Math B, 23:
Solve for x:  $x^{\frac{1}{3}} = 27$
Why equals 27? Because they were hoping to trick kids. Wow, clever adults.

Do you agree? Disagree? Have other nominees?

Integrated Algebra, 30:
The value, y, of a $15,000 investment over x years is represented by the equation $y = 15000(1.2)^{\frac{x}{3}}$ What is the profit (interest) on a 6-year investmet? (1)$6,600  (2) $10,799 (3)$21,600  (4) $25,799 First off, quite wordy. Second, neither profit nor interest are ever defined (except as equivalent to each other). Leading to third, this was a trap question. In my school, it had by far the lowest correct response of any multiple choice. And these are kids who read fairly well. Algebra II/Trig, 29 The scores of one class on the Unit 2 mathematics test are shown in the table below. (There follows a frequency table, 7 lines, 22, tests). Find the population standard deviation of these scores to the nearest tenth. This is a 2-point free-response question. Kids use a calculator. They write down the right answer. 2 points. They write down the wrong answer. 0 points. They write down the right answer, but with an extra decimal place. 1 point. They write down something close to the right answer. Um, er, maybe they used sample standard deviation? 1 point. Or missed entering one number in the calc? We can’t tell, 0 points. Or double entered one number? We can’t tell, 0 points. What in the world is being tested here? Integrated Geometry, 6 A right circular cylinder has an altitude of 11 feet and a radius of 5 feet. What is the lateral area in square feet of the cylinder to the nearest tenth? (1) 172.7 (2) 172.8 (3) 345.4 (4) 345.6 This question is designed to punish, for 2 credits, a student who multiplies 2 digit numbers with pencil and paper. The correct answer is (4). It requires three decimal places of π. They know that a kid who is not using the calculator will use two decimal places. Back in the day, they told us that calculators can help a kid calculate. They told us the calculator can deal with tedious or repetitive work, and allow the kid to concentrate on mathematical ideas. I don’t know that I bought that 100%. But I understood. But requiring use of the π key is something else. It says the kid may not calculate without the calculator. The kid does not have permission to multiply. They have crossed a line. I hope everyone notices. 19 Comments leave one → 1. Anonymous permalink June 22, 2010 am30 8:26 am 8:26 am When are you posting geometry answers? 2. June 22, 2010 pm30 1:40 pm 1:40 pm If I was a student who got the Geometry one wrong for the reason you describe I would likely appeal. (Our state test even explicitly lists 3.14 as a possible approximation for pi.) 3. esther permalink June 22, 2010 pm30 2:09 pm 2:09 pm i don’t blame u all people so of the questions were hard they are missing with us. • esther permalink June 22, 2010 pm30 2:12 pm 2:12 pm The value, y, of a$15,000 investment over x years is represented by the equation y = 15000(1.2)^{\frac{x}{3}} What is the profit (interest) on a 6-year investmet? (1) $6,600 (2)$10,799 (3) $21,600 (4)$25,799

THIS WAS THE QUESTION THAT MESSED ME UP, BUT THIS QUESTION IS REALLY GOOD

June 22, 2010 pm30 3:17 pm 3:17 pm

I know. I got this and a distance question wrong, but I have to say, they were GOOD questions. They taught me something, though – read test questions until your eyes bleed.

June 22, 2010 pm30 2:10 pm 2:10 pm

i don’t blame u all people so of the questions were hard

they are messing with us up.

5. June 22, 2010 pm30 10:44 pm 10:44 pm

They need to give the teachers a little more leeway in the rounding. When I walked around to the classes at the start of the IA test, I implored the students to read carefully when it says to round, and make sure that they round to the correct number of places. There were TWO questions where you lost HALF credit for incorrectly rounding. One was on relative error and the other was a trig problem, finding the angle. Plenty of places to make a mistake on your way to those two points and an extra whammy on the end.

June 24, 2010 pm30 11:47 pm 11:47 pm

I AGREE!!!They need to give us questions where we can actually show our work and the steps we used in order to get to the answers (SO TRHAT WE CAN GET SOME PARTAIL CREDIT)…like the standard deviation one…or else what is the use of the test…we will just be a bunch of mindless idiots that plug in #’s into a calculator an when we head off to college we wont understand the material at all and will be a bunch of mindless jackaes\$!

7. June 26, 2010 pm30 3:34 pm 3:34 pm

I’m not sure I agree with a few of your criticisms. In particular, your nominated worst question actually seems to me to be a pretty good question. x^3 = 27 is artificially easy, cued by the perfect cube. x^1/3 = 4 is almost equally artificially easy (I *suspect* – can’t be sure without knowing your exams well, and I don’t), cued by the fact that only one route is “nice”. The question given checks whether they know which method to use, and is *not* a trick question.

I agree about the standard deviation question. I also agree about the interest question, since we’re supposed to be testing mathematics, not financial English. (And since the question contained almost no mathematics – and since it’s multiple-guess, which I’m opposed to on every level anyway.)

The curved surface area (as we would call it, I had to guess what a “lateral area” was :)) – this surprises me on two levels.

Firstly, it surprises me that any kid who possesses a calculator would not use it for a question of this kind, or that any kid would not bring a calculator to an exam where it was permitted. Really? Wow.

Secondly, it surprises me that you are unhappy about it. There are two multiple-guess answers separated by very very little, requiring four places of precision to separate them, that’s apparent from the start, and you’re unhappy that a kid using a constant to only three places will get the wrong answer? That seems to me to be what’s being tested. We spend a lot of time telling kids that they must always be calculating with more precision than they want to present at the end.

My nomination for worst question I’ve seen you post is either the (not very pointful) standard deviation question here, or the “Use the discriminant… x^2 – kx + 4” question, on which no talented student would ever normally use the discriminant. If you want to test that method specifically, don’t use a perfect square as the constant term!

• June 26, 2010 pm30 7:49 pm 7:49 pm

Dr Rick,
I meant the last to be worst… not that it makes much difference.

On the first, why ask to solve $x^{\frac{1}{3}} = 27$ and not $x^{\frac{1}{3}} = 26$ ? I understand what you are pointing out, that from the tester’s point of view the latter suggests the right route, but I am suggesting that the former leaves an ultra-obvious wrong route that will lure students who otherwise would not have stumbled into that error.

For the π question, I vigorously disagree. Students do not study significant digits (apparently anywhere in New York State). That is, in fact, what could have been tested by this problem, but it is totally absent from the curriculum. Further, even a student with a calculator will perform simple calculations without. I did here, and then glanced at the answers and thought oh ____! Finally, the State was not looking for 4 digits of π; it was looking for the calculator to be used, and deducting more points for a hand calculation than it does for a rounding error.

Strongest agreement on your additional nomination. When I read the test I thought it wasn’t a problem. But when I graded the exam, you would not believe how many of my students completed the square (and effortlessly as well … I probably overemphasized the skill) I even had a kid solve #30 by completing the square. Dedication! And there were different approaches as well. Speaking of that, quite a few of my students half-credited 30 by finding the roots and adding them. The multiplication was tougher without formula.

• June 27, 2010 pm30 5:24 pm 5:24 pm

First question: I have no problem with leaving an obvious wrong route open. To me that’s a long way short of being a trick question. I guess we’ll have to differ.

On the pi issue, if they don’t test or teach precision and significant digits, that makes your unhappiness a lot clearer. As to the calculators, this appears to be a cultural difference. I would be prepared to bet that if I set that question or a similar to every pupil at my school who’s been exposed to curved surface areas, the vast majority would first obtain “110pi” (or a mistaken answer as a multiple of pi) – often by calculator, often mentally – but not a single one would do anything other than use the pi button to obtain a decimal result. It would not have occurred to me that anyone would do otherwise in 2010, other than on a non-calculator paper. My mental arithmetic is good, but I would not have considered doing anything else – and I certainly wouldn’t be writing out pen-and-paper multiplications if I had a calculator unless it was being specifically tested!

June 30, 2010 pm30 9:19 pm 9:19 pm

There are free-response (“constructed response”) questions in the elementary assessments (somewhere between 4th and 6th…) that ask students to estimate the value of a sum or product. The questions are explicit and emphasize the word “estimate”. The grading rubric expects students to round the inputs to the calculation prior to computing: so e.g. “estimate 4.2 x 8.7” would expect the student to first round to 4×9 then compute an answer of 36. The rubrics clearly penalize a student who first computes 4.2×8.7 = 36.54, then rounds to an answer of 37.

If we’re teaching in 5th grade that one estimates answers by rounding during the process of a calculation, doesn’t it then follow that one shouldn’t round at the start in general situations?

I haven’t looked closely at the relevant parts of the NYS Curriculum Standards for 7-12, so it may well be that the guidance to teachers is ambiguous. But count me firmly in the pi-key, not 3.1 or 3.14 or 22/7 camp. If you’re going to use a calculator at all, use it to its full potential. Let it do what it is good for.

• July 1, 2010 am31 1:18 am 1:18 am

I’d like to start by looking at what the question is testing.
1. Can they plug into the formula given on the accompanying formula sheet?
2. Do they know to use the π button on the calculator?

They’re taking 2 points, which could translate into a 3 point difference, on a high stakes test, for using 3.14 instead of 3.1415….?

And they are doing so in a measurement problem, where there is arguably one significant and one semi-significant digit?

Jeez, even if they were right about using all the digits, they’re putting this on a high stakes test?

But I’m not allowing that they are right.

Calculators supporting kids’ math learning is one thing. But setting up the kid who multiplies without the calculator to be wrong – I’ll never be okay with that.

June 23, 2011 pm30 3:41 pm 3:41 pm

No the worst question is #6 on the geometry June 2010 regents: A right circular cylinder has an altitude of 11 feet and a radius of 5 feet. What is the lateral area, in square feet, of the cylinder, to the nearest tenth?
Two of the choices are 345.4 and 345.6. If you use 3.14 as the approximation of pi you get the first. If you use the calculator approximation of pi you get the 2nd. Nothing in the instructions says to use the calculator value for pi.

9. September 12, 2011 pm30 9:20 pm 9:20 pm

Once I originally commented I clicked the -Notify me when new comments are added- checkbox and now each time a comment is added I get four emails with the same comment. Is there any approach you possibly can take away me from that service? Thanks!