Recent discussion about the problems with our educational system reminded me about the story of why my friend J almost didn’t make it into his high school honors math class. Now, to clarify, J is easily one of the smartest people I know. But he is also a smartass, and thirteen-year-old J was certainly no different.
On the entrance exam for his honors math class, several of the problems asked you to fill in the next number in the sequence, such as: 2, 4, 8, 16, _?_. Obviously, whoever wrote the exam wanted you to complete that sequence with “32,” because the pattern they’re thinking of is powers of 2. For n = 1, 2, 3, 4, 5, the formula 2n = 2, 4, 8, 16, 32. But J didn’t write “32.” He wrote “π.”
When his teacher marked that problem wrong (as well as all of the other sequence questions, which J had answered in similar fashion), J explained that there are literally an infinite number of numbers that could complete that sequence, because there are an infinite number of curves which go through the points (1, 2), (2, 4), (3, 8), and (4, 16). Sure, he said, one of those curves is the obvious one which also goes through (5, 32), but you can also derive a curve which goes through (5, π). He showed her an example:
As you can see if you try plugging in the numbers 1, 2, 3, 4, and 5, to the equation above, you get the sequence 2, 4, 8, 16, π. Here are the two curves plotted on a graph, both the “correct” curve and J’s smartass curve (hat tip to the mathematician at www.askamathematician.com for graphing this for me in Mathematica):
Anyway, after thirteen-year-old J explained the math behind his unconventional, but admittedly accurate, answer to the original problem, his teacher replied, “Oh come on, you knew what it was asking for!” and refused to give him any credit. I can’t think of a better illustration of the triumph of the stick-to-the-book method of teaching over kids’ innate creativity… or of the triumph of math education over actual math skills.