The other day I read this article about math performance in Rhode Island. Ignoring most of the rest of the article, I focused on the problem given from the standardized test, and percentage of the students who got it right/wrong.Â The problem calls for students to recognize the need to multiply a quarter of a mile by 3, then convert the total distance to feet.Â Here’s what I found interesting: 69% got the answer wrong, and while the author doesn’t explicitly say that 31% understood how to get the right answer, they make no effort to explain what this means.Â I don’t really fault the author for that, but there is an important point to be made.

It’s interesting to note that one of the three incorrect answers is less than 1/4 of a mile, one is equal to 1/4 of a mile, and one is greater than a whole mile.

Suppose we begin with the naive assumption that a student who takes a guess at the answer gets it correct 25% of the time.Â I would hope this percentage would be higher given that an educated case, which seems more than plausible, would have a better chance of success.Â Then again, a partially informed educated guess might lead to a certainty of an incorrect answer.Â Still, suppose 100 students take the test, and n understand the problem and answer is correctly, while the other 100 – n guess randomly.Â Our expectation is that 1/4 of the guesses are correct, meaning the number of students who bubble the correct answer is

n + (100 – n)/4 = (3/4)n + 25

When this total is 31 (as in 31% get the answer correct), that means that n = 8.

Let’s reflect on this observation.Â Only 8% of Rhode Island high school juniors can recognize and compute 3 times 1/4 times 5280.Â Granted, there is some context involved, but the context is simple and ordinary.Â I doubt that many students can do the math who can’t comprehend the problem.

Maybe there is some variance and perhaps my naive modeling assumptions aren’t perfect, but I doubt that the number of students who truly solved the problem is particularly close to 31%.Â Maybe 10% or even 15%, but not 31%.Â Then again, haven’t a substantial fraction of the lowest performing students dropped out by the point this test is administered?

The article states that there is an epidemic in education, but if this problem and performance are at all indicative (it’s just one data point, but…), then math education is broken far beyond what most people imagine.Â There must be entire schools where a single-digit percentage of the students can demonstrate a correct solution.