### Fuzzy Math

In today's Class Struggle, Jay Mathews talks about the strange math that schools in Virginia have apparently been using when determining what percentage of students passed 3rd grade reading tests. Here's the explanation from Alexandria schools testing and assessment director Monte Dawson:

"Remediation Recovery, which has been around since 2001, means that fourth grade students who failed the third grade test in 2004, got to retake the third grade test in 2005. Up until this year (2005), if they passed the third grade test, then they were included in the numerator only of the calculation to determine the third grade passing score. As illustration, if 4 out of 5 third grade students passed and 1 out of 5 fourth grade Remediation Recovery students passed, the passing percentage would be 100 percent."

Mathews explains the reason for this. "...the state school board changed the counting procedure to encourage more schools to [...] give the students who failed some extra help and let them try again. Often the second-test passing rates of students who flunk a test initially are lower than their class's overall passing rate, since they are the class's weakest students. So if those second-test results were combined with the first test results in the usual way, it would likely lower the overall percentage and make the school look worse than otherwise. School districts in Virginia figured this out and resisted the urge to work with their lowest-performing students and test them again."

Okay, fair enough. But (if I understand correctly) using this math, it is possible to have a greater than 100% passing rate. Let's say 9 out of 10 third graders pass this year, and 3 out of 5 fourth graders who failed last year and retest this year pass. Add the 3 to the 9 (but not the 5 to the 10) and you get a passing rate of 120%. I don't know about you, but I would start seriously questioning the educational standards of a school that had a 120% pass rate on a test. If the goal is to encourage schools to give extra help to the ones who fail, why not add the number of students who passed the second time to both the numerator and the denominator? It's still fuzzy math, but it will neither lower the score based on first time testers nor result in a hugely over-inflated and possibly unrealistic pass rate. In my example, the 90% pass rate of this year's third graders would become 92% instead of dropping to 80%(if you use non-fuzzy math) or jumping to 120%. In Monte Dawson's example, the 80% pass rate of first-time testers would become 83% instead of 50% or 100%.

Of course, if they would just take the freaking delta, they wouldn't have the play these numbers games in the first place! Why is this such a difficult concept? You have to know both your inputs and your outputs to know if the system in the middle is working the way it's suppose to. But no! We want to pretend that a value of ten represents a gain of ten, even when we have no idea if the input is 1 or 2 or even that very same ten. Why, why, why, why, WHY? Stupid NCLF! Stupid SOLs! Grrrrrrrr...

"Remediation Recovery, which has been around since 2001, means that fourth grade students who failed the third grade test in 2004, got to retake the third grade test in 2005. Up until this year (2005), if they passed the third grade test, then they were included in the numerator only of the calculation to determine the third grade passing score. As illustration, if 4 out of 5 third grade students passed and 1 out of 5 fourth grade Remediation Recovery students passed, the passing percentage would be 100 percent."

Mathews explains the reason for this. "...the state school board changed the counting procedure to encourage more schools to [...] give the students who failed some extra help and let them try again. Often the second-test passing rates of students who flunk a test initially are lower than their class's overall passing rate, since they are the class's weakest students. So if those second-test results were combined with the first test results in the usual way, it would likely lower the overall percentage and make the school look worse than otherwise. School districts in Virginia figured this out and resisted the urge to work with their lowest-performing students and test them again."

Okay, fair enough. But (if I understand correctly) using this math, it is possible to have a greater than 100% passing rate. Let's say 9 out of 10 third graders pass this year, and 3 out of 5 fourth graders who failed last year and retest this year pass. Add the 3 to the 9 (but not the 5 to the 10) and you get a passing rate of 120%. I don't know about you, but I would start seriously questioning the educational standards of a school that had a 120% pass rate on a test. If the goal is to encourage schools to give extra help to the ones who fail, why not add the number of students who passed the second time to both the numerator and the denominator? It's still fuzzy math, but it will neither lower the score based on first time testers nor result in a hugely over-inflated and possibly unrealistic pass rate. In my example, the 90% pass rate of this year's third graders would become 92% instead of dropping to 80%(if you use non-fuzzy math) or jumping to 120%. In Monte Dawson's example, the 80% pass rate of first-time testers would become 83% instead of 50% or 100%.

Of course, if they would just take the freaking delta, they wouldn't have the play these numbers games in the first place! Why is this such a difficult concept? You have to know both your inputs and your outputs to know if the system in the middle is working the way it's suppose to. But no! We want to pretend that a value of ten represents a gain of ten, even when we have no idea if the input is 1 or 2 or even that very same ten. Why, why, why, why, WHY? Stupid NCLF! Stupid SOLs! Grrrrrrrr...

## 5 Comments:

What's the point? When you do stuff like that, it just makes the numbers meaningless.

Haven't you ever given 105%?

no

The numbers are meaningless anyway. Without knowing what level the kids were at when the year began, you have no way of knowing whether the school's efforts actually did anything to add to their level of knowledge. If you take the delta, it encourages the schools to make an effort to help

allof the kids improve - not just the ones who are failing.VDOE changed the calculation formula in July, 2005. Unless the formula is changed again, 2006 pass rates will be determined by the formula you proposed. As you indicated, the public relations and political value of the change is to prevent pass rates from exceeding 100%.

This isn't fuzzy math, however. It's simply bogus and fraudulent.

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