Story problem time!

image028Have a math problem:

A boat travels 60 kilometers upstream against the current in 5 hours.  The boat travels the same distance downstream in 3 hours.  What is the rate of the boat in still water?  What is the rate of the current?

If you are a reasonably educated person, you should be able to make headway with this fairly quickly:  the boat travels 12 km/h upstream (60/5) and 20 km/h downstream (60/3), which means that the boat’s speed in still water is the average of the upstream/downstream speeds, (20 + 12)/2 km/h, or 16 kilometers per hour, and the current is 4 km/h, which is the difference between either of the measured speeds and the average.

I spent about half an hour last night texting back and forth with a former student trying to work her through this problem and becoming more and more bewildered about what it was she didn’t get about it as the conversation went on.  She got the math– the math isn’t really that complicated, right?  Just division and an average.

What she didn’t get?  Rivers.  As it turns out, “downstream” and “upstream” are not terribly salient terms to kids who have lived in cities all their lives– and while, granted, the town I currently live in is actually called South Bend because the river bends south while wending through it, the terms “downstream” and “upstream” hadn’t managed to really ensconce themselves in her vocabulary as of yet.

This young lady is generally one of my brightest kids, mind you.  I’m not mocking her at all here, although maybe she deserves it a little bit– but the entire conversation got me thinking about how incredibly easy it is to write standardized test questions that you think are questions about math but turn out to hinge on some other kind of non-mathematical knowledge.  She could not wrap her head around the idea that the boat wasn’t going at its full speed “downstream” and that the current wasn’t slowing it down by (20-12) 8 km/h going upstream.  Which, of course, was one of the answers, because whenever anyone with half an ounce of sense writes a multiple choice test, one of the horrible tricks you do is thinking “Now, how might the students screw this up?” and then writing answers that match what they might have gotten if they did something predictable wrong.

The math?  She’s got it.  The geography lesson that the writer of the question no doubt didn’t realize was embedded into being able to get the question right?  Not so much.

I’ll talk more about this later; just wanted to get the thought down before it fell out of my head.  This is part of the longer series of posts I alluded to the other day before hell fell on my face and knocked me out for a couple of days, I think; I’ll get back to it soon.