What is wrong with this question?

Which of the following is not a real number?

a. 0/5

b. -sqrt(23)  [for you non-math people, that’s the best I can do for square root]

c. 12/sqrt(6)

d. 0 degrees

e. pi  [or, if you prefer, the symbol formerly known as pi]

The above question was presented to us just hours ago as part of what I surmise to be an advertisement for why we should hire this lady to come in and tutor our students on how to take the ACT. Why every teacher in the school needed to sit in on this lecture is beyond me, because I don’t really have the time in my already overburdened course to teach students how to properly manage their reading comprehension of essays. [I’m not trying to get into an argument on reading across the curriculum – just bear with me]

What really bugs me about this question is that on a very important standardized test (thanks to No Child Left Behind, we look like an inept school if our students fail to do well on this test) a question as ridiculous as that above might be considered typical.  Are they testing for understanding of what a “real number” is?  Doesn’t look like it.  If they were, they’d throw in an imaginary number.

I’d like to think that I’d eventually arrive at the correct answer because it’s the “least bad” alternative, but that doesn’t seem to me an appropriate way of testing for a students’ aptitude.  And I’m not even trying to start a debate on the usefulness/efficacy of standardized tests!  I just am offended that such an inane question (or a group thereof) could separate those accepted to a given college from those who are not.  It reminds me of someone holding up an open palm and asking “How many fingers am I holding up?”  When you answer five, they laugh and say, “Silly rabbit!  The thumb is not a finger!”  C’mon!  What are we really testing for here?

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6 Responses to “What is wrong with this question?”

  1. Um. Which one is the ‘least bad’? They are all real, right? Is there a “kind of real” category that I don’t know about? Is it d, because of the units?

  2. Yeah, it’s supposedly ‘d’ – as you said, because of the units. But, to me, units don’t make a number less real…

    Standardized tests already have a sketchy reputation because of educational bias, but to add just plain bad questions to the mix really gets me hot under the collar!

  3. I agree – it’s a terrible question, and implies a lack of understanding about what units are by whoever wrote it.

  4. (and also a lack of understanding about what a real number is… there’s nothing about being ‘dimensionless’ in the definition of real numbers.)

  5. What’s wrong with this question? The fact that I’ve had 12 years of college, and couldn’t answer it!

  6. Well, Repercussio, that does beg the question why such a question should be considered a basic prerequisite to graduating high school. I mean if you managed to get your PhD without needing to know, how is it all that important to the population in general?

    I think we suffer from a lot of inertia in education – it’s always been done that way so don’t think about it too hard and don’t change anything. The path to college used to be for the elite, the highly educated, and so it entailed a lot of higher-order thinking and esoteric knowledge that probably had some bearing on a future career (OR, come to think of it, it just maintained their elitism). But these days college is viewed as a goal for everyone, yet incoming students are still measured against an outdated standard.

    I’m not trying to imply current students are incapable of anything, rather that we’re using a rating system for apples on a basket of oranges.

    In fact, Rep, I’d wager that you don’t recall how to multiply two matrices or factor the difference of cubes (two topics currently covered in Advanced Algebra, which is required of ALL students at minimum in order to graduate). Why in sheol does EVERY kid need to go through this stuff? That’d be tantamount to making ME take Art III in High School! Not only are there more interesting things for me to take (and pleasant), but I’d quickly drive the poor art teacher crazy… trying to teach a COMPLETELY incapable person how to construct art — Writin’ Wrong can verify this. 🙂

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