Monday, October 5, 2009

Who Gets It?

Here's the problem:

An airplane is flying at 36,000 feet directly above Lincoln, Nebraska.  A little later the plane is flying at 28,000 feet directly above Des Moines, Iowa, which is 160 miles from Lincoln.  Assuming a constant rate of descent, predict how far from Des Moines the airplane will be when it lands. [1]

Question: Which student demonstrates better understanding? Why?

Student D

[1] Problem courtesy of Phillips Exeter Academy.  Hat Tip: Alison Blank

David Petersen said...

Student A has some incorrect wording I think (subtract 720 from 160?). The work is there, but the reasoning is not obvious: where did the 4.5 come from at the beginning?

Student B seems to get the scenario, but the method does not scale well.

Student C seems to have done the same method as B, but with more words.

Student D has the correct answer and the most scalable method, but lacks the explanation of the others. I would probably have done it in this same way: Interpret the words as a more traditional math problem, work through the math problem, reinterpret the answer.

Will Farris said...

It is a basic linear problem and they all "get it." Being able to effectively communicate the complex processes of the mind in arriving at a solution is an entirely different thing. Mathematicians will appreciate D while engineers might appreciate B but english majors and other right-brainers might better appreciate C. In the end I consider A the brightest of the lot in general terms.