Why are you surprised?
Some research supposedly about real-world math....

Researchers from UNIGE and the University of Bourgogne Franche-Comté tested the degree to which our worldly knowledge interferes with mathematical reasoning by presenting twelve problems to two distinct groups. The first group consisted of adults who had taken a standard university course, while the second was composed of high-level mathematicians. "We speculated that the adults and mathematicians alike would rely on their knowledge about the world, even when it would lead them to make mistakes."

Seems reasonable that mathematicians and adults would make different kinds of mistakes.

The given example: "Sarah has 14 animals: cats and dogs. Mehdi has two cats fewer than Sarah, and as many dogs. How many animals does Mehdi have?"

For adults there are three things wrong with this example.

1. This isn't a simple subtraction as the researchers claim. It's two equations in two variables, requiring an algebraic solution.

2. In most cities it's illegal to have 14 animals. In Spokane the limit is 4 dogs and 4 cats. Both Sarah and Mehdi should be reported to Animal Control.

3. Mehdi is Arabic so he probably doesn't have any dogs. But the problem states that both people have the same nonzero number of dogs.

Before you can even start the math you have to allow two violations of law and one violation of cultural norms.

The researchers were surprised at the amount of trouble:

In 53% of cases the respondents thought that there was no solution to the statement, reflecting their inability to detach themselves from their knowledge about the elements mentioned in the statements. Regarding the expert mathematicians, 95% answered correctly for the axis problems, a rate that dropped to only 76% for the sets problems! "One out of four times, the experts thought there was no solution to the problem even though it was of primary school level!

Well, you shouldn't have been surprised. If this example is typical, many of the problems are specifically unsolvable.

Why should people detach themselves from KNOWN FACTS about religions and laws? We're constantly barraged with PETA messages about animal neglect and hoarders, and we're supposed to respect and understand Muslims except when we're bombing non-Saudi Muslims down to bedrock to satisfy the desires of Saudi Muslims. But the Saudis are the strictest of all about dogs, so there's no room for exceptions here.

= = = = =

Sidenote: I tried it algebraically, but there isn't enough info. I had to use brute force. Draw the collections visually and use induction. Both have the same number of dogs. Start by assuming 1 dog for each, which means Sarah has 13 cats and Mehdi has 13-2=11 cats.

S DCCCCCCCCCCCCC
M DCCCCCCCCCCC

At that point Mehdi has 12 animals. Increase the number of dogs, reapply the rules, and the total for Mehdi is still 12,

S DDCCCCCCCCCCCC
M DDCCCCCCCCCC

S DDDCCCCCCCCCCC
M DDDCCCCCCCCC

until the number of dogs hits 12 which would zero out Mehdi's cats. So Mehdi has a constant 12 animals as long as the rules of the problem are valid. The number of dogs per person could be between 1 and 11, but the problem isn't asking the number of dogs.

I'm glad I decided to push through this problem. It was good mental exercise! I suspect it would be a lot easier for those 1812 clerks who were accustomed to thinking in columns instead of decimals.

Labels: coot-proofing, Real World Math

  ¶ 2:18 PM