Friday, March 25, 2016

Math problems of the week: reducing words without reducing math

I've often complained about the wordiness of Common Core-inspired math problems, and, in a recent post, I complained about the excess verbiage in this problem:

Imagine a rope that runs completely around the Earth’s equator, flat against the ground (assume the Earth is a perfect sphere, without any mountains or valleys). You cut the rope and tie in another piece of rope that is 710 inches long, or just under 60 feet. That increases the total length of the rope by a bit more than the length of a bus, or the height of a 5-story building. Now imagine that the rope is lifted at all points simultaneously, so that it floats above the Earth at the same height all along its length. What is the largest thing that could fit underneath the rope: bacteria, a ladybug, a dog, Einstein, a giraffe, or a space shuttle?
[121 words]
Here's a rewrite of the same problem, shortened by about 50%:
Assume the Earth is a perfect sphere and imagine a rope running tightly around the equator. Suppose the rope is lengthened by 710 inches and made to float above the Earth at a uniform height all around. What is the largest thing that could fit underneath: a microbe, a bug, a dog, a person, a giraffe, or a space shuttle?
[60 words]
Some people point out that what looks like excess verbiage may serve a mathematical purpose: part of what's mathematically challenging about some problems is sorting out which part of the description is relevant to the solution. But that's different from plain old wordiness. When it comes to math problems that entail complicated scenarios or extensive directions, many words may indeed be necessary. But beyond a certain number, each new word strains working memory. The more words appear beyond what's mathematically necessary, the harder it is do the problem--for non-mathematical reasons. So, sure, include the distance that the cars have already traveled in a problem that where only their subsequent distance matters. But don't tell us what color the cars were, or assign colorful names to all the drivers.

Color raises another point. Some words are more distracting than others. Gratuitously unusual words or words that evoke specific, irrelevant images contribute additional distraction beyond the numerical word count. This is why I've replaced "Einstein" with "a person" and "a ladybug" with "a bug." (I replaced "bacteria" with "a microbe" for a different reason: "bacteria" is distracting because it raises questions about quantity.)

Minus the excess verbiage and non-mathematical distractions, some of today's word problems are perfectly fine. Revising them may take time, but much less time than they otherwise waste.

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