"New" math?

March 21, 2011 10:40 AM

Multiple students taking an exam at different times come up with the same baffling answer. Help!

Creative minds, please apply.

Easy enough college-algebra level question on an exam. The students were asked to compute log₃ 81. Of course, the answer is 4.

At least 4 different people answered something strange. Three get 38.65, one gets 38.64 (as if there is some rounding involved). None of them show any work. I'm trying desperately to figure out what they were thinking (or what they may have been typing into a calculator). These students could not have been cheating off each other. Any ideas?

posted by King Bee to education (24 answers total)

Bing!
posted by MrMoonPie at 10:44 AM on March 21, 2011 [3 favorites]

Thank you so much! I can't believe I didn't try that.
posted by King Bee at 10:47 AM on March 21, 2011

Pity they didn't try Wolfram Alpha. (If they're allowed to use the internet on this sort of thing, you may want to point them at it as a more specific source for calculations.)
posted by restless_nomad at 10:49 AM on March 21, 2011 [2 favorites]

Well if you type it wrong as they probably did, then google/Bing/wolfram everyone gives the 38.64 answer, since its correctly answering log(3)*81

If you enter it as log(81), google and Bing don't know what to do with it, and wolfram alpha does.
posted by wildcrdj at 10:52 AM on March 21, 2011

Err log3(81).
posted by wildcrdj at 10:52 AM on March 21, 2011

Wolfram Alpha is allowed, and as restless_nomad points out, it does take care of the syntax situation for you.

Many of them tried to use their fancy TI calculators instead. As MrMoonPie shows, the typing of the "log" button followed by a "3" makes you want to close the parentheses, then type "81", which it reads as juxtaposition (and hence multiplication).
posted by King Bee at 10:53 AM on March 21, 2011

You know, I probably have an advantage here because I'm a math agnostic--I have no idea what log3 81 means or is or how it's supposed to be written or calculated. I simply copied and pasted it into bing to see what I'd get.
posted by MrMoonPie at 10:56 AM on March 21, 2011 [6 favorites]

And I used bing because, of course, google gave the correct answer.
posted by MrMoonPie at 11:05 AM on March 21, 2011 [45 favorites]

You know, I probably have an advantage here because I'm a math agnostic--I have no idea what log3 81 means or is or how it's supposed to be written or calculated. I simply copied and pasted it into bing to see what I'd get.

To what power do you need to raise 3 to get 81?

3*3*3*3 = 3^4 = 81

It's kind of sad that they even needed to use a calculator really, and indicates that they haven't a clue what 'log' means.
posted by empath at 11:32 AM on March 21, 2011 [5 favorites]

It's kind of sad that they even needed to use a calculator really, and indicates that they haven't a clue what 'log' means.

Story of my life.

One particular student even wrote "3^4 = 81", then wrote 38.65 as her final answer.
posted by King Bee at 1:37 PM on March 21, 2011 [13 favorites]

And I used bing because, of course, google gave the correct answer

How do you get that to work? log(3)81 doesn't give anything, neither does log3(81). log(3)*81 gives 38.65 of course. (I'm talking about onebox, both bing and google give search results with the correct answer somewhere).

Was actually going to file a bug on this but if I'm just clueless as to formatting then thats something else.
posted by wildcrdj at 2:36 PM on March 21, 2011

I hate to ask, but I'm just curious.

How did the students access Bing to search for said answers?
posted by santojulieta at 6:48 PM on March 21, 2011

I allow the usage of laptops on some exams.
posted by King Bee at 6:49 PM on March 21, 2011

When I search Bing I get the right answer from a whole bunch of websites. What am I doing right?
posted by Joe in Australia at 7:29 PM on March 21, 2011

What you're doing right is that you're looking at the results for confirmation instead of just writing down the calculation it performed for you.
posted by flatluigi at 11:07 PM on March 21, 2011

Now that the answer has been found, I hope that this slightly off-topic comment will be allowed to stay. I hope that you use this as a learning opportunity for both you and your students. A lot a students will (arguably rightly) think that any math past basic arithmetic is a useless skill to have. My phone can do multi-variate calculus. My car radio could probably graph a y-intercept if it had a better display. And you're obviously aware that Wolfram Alpha and Google (but apparently not Bing) can understand complex statements. So the skill of being able to do the math is uninteresting to all but the most nerdy students (yes, I'm in that group).

But there are two -- possibly more important -- skills that you can teach the students. One is "what tool do I need to solve this problem?". I'm trying to measure the area inside a strangely shaped fence, I should be able to identify that as a Riemann Sum. I'm trying to model a correlation, I should be able to remember "linear regression". I don't need to be able to do these things -- even if I had to do them by hand, I can Google the how in ten seconds.

The other skill is "does this answer make sense?" I know what log is. I know these numbers. Even if I can't do the math without an advanced calculator, log₃(81) = 38.65? That fails the stink test. I just calculated that the earth is 10^-15 meters from the moon. No, that doesn't make sense. I predicted that Big Papi will hit 98 HR this year. No, no, there's a problem in my math.

The people who used Bing and got the wrong answer and got a really wrong answer should get points deducted. Or maybe a warning -- wrong answers are fine, but you'll get points deducted on the next test for ridiculous answers.
posted by Plutor at 5:25 AM on March 22, 2011 [8 favorites]

Agree with Plutor. They don't know what log means. And they clearly never did any homework, because if they had, they would have already learned how to use Bing for log3.
posted by gjc at 8:12 AM on March 22, 2011 [2 favorites]

I totally didn't have the *oh duh...* moment when trying to get the search engines to do the right thing.

I did however get them to do the right thing:

log(81) / log(3) = 4

posted by slactoid at 8:30 AM on March 22, 2011

Is it possible to dedicate a few minutes of the class (post-test) to go over the problem(s) missed. Something like

"Hey, everyone close your laptops for a couple of minutes... okay, I know a lot of you guys missed this, so we're going to take a couple of minutes and go over this again—and once I'm sure we all understand it (and I might ask you to explain it to me on the way out of class), then I'll explain how to plug it into you calculator—but remember guys, you should always go back and check your answer using your brain. Say to yourself

"Does the answer I just got actually make sense?
Does 3^38.65 actually equal 81? Hmm, that seems incredibly wrong..."

Because right now, the students access to Bing is a crutch/pacifier that is actually hurting them. It's giving them an express route to bypass a few seconds of thinking, and instead leading them straight to (any number of) wrong answers.
posted by blueberry at 1:33 AM on March 23, 2011 [1 favorite]

In fact, I might go so far as to create a silly visual aid to show at the end of my little explanation. Something for those visual thinkers among us. Something like people in a log ride, with a talk balloon from one of the log-riders shrieking the question "What power?!" And then be like:

"Remember, when you see a 'log', think 'what power!?' ...does this number need to be raised to to get..."

posted by blueberry at 2:13 AM on March 23, 2011

blueberry: The problem with that is if you hand back an exam and then want to "go over it", if a student has done poorly, they will tune out for the next hour. They will see the bad grade and feel bad about it. They won't listen. If I say "you clearly don't understand log" or "this answer is incredibly wrong", what they hear is "you're a complete idiot" and "get out of my class, you're too stupid for this".

You have to be much more tactful than that. As I mentioned above, a student did write "3⁴ = 81" on her exam, then wrote "38.65" on her exam as her answer.

I know that using bing/google/calculators/anything but your mind is a crutch when it comes to doing mathematics. It's a different discussion for me to complain about how the curriculum is all screwed up (because it's determined by lawmakers, not instructors), and how if I don't tow the line and allow "technology" to pervade every inch of the classroom, I get poor reviews and can lose my job. :(
posted by King Bee at 5:46 AM on March 23, 2011 [2 favorites]

Ah... for some reason, I had it in my mind that this was a college freshman class (where the students are probably a bit thicker skinned, and might appreciate a silly mnemonic-like thing to help them).

Still, it seems like if all they are learning is to rely on a search button, something needs to happen (today!) or these kids are only being taught to be helpless.

Here’s a quick story about one of my greatest math teachers:

The greatest math teacher I've had, a grad student named Dave ("Call me Dave."), made an announcement after he heard a student talking down about her math intelligence—"Listen, no one in this class is stupid! If you are having trouble, that's on me—that is because I am not teaching it to you the right way—remember, I'm hear to teach you." Guess what, people did really well in his class.

I understand that "higher ups" in schools can have their heads completely in their asses, more attached to buzzwords and questionable high test scores than about actual learning, but if these kids are not leaving your class prepared for their next step/class/school/opportunity, then they are literally being stolen from;their time, their potential, their promise from adults that they would be educated.

If my child were being passively taught to take shortcuts without thinking, I would furious and raising hell—with the principal, the school board, the newspapers, whatever needed to be done to make people live up to their promise.

Are there other math teachers in your school that you can meet with and say "Hey, I'm having this problem... how did you guys handle it?"
posted by blueberry at 12:58 PM on March 23, 2011

Still, it seems like if all they are learning is to rely on a search button, something needs to happen (today!) or these kids are only being taught to be helpless.. If my child were being passively taught to take shortcuts without thinking, I would furious and raising hell

I don't think King Bee is "passively teaching" any such thing, and his even asking this question shows that he is more thoughtful about the situation than many math teachers I've had have been. As you said in your answer, it's the kids' parents that need to get upset about this situation and put pressure on the administrators - there's only so much teachers can do. If his department has a policy that laptops are allowed on certain exams, he can try to change that policy, but he still has to follow it in the meantime.

Cheating and mental shortcuts are a problem that is particularly intractable in math classes. This sort of laziness is just really, really common for some reason (probably because math is hard, and cheating is easier when there's a "right answer"). If it wasn't Bing, it would be a downloaded program on their TI, and I haven't met a math teacher yet who has a perfect solution to the technology problem other than really tough story problems that require a complete understanding of the concepts involved - and teachers that have these high standards usually get so many complaints that they really need department backup to keep teaching this way.

I have had exactly one math professor who wrote tough enough exams to require a deep understanding of the material (not just the ability to plug stuff into the calculator), and his integral calculus course was the best math class I've ever taken - but he was the head of the department, and I think he was still under a fair amount of pressure from the community college to pass kids that he knew didn't understand the material very well at all (because otherwise he would only be passing about half of the class because the other half showed up completely unprepared for the course due to their insufficient prior instruction).

I really loved that class because he was so passionate about math and how beautiful the ideas were, and I felt so bad for him because he really wanted to share that with everyone, but most kids didn't want to or weren't prepared to hear it. He tried so hard to help everyone succeed and always had time for everyone, but most kids were simply not willing to put in the effort to make up for the (often gaping) holes in their educations. Math education is additive in a way that, say, literature education is not. You can probably understand Kurt Vonnegut even if you never got Jane Austen, but if you don't understand logarithms, you don't stand a snowball's chance in hell of passing a good calculus course.

I guess I'm just trying to say that the technology situation in math instruction is not at all straightforward, simply because cheating is pretty easy, students (especially engineering students) tend to feel completely entitled to the right to plug stuff into the calculator (and shortcut their learning), and students are often just woefully ill prepared for the course in the first place. I have seen these problems in every math class I've taken, so I don't think it's at all unique to King Bee's institution (though I doubt that makes you feel any better, King Bee).
posted by dialetheia at 2:42 AM on April 1, 2011 [2 favorites]

but you'll get points deducted on the next test for ridiculous answers.

Oh hell yes. Some of the exams I've given require more information than I can really practically write into a question, so some assumptions have to be made. The general policy is, assume something, write down your assumption, and I'll go with that when I'm checking your answer.

Until someone assumed the volume of my lab was 10^3 ml (to calculate airborne radioactivity when the radioactive sources hypothetically caught on fire.) I couldn't bring myself to let that one stand. Can we think about what we're writing just a little bit, maybe?
posted by ctmf at 5:00 PM on April 14, 2011