An article at Education Week includes an interview with one of the math consultants for Smarter Balanced. Smarter Balanced is the lesser known of the two groups that are backed by the US government to write tests for the Common Core (you may know the other one, PARCC, a little better). His 30 point critique of the testing gets to the heart of the matter, I think.
Here is one practice question that he gives up for discussion:
A circle has a center at (6,7), and goes through the point (1,4). A second circle is tangent to the first circle at (1,4), and has the same area.
What are the possible coordinates for the center of the second circle? Show work or explain how you found your answer.
For you old timers, that last part is pretty important. In the past, “showing your work” on a standardized test was unheard of (especially beneath the graduate level). This is one of the points about the new standardized testing that I actually approve of (assuming that it can be properly scored … the jury is still out on that … and this is the crux of the critique here).
According to our math consultant, the first thing that anyone would do in trying to “show work” is to draw the circles. This is not an option for the online test. Students are given scratch paper (4 pieces, carefully counted), but the scratch paper cannot be collected for further consideration. Thus, in an attempt to find out not simply what students know, but how they think (which is good) the test designers have designed a test which very specifically makes it impossible to represent a great deal of geometry on these tests.
Another critique is the equation editor. Both PARCC and Smarter Balanced allow students access on line to an equation editor to help them construct equations to show in their work. This is not a calculator (there is an “=” key, but it does not allow you to find solutions). It lacks trig functions and exponents which can be handy when needed (they are). For odd reasons, the interface is designed the opposite of a calculator interface, and includes some forward and back buttons that are unlabeled as to their purpose (Do you want to take an online test where you have to wonder what “THIS” button does)?
The article, briefly summarizing the 30 page critique, notes that there are also errors with precision that are not consistent with what students are taught according to Common Core.
I just want to be one more voice in the chorus: when you see test results, before blaming “stupid kids” or “lazy teachers”, keep in mind that no one knows what they are doing, and that starts, apparently, with the people who are writing or editing the tests. Until these tests are filed under “nice idea, but not going to work”, they are going to continue being a drag on U.S. education instead of its saving grace.