Monday, June 07, 2010

Wrong but scoring points

Maybe the reason kids put forth such bloopers on their AP history tests is that they're used to getting credit for writing silly stuff and just haven't ever gotten out of the habit. For an example, check out how New York scores its state math tests where the test graders are instructed to give partial credit if the student demonstrates some clue about how to approach the problem even if it's totally wrong.
Examples in the fourth-grade scoring guide include:

* A kid who answers that a 2-foot-long skateboard is 48 inches long gets half-credit for adding 24 and 24 instead of the correct 12 plus 12.

* A miscalculation that 28 divided by 14 equals 4 instead of 2 is "partially correct" if the student uses the right method to verify the wrong answer.

* Setting up a division problem to find one-fifth of $400, but not solving the problem -- and leaving the answer blank -- gets half-credit.

* A kid who subtracts 57 cents from three quarters for the right change and comes up with 15 cents instead of 18 cents still gets half-credit.

* A student who figures the numbers of books in 35 boxes of 10 gets half-credit despite messed-up multiplication that yields the wrong answer, 150 instead of 350.

These questions ask students to show their work. The scoring guidelines, called "holistic rubrics," require that points be given if a kid's attempt at an answer reflects a "partial understanding" of the math concept, "addresses some element of the task correctly," or uses the "appropriate process" to arrive at a wrong solution. Despite flubbing the answer, students can get 1 point on a 2-point problem and 1 or 2 points on a 3-pointer.
Imagine how these kids will be after a few more years if they get used to getting half credit just for knowing that subtraction is involved in figuring out change or that multiplication is involved in figuring out the books in boxes problem.

For a contrast, check out this video from Uncommon Schools of these seventh grade students being called on to answer math questions.
That's what students can do if you set high expectations for them instead of giving them partial credit for figuring out that a division problem involves division.


ChrisA said...

Excellent. It does look like a fairly small class but it's hard to tell.

equitus said...

Those NY students have brilliant careers ahead of them in the White House Budget Office.

alex said...

Why should the student who has no idea what to do be given the same grade as the student who partially knows what to do?

Christopher said...

Alex: One answer is that an engineer who accidentally doubles the length of the span doesn't create a "partially correct" bridge. Standardized testing is only valuable to the point where it accurately predicts real-world mathematical ability.

Another answer might be that, while some partial credit is acceptable, getting one 1/3 or 2/3 for these answers is excessive.

But in my mind, the answer is this: Steadily and quite consistently the City and State of New York have made these exams easier and easier to pass. Most Regents exams now require a point percentage around 30-40% to pass. Meanwhile, the mayor brags that passing rates in New York City have risen drastically. Those who know the tests know better.

tfhr said...

These children are being short-changed in ways that will last them a lifetime. But since they can't do the math, how will they know?