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The Case of the Missing Dollar (or Why Critical Thinking Matters)

by Dick Foreman

I would like to share a story.

Three men go into a hotel and ask for a room with twin beds and a roll away.  They are traveling together and wish to split the costs.  The clerk says, “You’re in luck.  I have a room with twin beds for $25 and the rollaway is $5.”  The three men quickly do the math.  $25 plus $5 is $30.  There are three of us, so that’s $10 bucks apiece.  They take the room and each give the clerk $10.

Later that evening, the clerk sees that the room was actually only $20.  With the $5 rollaway, he should have charged his guests $25.  He calls the bellboy to the desk, hands him five, one dollar bills, and instructs him to refund the three men the overcharge.
 
The bellboy was well versed in math.  He’d learned his math tables, memorized them, and quickly assessed that the men could not evenly divide $5 among the three of them.  So again, using the “old way” he had been taught math, decided to give each man a dollar back and keep the other two dollars for himself.  Everybody was happy and he’d make a nice little $2 tip for being so smart.

The men each got a dollar back.  They were happy.  The bellboy was happy.  But the math failed us, didn’t it?  Each man had originally paid $10 for their share of the room bill.  They each got back one dollar from the bellboy.  Surely, they could each say that they now only had to pay $9 apiece for the room, right?  So they wound up paying a total of $27, or three times their $9 apiece.  The bellboy kept two dollars for himself.  27 plus 2 equals 29.  

?

What happened to the missing dollar?

If you, like me, were taught math the “old way” and think the “new way” is too tough, good luck finding that missing dollar.  Because understanding the concepts and theory of math teaches critical thinking and that’s what it’s going to take to find that missing dollar!

If you do not utilize the critical thinking component as it applies to this math, you will never find that missing dollar.  You will never find in the multiplication tables or the mathematical rote you have always assumed is perfect and unfailing, that missing dollar.  It will drive you mad.  Because who can grasp where that darn dollar went otherwise?

The only way you will find that missing dollar is to permit what the vast majority of teachers and professionals are now urging as the highest achievement standard we could ever hope for in Arizona.  We must maintain critical thinking as the key component of learning as embodied in our current standards, especially math.  Without doubt, critical thinking, divorced from our expectations for educational achievement, will give you this result from the little story above: “Two plus three is five, except when it is four.  And, I’m okay with that because the math tables tell me so…”

Oh.  Click here for the answer, with a little critical thinking thrown in!

Dick Foreman is President & CEO of The Arizona Business and Education Coalition (ABEC).

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