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Dear Mitch,


You've stated that there are several questions that appear on standardized tests that you think are so terribly written or illustrated that the 'best' answer and most true answer is usually NOT the one that the test-makers credit as the correct one.  OF all the questions you've seen over the years, which would you say stands out as the absolute worst?


From Frank W.


Dear Frank W.,


Good question!  However, to be totally honest with you, there are several that stand out as so poorly conceived and/or so poorly written or illustrated that I find myself unable to pin this answer down to just one. So, for the sake of completeness, here are a handful that stand out as, well, shockingly stupid:


1) The probability questions that show a bag or jar of different colored marbles or candies (or whatever), and ask which one would a person reaching into the bag or jar be most likely to select.  I'm sure you've seen this type.  It's SUPPOSED to be basic probability.  HOWEVER!!, the bag or jar is illustrated in a way that indicates that it is clear.   CLEAR!!!!!!!!  Which candy would a person most likely select from a CLEAR receptacle?  The candy whose flavor he likes the most!!!!!   A CLEAR JAR???  Probability????? Hello??!!??


Nevertheless, if we overlook that particular facet of the ill-conceived question, the next best choice (at least to my way of thinking) is the candy that is nearest to the top of the clear canister!! Aren't most of us taught that it is rude to reach too deeply into such a grab-bag and unnecessarily slime up all the choices our fingers squirm around and bypass on our way to the favorite we crave?  So, if there are two blues at the top, and four reds at the bottom, well, it's a tough call – manners over math or math over manners??...??


Finally, there is one more version of this type of probability question that has always fascinated me:  This time, the bag is opaque (thank heavens!), and has an assortment that goes something like this:  2 red marbles or candy, 3 blue marbles or candies, one purple marble or candy, and one orange marble or candy.  And the question asks:  Which color is a person most likely to pull out without looking if given only one chance?  Well, the obvious answer, of course, is blue.  Why?  Because there are more blue marbles (or candies) than there are of any other color.   BUT.... Notice anything odd about this scenario?  Well, I do, and it is this: While it is true that there are more blue items in the collection than there are of any other particular color, it is also true that there are more items that are NOT blue than there are blue.  Thus, the blues are actually in the minority and a person is in fact LESS likely to select a blue than he/she is to select a marble or candy of another color!  So, if you ever encounter a question such as this one, choose at your own risk.


Finally, for the sake of completeness (or something resembling completeness) I would be remiss if I did not draw your attention to one of the all-time stupidest questions that can still be found on standardized test after standardized test!  Coincidentally, it's another probability question:  A spinner is shown.  (In case you haven't seen such a question in a while, a spinner is one of those things with the arrow pivoted in the center that you fling a finger at and it circles until slowing and then stopping on one particular part.  They are a popular device, and probably the one most people encounter at one time or another is the one that goes with the Milton Bradley game 'Twister'.  Anyway, for a spinner to spin fairly, it must, of course, be positioned on a flat surface. However, when the game is not being played, spinners are frequently stored in an upright position, either leaning on a shelf, or hanging from a wall-hook.  (When running my math department, I developed the habit of Velcro-ing everything to walls or shelves, so that teachers could easily locate them and just as easily return them when their math class ended.  Well, can you smell the problem yet?  Of course you could! In the world of vertically stored spinners, GRAVITY trumps probability every time.  All spinners that I know of come to rest with their arrow pointing straight down, regardless of how thin the southern-most sliver may be in relation to the rest of the circle of possible landing fields.  Now, consider the average standardized test... do their designers seem committed to hiring artists whose craftsmanship is keen enough to employ the kind of atmospheric perspective necessary to make it clear that the spinner is NOT really vertical despite its apparent vertical orientation on the page? 

            No, they do not.  So, even if the southern-most portion of the spinner's subdivision is the slenderest, many intelligent students would be justified in selecting that region as the arrow's most likely destination.




I'll leave that determination up to you,


Hope this helps, particularly the next time you choose an answer that makes the most sense but receives no credit.  Standardized tests serve an important function, though the nature of that function is unclear.


- Mitch