A very old ‘brain teaser’:  A man buys a horse for $60, sells it for $70, buys it back $80, and sells it a final time for $90.  How much money – if any – does the man make on this series of transactions?
For decades, this has been one of my favorite brain teasers to share with students, as it has at least 3 believable ‘answers’, and they often all surface with equal regularity.  Good discussions. Try it yourself, if you want.  No one is watching (or grading).
But this brain teaser – and my wife’s reaction to it – created a sequence of events that started out as funny, and ended up as highly enlightening, at least for me.  Quick background:
1)  For a year now, I’ve been sending out a free weekly mailing every Monday morning.  It always includes one of my photos as an amateur photographer, but it also includes other fun ‘stuff’ from week to week, always designed to brighten Monday mornings.  Often, I include some fun brain teasers and/or a math tidbit of some kind, and none of my subscribers have thrown up yet, at least that I know of.
2)  Before her retirement, my wife Pat was a highly successful business woman, but she has the stereotypical dislike of all things mathematical.  She definitely thinks math is a four-letter word, and she thinks (incorrectly) that she’s ‘bad at math’.  Sound familiar?
So.  A few months back, I included the brain teaser above in one of my Weekly Photo/Sharings.  Mostly to have fun with her, I tried to get her interested in tackling it, but she was having none of it, as usual.  For some reason, she finally agreed to listen to the brain teaser.
When I read it, she said “Oh, well, that’s easy!”  She pulled out a piece of scrap paper, grabbed a pencil, and in about 20 seconds had her answer.  “I don’t even need you to confirm it,” she said, “I know it’s right.”  (It was.)
First I laughed with delight.  Then I stared.  Who was this woman, and what had she done with my wife?  And finally, later, I reflected on what had just happened.
It’s clear that Pat had viewed this NOT as a ‘math problem’, but as a ‘business problem’.  Now she was in familiar territory.  She ate business problems harder than this for breakfast.  She cut through the often confusing nature of this teaser and didn’t blink an eye.
Suddenly the implications for the classroom in terms of having students find and solve problems they are actually interested in is more than just academic.  It’s one of the reasons I’m such a big fan of fun brain teasers and math-related puzzles & games.  Students of all ages enjoy them, and students are secretly solving problems and doing ‘math’ at the same time.
Take this out a level, and this is really the point, isn’t it?  After all, outside of a classroom, there’s no such thing as a ‘math problem’.  There are only ‘real world’ problems that may need math tools to solve them.
And now take it out a final step:  Education in the ‘real world’ is so much more than doing/knowing ‘subjects’.  We don’t learn ‘subjects’, we learn ‘tools’.  You don’t ever need to diagram a sentence, but you need to write well.  You don’t need to recite important dates, but you need to know the broad lessons of history. It goes on. Being educated is about applying tools we’ve learned to navigate life’s situations.
But does all this mean my wife now loves math?  What do you think?