Wednesday, March 23, 2016

Doing it in your head or with pencil and paper?

One activity that my wife and I share, but not at the same time, is doing the Daily Jumble from the local newspaper.  Here's one from yesterday that I got stuck on for a while.  I'll give the answer at the end of this post, in case you haven't gotten it by then.  


My wife likes to try out various combinations by writing them out.  I prefer to do it in my head.  If she reads the letters aloud to me, I can then pace around for a bit and usually come up with the word in less than 30 seconds, though once in a while I do get stuck.   That I can "see" through to the answer better without having text in front of me I attribute to how I learned arithmetic back in grade school.  I developed something of a penchant for mental calculations.  You find patterns of one sort or another and that helps to visualize the answer in your head.  When calculators first came out, then later when personal computers made their appearance, the issue arose whether students should learn arithmetic the way I did or if, instead, they simply come to trust their devices and therefore can devote their attention to other things.  I'm really not sure of the answer to that one, but my bias is that learning arithmetic the way I did develops habits of mind that have value elsewhere, so we should still do it the old way and encourage "mental arithmetic" where we can.

On the Jumble questions, consider only words where all the letters are different.  For a 5-letter word there are 120 possible orderings of the letters.  (5! = 120.)  For a 6-letter word, like the one given above, there are 720 possible orderings.   Pure brute force would produce all the orderings and then do a lookup of each in the dictionary, to ultimately identify the one ordering that is listed.  We definitely don't think like that.  Many of the orderings are nonsense.  Having all the consonants come consecutively won't happen.  That observation gives the basis for finding patterns that are plausible.  Perhaps our thinking is like a search through the plausible patterns.  Sometimes, however, you just see the answer immediately.  How you do that is still a bit of a mystery to me, but that it happens once in a while I have no doubt.

The Jumble is done so there are 4 different words that need to be unscrambled.  Each word then supplies two or three letters for the bonus phrase or word, which is the answer to some pun.  That there is a pun is an enormous clue as to the right bonus phrase.  Searching among possible puns (there really aren't too many that might fit) seems like a different sort of thinking.  The harder part is merely to come up with a possibility.

Being able to do the Jumble is rewarding for my wife and me.  (We used to do the New York Times Crossword Puzzle.  She still does, but I've given that up long ago. )  That it is a reward, not a punishment, is also a bit of a puzzle.   I wish I could make my course stuff more like the Jumble and/or make my students in doing the homework more like me in solving the Jumble.  School would be much better for all if that were the case.

Have you unscrambled the word above?  If not, here's a hint.  It's one of Winnie the Pooh's good friends.

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