they're bound to cause undue confusion.

First, please don't reference the dictionary when teaching mathematics, unless you teach out of the dictionary (in which case, Duck help your students). If you want to argue about math, it's important that you reference a math book. The reason is that mathematics has its own language, with words that have more specific meanings than they do in everyday English. For example, confusing "factors" and "terms," which have different and more precise mathematical meanings than they do in standard conversation, would cause many problems for a basic algebra student. Just like telling a maintenance worker that there was a shaky doohickey on the tall thing wouldn't really tell them that there's a loose rung on the ladder. We use precise language for a reason, at all levels of mathematics.

Second, if you open any basic algebra book (or at least, any one I've seen; I'm using Elementary Algebra by Tussy, 5th edition, for my reference), and go to the section on ratios and proportions, you'll see that the section is full of fractions, not decimals. It is common practice with ratios and proportions to deal with fractions, period. Why do we do this? Because when the total number of rodents isn't 100, the decimal answers get harder to work with mathematically.

Consider the problem where four rodents out of seven are hamsters. What is the proportion of rodents there? Clearly it's 4/7. That's a nice answer, and easy for the brain to digest. If one were to try to convert that to a decimal, they'd get 0.571428571428..., which is a lot harder to work with. If we had to take this number and then use it in other calculations, 4/7 is an exact answers, where 0.57 is an approximation (and trying to do math with a repeating decimal is just nasty).

It is common practice to use fractions when dealing with ratios and proportions. Therefore, I take issue with an instructor not wanting to accept that as an answer. That's why I'm commenting. That's all.

9. What I'm loving about this thread is listening to everyone argue about an exam question that is almost totally fictional. The only bit that's real is the student's inability to move a decimal point two places to the left. Everything else was just made up to illustrate the misery.*

Pace, Matthew - I'm perfectly willing to accept the fraction as an answer. As I said to Pete, "what's the problem?" Where students will likely stumble is if they have to figure out the probability of drawing a hamster on two successive draws from the rodent sample (with replacement to keep it simple), and they need to square the proportion. I do discourage them from using percentages to avoid the whole "50% squared equals 2500%" nonsense. I'd be perfectly happy for them to use fractions (in many of my test questions that's actually easier, but nope - they hate it). And ask them to square 4/7 and many of their heads explode.

* and perhaps to save time, I should add that my real name isn't Rosencrantz, Hamster Husbandry isn't really a thing, and Tuktoyaktuk has no university of any kind (honestly, I've never been there, but I'm sure it makes Oilmont seem like Cambridge, Mass).

10. I just looked it up, and I love the fact that there's an actual Tuktoyaktuk. I've always thought that it was a contrived place name.

11. R Andor G:

I'm old enough to remember when "Tuk U" sweatshirts were a popular item of apparel in my high school. That was around the time of PET's infamous "fuddle duddle" incident in Parliament. (You have to be a Canuck of a certain vintage to know about that or, for that matter, who PET was.)

12. As a 'Murican of slightly later vintage, I still know PET. Granted, my mother's side of the family is entirely Kanuckistani and I took a number of Canadian history courses in grad school just because I could.

Also, apparently "Tuk U" shirts are still available. Man, I love the internet.

13. Pat:

The shirts I remembered were more like:

http://photos1.blogger.com/blogger/5025/424/1600/tuktoyaktuk.png

14. Upon re-read, I see my perception of my own writing was primed by my flabbergast over the original situation, and I missed the chance to phrase things less ambiguously.

Me: ...37% and 0.37 are acceptable responses, and I would probably (slightly grudgingly) accept 37/100 because...

MM: OPH said that they prefer 37% or 0.37 to 37/100, which I found greatly confusing.

The only preference I meant to imply was that the student not feel the need to ask the question. What I was thinking -- which apparently did not translate into my actual words -- was that had it been a different student who wrote 37/100, I would have accepted it without hesitation. But in asking his quesion as he did, THIS student revealed two very troubling things: 1) he can't figure out 37/100 = 37% = 0.37 in his head, and 2) he doesn't know that 37/100 is a perfectly acceptable answer. Thus his writing 37/100 for lack of a calculator in this case does not satisfy me that he really understands the concept. He would get my slightly begrudged 'pass' anyway for getting it right, even if for potentially the wrong reason, because evidence of his absence of understanding does not transcend reasonable doubt.

The idea that arguments among academics are so bitter because the stakes are so low has been expressed as Sayre's Law, attributed to Woodrow Wilson and Henry Kissinger, and presaged by Samuel Johnson. One can't get much lower stakes than a nearly totally fictional exam question on the internet. All in good fun.

5. Monica, a proportion is not an approximation, nor is a proportion described as a fraction (one-third); the proportion is 0.37. A percentage is 37%. The question is not asking for the percentage. There should be no ambiguity in the answer. There is no confusion but in the mind of the student who is numerically illiterate. I get this exact same kind of grief from students who, I know for a fact, were having to hand-graph various convoluted sin and cos functions in their grade 12 calculus course one year ago, which was a requirement to get into this university program. But yet now they're giving me grief because they don't know the square root of 0.5, or don't know how to solve 12 divided by 48, without the help of a calculator. My kid in grade 5 can do more complicated division than this.
I think you're missing the point of OPH's post - if the student "needs a calculator" to 'solve' 37/100, as OPH stated, if they've got problems like these, they need to GTFO of a university-level science program.

1. ** sqrt of 0.25 ... (which is 0.5...)

2. I thought your example was perfectly fine, as sqrt(0.5) is 0.707, which is easy enough for even high schoolers to remember because it's sqrt(2)/2, and they should also remember sqrt(2)=1.414

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7. Jesu Christu Herrgott im Himmel, how helpless they are, how they whine, how needy-needy-needy they are, how they act like SUCH young children. Now you know why I always bring to exams 3-4 extra scientific calculators, cheap TI-30Xa and TI-30X IIS models, invariably lost by former students. I have strings tied and duct-taped to their backs: the other end of each string is looped, so I can quickly duct-tape them down to the front table as the students are getting into their assigned seats, so they won't be removed. I tell the students they may use these, but they’ll need to come down to the front table to use them. I make it a point to clear the memories between uses.

I also bring bags of dozens of extra pencils, 3-4 battery-powered electric and manual sharpeners, extra erasers, at least two extra STAPLERS and plenty of extra STAPLES (TWITCH! TWITCH!), and at least two white-board markers and a box of chalk, in case I need to write anything on the board for everyone to see. I make it a point not to bring extra Scantron forms: if students show up without them, I tell these students to go get Scantrons at the campus bookstore, it'll take only a few minutes. It’s also written on the front page of the exam, and will have been announced in class, multiple times.

I also bring a Canon Rebel 300 DSLR camera with a Canon EF-S 17-85mm f/4-5.6 IS zoom lens, on a neck strap. I make sure the date stamp is set (but then, it’s calibrated by any pictures it gets of the clock in the room), just in case I get another asshole with the temerity to argue that he wasn’t late even though all 100 other students were in their assigned seats and taking the exam. The zoom lens is useful: at 17mm it can get the whole classroom, whereas at 85mm it can get close-ups of the pair in the back of the room sitting so close together, I walk up and ask them, “Are you two DATING?” I am considering also bringing in a Canon 5D DSLR with a 15mm Canon fisheye lens and a 160-degree field of view, mounted on a tripod and with an intervalometer set to take a picture of the whole room automatically every 30 seconds.

Years of bitter experience have shown me the need to put together an “exam box” containing all these goodies, to be brought to every exam and ready in my lab immediately upstairs at a moment’s notice. Just about the only things I don’t usually bring to exams that I occasionally want are a chair, whip, and loaded pistol.

I have more than once told an engineer wanna-be that if they don't know how many radians are in a circle, they shouldn't be an engineer, because that level of INCOMPETENCE is DANGEROUS. After one went crying to the department Chair, even though I’m a bullet-proof, tenured full professor who’s served as Chair, I also put that one on the “formula list”: you know, the cheat sheet they won’t let you have on the GREs.

8. Since you are going through all this trouble, why don't you buy some Scantron forms as well? For someone who was not even allowed to introduce any papers into the exam room, having to actually buy a piece of paper (or cardboard) for an exam feels rather strange.

1. I don’t give out Scantrons for several reasons. One is that there’s a difference between giving and lending. Scantrons can only be used once per student per exam (although I once did have a fight with a fool who thought he could use the back of one, because he claimed one of his other proffies told him to: he cried, which led me to put yet another note about this in my syllabus, now 20 pages and counting). All the other items in my exam box for student use can and are to be returned to me, since I am lending them. Whenever anyone asks to "borrow a Kleenex," if I have one I say, "You may HAVE a Kleenex,” since I really don't want it back.

You might think that Scantrons don't cost much, but with multiple classes of 100 with 3 exams, labs, and some homework assignments that use Scantrons each semester, it comes to more than I care to pay for, on my faculty salary. Also, if I give out Scantrons, I’d be one of very few proffies who do, which will inevitably get me in trouble (as with the fool mentioned above who thought he could use the back of a Scantron in my class, because as he claimed some other proffie said it was OK in a different class.) Also, students who don’t bring Scantrons occur only about once per semester: it’s easier just to tell them to go to the bookstore, which is not far away.

Also, my students are allowed to introduce papers into the exam room. These are their formula lists.

I also trust that you know that all pieces of paper are not the same? If not, do you have change for five bucks?

2. Well, schools sometimes do supply customized versions of scantron forms, free of charge. They're called student evaluation forms.

When I was an undergrad, the school supplied blue books as well (probably partly to deter cheating, but it was a fancy private school that probably could have bought up the entire current blue-book supply of earth without making a dent in the endowment). I was a little surprised to learn that students have to buy their own in many places (in part because, yes, we weren't allowed to bring in our own papers, including blue books, unless the professor specifically allowed a "cheat sheet" of certain dimensions, format, etc.), but I think that's true more places than not. If it's part of the school culture, it works, and transfers catch on pretty quickly. We've got a vending machine in the student center that dispenses scantrons, blue books, and few-packs of sharpened #2s. Since the scantrons come in packages of 5 or 10, a student who has forgotten can usually borrow or buy one from a neighbor.

The problem with professors buying scantrons is that students will come to expect it. Of course, they'll also come to expect Frod (and perhaps other proffies) to have calculators, pencils, stapler/staples (twitch), etc., but we all have to weigh the various hassle factors, and make the best choice we can. Besides, whether or not students should have to buy supplies, professors definitely shouldn't; everything except calculators Frod mentions is available from the supply closet in most places -- or used to be, before budget cuts, and there are still a reasonable number of school-owned supplies floating around. Whether or not the supplies are available to adjuncts is yet another question, but that's all the more reason not to start a pattern of professors buying stuff for students to use. Adjuncts definitely shouldn't be spending their food stamp money on school supplies. I do like Frod's calculator solution, since it involves a certain hassle (and possible embarrassment) factor for the students, which may serve as a mild disincentive to forgetting again, while still solving the problem in a perfectly reasonable way. It also allows a proctor to forbid a student who has forgotten (or "forgotten") hir calculator from using a note-laden smartphone instead.

3. I was replying to Frenna. Frod and I were composing at the same time.

4. One other interesting tidbit: as far as I can tell, even in our newest, highest-tech classrooms, a good old-fashioned wall-mounted rotary pencil sharpener is still part of the standard equipment.

5. But why are you even using Scantrons instead of having students write, or check the appropriate boxes, directly on the printout containing the questions? Since each student gets a copy anyway, that wouldn't cost you extra. One would think that for all the tuition money paid by students or on their behalf, students deserve the basic courtesy of having you actually correct their exams.

6. There is a rotary pencil sharpener in the classroom I usually use too, but I’m not the only person who teaches in this classroom, which has classes in it every hour of the working day. This means that it's not so easy for me to check if this pencil sharpener works before the exam, with only 10 minutes between classes. If at the last minute this pencil sharpener turns out to be broken or otherwise inoperable, the children will whine and cry, so I bring my own. I do point out the pencil sharpener before starting an exam, however.

Likewise with staplers and staples (TWITCH!), and likewise with everything else needed, except Scantrons and well-prepared, intelligent minds. Both of those are the responsibility of the students, as I do my best to make clear.

Just to do the math for Monica, too: (\$0.20/Scantron)(3 exams that use a Scantron + at least 1 lab using a Scantron + at least 1 homework using a Scantron)(100 students/class)(at least 2 classes per semester) = (\$0.20)(5)(100)(2) = \$200/semester, at least. If \$0.20/Scantron is an underestimate, that's because it's been a while since I bought any.

7. "I was replying to Frenna."

Do you mean Monica? Frenna does not appear to have commented.

8. Frenna does not appear to have commented.

No, but her points were equally valid....

9. You guys just knew I was going to be mind blown by this post. I had no idea that at some schools, students have to provide their own scantrons. It makes sense, since these forms are so very expensive. I wonder when my schools will start making kiddos bring their own?

10. Apologies, Frenna. I did, indeed, mean Monica. Blame it on some combination of rhyming names, exhaustion from too much grading, and middle-aged brain.

9. I spotted you from the first post. BAM!

10. My department has a Scantron machine that takes only specific forms (882-E or 882-ES), which I repeatedly tell my students to bring (and which is printed on the exam and in the good, old syllabus). It can't take customizable forms, as you recommend.

I use this machine because I get 100 STUDENTS PER CLASS, more than once per semester. At 15 minutes to read each student’s essay, I’d need 50 hours to grade one exam. Jacques Barzun didn't like multiple choice either, but I rather doubt he ever had over 15 students per class, all of whom scored over 29 on the ACT. Frankly, I think he had all the courage of a non-combatant, although he did have an intriguing perspective on the decadence of the West. Fresno State ain't Columbia, but then we don't charge \$60k/year, either.

11. "One would think that for all the tuition money paid by students or on their behalf, students deserve the basic courtesy of having you actually correct their exams."

This is the kind of thing whose problems should be evident the moment it is expressed.

One would think that for all the taxes paid by all the taxpayers, the taxpayers deserve the basic courtesy of having the IRS actually calculate their taxes from wadded-up receipts delivered in shoeboxes.

One would think that for all the whatever they have had to do to get into college, students possess the basic smarts to actually bring a fucking scantron form to the exam.

Professionalism is one of the competencies tested on the exam, albeit indirectly.

1. When I do give them feedback on their essays, they whine, scream, cry, make excuses, act like either very young children or lawyers, and ignore the feedback entirely, since all they apparently see is the grade. No thanks.

2. And I'll bet that when they go skiing, they understand quite well that they can't get on the lift without having displayed a lift ticket, and that the lift operator is almost surely not responsible for issuing said ticket should they try to board without one, and that any whining about this state of affairs will not be received well by the ticket-holders in line behind them.

The Scantron form is their ticket to take the exam.

3. OPH I love the Scantron as an exam ticket!