### The Modern-Day Math Test, or, How I Became a Curmudgeon

(Or, *Wherein the Author Learns Who Subscribes to the RSS Feed*.)

The other day, against my better judgement, I took on some contract textbook writing work with a company based in India. The main reason, I confess, is so that I can tell my friends that *India* is outsourcing work to *me*, something that I’ll also be sure to mention on my résumé when I inevitably overstay my welcome at my current place of employment. The bad news is that the textbook company produces books for use in the United States, which means that I get paid in American dollars, not rupees. Alas. But here’s the general procedure: someone from an American school board sends specs to the Indian company, which hires an American to write an outline for a text, which then gets sent to a Canadian (me) to turn into multiple choice questions. India the goes over the questions, and sends them to someone else (an American?) to review and revise. This seems to me like an awful lot of trouble to go to to produce (what appears to me to be) a text that is essentially indistinguishable from every other text in use in the public school system, but I don’t make the rules: I just get paid to follow them.

Fortunately, the Indian textbook company is not in any way affiliated with the body that produces and markets fucking graphing calculators. However, no company that mass-produces textbooks for use American public schools can remain solvent without permitting the use of some sort of scientific calculator at the high school level, which makes questions such as

5. Which of the following is equivalent to sqrt(50)-sqrt(8)?

a. …

b. …

c. …

d. …

several orders of magnitude stupider than their non-multiple choice equivalents.

You see the problem.

Calculator use aside: in coming up with the incorrect multiple-choice options, I am finding myself borrowing liberally from some of my earlier work in the field. Needless to say, I’m milking the “everything is linear” fallacy, which features prominently in every single option set I’ve written so far, for all it’s worth. So far, India seems happy with my work, which can only mean that India is confident that, for example, hoardes of students will continue incorrectly expanding polynomials in exactly the same way that teachers have warned students against incorrectly expanding polynomials since time immemorial. Good instruction has minimal effect on the frequency of the most common types of algebra errors, I’ve found, so I don’t have to worry that there will be a classroom of students who overlook Option D *en masse* because *duh*, *everyone* knows that (x+y)^2 does not equal x^2+y^2.

No, I’ve done good work with this text, so far. My employers assure me that my questions will be sufficiently confounding to high school students, of whom negligibly few are even adept enough at plugging expressions into their calculators to compare multiple choice options to an unsimplified expression that it’s well worth asking several questions that can be solved that way; and of whom hardly any understand enough algebra to avoid half of the wrong choices I’ve provided.

A skilled teacher is one who acts as a positive influence on her students, and manages to inspire them. Lofty goals, those, and ones that are seldom attained. It’s far easier - and potentially more lucrative - to be a skilled multiple-choice math question writer, whose success is commensurate with the ability to correctly predict her subjects’ deficiencies, which are never in short supply.

Re: the “everything is linear” fallacy

High school students and all of first-order perturbation theory?

(x+y)^2 = x^2(1 + 2(y/x) + something order (y/x)^2).

Oh look! She’s back! At last!

(and yes, I subscribe to the RSS, and have been growing more and more surprised that no more bloggy goodness has been coming out of Canada lately…)

I’d actually forgotten that my RSS aggregator has TD&M in its listing.

You challenged me with your multiple-choice-example. I know it can be done without a calculator. Let’s see….

sqrt(50) = 5 sqrt(2)

sqrt(8) = 2 sqrt(2)

Thus, the correct answer would be 3 sqrt(2), also known as sqrt(18).

No, I do it the hard way… (or easy, as the case may be) - I’ve got you in my top blog grouping, which I open all at once at least once a day, and usually more often.

Of course I have you in my aggregator. Life is not, after all, nothing but roses and good times.

And congratulations on your insourcing work, frustrating though it may be.

I did a similar test bank project myself last year. Many of the multiple choice questions I wrote had the format: “Here is a particular situation, and here is some information you know about it. Which of the following conclusions may be correctly drawn, based on this information alone?” Then you list five options, one of which is “none of the above”.

Example: Suppose you have a function f, and you know f(2) = 1, f’(2) = -1, and f'’(2) = 0. Which of the following conclusions can you draw? (a) f is increasing at 2; (b) f is negative at 2; (c) f is concave down at 2; (d) all of the above; (e) none of the above”.

I like that kind of MC question because it’s more than just plugging something into a calculator and choosing from a menu.

However, I think it’s totally appropriate to include “everything is linear” meme in writing a test bank. That’s a concept students need to get right.

And yes, you’re in my RSS aggregator.

I will admit that I said to myself “sqrt(50) is 7+ and sqrt(8) is 3-, so the difference is 4 and change” - but “3 * sqrt(2)” or 4.24+ is a better answer.

Yes, NetNewsWire checks every day. ;-)

(e) sqrt(324^(sqrt(1/4)))

When I was in high school, one of my English teachers made us make up sentences with four or five different sentence elements — correctly punctuated of course — and then diagram them. “Write and diagram a sentence in which (1) the subject is a gerund, which is modified by an adverb, which is modified by a prepositional phrase; and (2) the indirect object is modified by a relative clause.” Every week the instructions would get more complicated. On the “final exam”, there were 15 required elements; the sentence took up almost a whole piece of paper.

I always wondered why we didn’t do the same thing in math class. “Write an arithmetic expression that includes (1) nested square roots, (2) at least two logarithms, (3) an improper fraction, and (4) all four arithmetic operations (+-x÷). You may not use the digit 5. The value of your expression must be 5. Show your work.”

[RSS++]

Semi-off-topic, but I was actually able to get a class (I believe it was a calculus class) to quit making the (a+b)^2=a^2+b^2 error. When half the class did that on the homework, I chastised them and put the exact same problem on the quiz. When half of them did it again, I told them that they were calculus students who should know better by now than to make that sort of sloppy error; they had been taught this, AND they had been warned, AND they had been remediated, and if they did it again on the test it would be an automatic zero on whichever test question they did it on. Since each question would drop their grade by a full letter if its points were missing, this was a serious penalty.

There were only two of that sort of error on the subsequent exam.

Robert - I like that style of question. However, the specs I was given are things like “Question 4: scalar multiplication of matrices” and hell if I can figure out three ways to do that one incorrectly. (And double hell if I can figure out an

applicationfor same.)Wacky Hermit - Oh, I got my precalculus students to stop making that mistake, too, but like you, I needed to resort to threats and it took a few tries. I put such a question on the first quiz; close to three quarters of my students got it wrong. I spent ten minutes the next day going over that question, and then put it on the next quiz. Nearly as many got it wrong again. I spent ten minutes the day after

thatgoing over the question, and announced, “This very question will be on next week’s test. If you make this mistake, you will get a zero on the question. You have been warned.”I put the question on the test, and four Einsteins made

the same goddamned mistakeon it. Easy: zero. One of them came up to me after the test, and said that I’d given him 0/5 on that one question, and really, hepracticallygot it right, so he should get like a 4/5, and didn’t I agree?BRING IT ON, kid. I told him that if he were in a biology class, and there had been a question about human reproduction, and he’d written “the stork brings babies to their parents”, he’d have gotten a zero, regardless of what he wrote after that. The stork, I explained, is a fiction. It is false. It is a simplification that has no explanatory power. It is useless. Similarly, the notion that (x+y)^2=x^2+y^2 is a fiction that does no one any good, and quite frankly, university students are too old to be clinging to such childish fantasies.

Harsh? Yeah, but I’d warned them about this, dammit.

Similarly, the notion that (x+y)^2=x^2+y^2 is a fiction that does no one any good, and quite frankly, university students are too old to be clinging to such childish fantasies.But .. but .. I use that fact very often right now!

Of course, I use it while calculating in group rings for 2-groups over the field with two elements; so it actually IS true there. But still!

Apparently induction is something that some students never understand how to do either. 42% of my students got the induction question wrong on the midterm. Alas, I don’t have quizzes or something where I can make them do induction proofs again and again until they get it right.

I was telling the prof that usually teaches this course about my adventures in induction and he said ‘Yeah, some people never understand induction, no matter how much you talk about it.’

Yeah, I knew someone was going to bring up fields of characteristic 2 or somesuch, and it even crossed my mind while I was talking to this student, but decided against confusing the kid further.

Hi, MS. Long time! Glad to see you’re posting again.

Every textbook project I’ve ever been involved in has involved an amazing number of levels. You’d think the results would be better, but sometimes it just seems to provide more ways to go wrong. Hey, do you want my expertise, or do you want my expertise as screwed up by some person who futzes with it? They always want the latter.

I’ve been busy getting ready for summer school. I’m teaching calc. Today I found our college’s legendary one-size-fits-all syllabus.

A propos of very little, you might be interested in Good Math, Bad Math, and might consider adding it to your blogroll. (And I have your RSS feed in a Firefox livebookmark in the folder I check every once in a while, rather than the folder I check multiple times a day.)

MS,

I don’t know if this helps, but back in my test taking days, I was told that the answers to multiple guess questions always had the same format: one correct answer, two wrong answers that might be computed depending on what sort of mistake you make, and one obviously wrong answer that would be impossible to reach.

I’m still trying to suss out the chain-of-command here. You’re saying the company is in India, serving American schools, but they’re just the middleman - all the actual work is done by Canadians?

That makes my head hurt. Although if the Indian company has figured out how to make money by taking orders and then delegating all actual work, good for them. (And yes, the idea that an Indian company is outsourcing is pretty funny)

I do earn a bit of “mad money” myself by reviewing (college) textbooks - mostly statistical ones - and I find the “all of these things are just like the other” phenomenon on a regular basis. At least I bother to mark the typographical errors and the mistakes in formulae, so hopefully future introductory stats students won’t wind up having to learn from an error-filled book, like I did.

Hi, MS. You’ve been silent for an awfully long time, now. What gives? Have you fallen into some kind of philosophical or metaphysical black hole of the soul, or what? Please come back!