I was recently helping a student at Wilson SHS in Washington, DC with something called a ‘Paced Interim Assessment’, written and published by one of our major educational publishing monopolies. It was filled with questions that were pompous, absurd, and filled with errors. Here is one of them.

Given: line p is parallel to line q.

Prove: the measure of angle 1 equals the measure of angle 2. Show all steps of a two-column proof.

The reason I think this problem is goofy is that the “given” information is not needed at all: Angles 1 and 2 are congruent (or have the same measure, or are equal) no matter whether the two lines are parallel or not, by virtue of something we call the Vertical Angles Theorem, and which students by this point have already proved and have been using for a long time. In other words, there is nothing to prove at all.

Is this a simple typographical error, where the author(s) really meant for the student to prove that angle 1 is congruent to angle 3? I don’t know. If so, that would be fairly easy to do – it’s asking the student to prove the alternate exterior angles theorem — but they’ve probably already proved that as well!

Over and over I found the problems in this PIA to be shoddily written and not requiring any thought whatsoever, while at the same time adding lots of extraneous words that will certainly discourage anyone who doesn’t read well. We found about five questions that had no correct answer given, and a few that looked like this:

Notice that there is nothing at all given about the relationship between angles ADB and BDC. Is ray DB an angle bisector? We don’t know. Perhaps that was the intention, but it is nowhere stated, so you cannot figure out anything about any of the angles in the diagram whatsoever.

Yeah, I admit to having made up quite a few bad questions in my career as a teacher, but when students pointed out my errors I would graciously thank them for showing me up. Here, I am pretty sure that the student would be penalized for not reading the minds of the low-paid hacks who wrote this trash.

I also tutor students from Sidwell Friends and Saint Alban’s in much the same subjects. What I find is that the students at SF and StA are given problems that require thought — much like the problems I used to assign when I taught at Alice Deal JHS — all of which schools are in Washington, DC.

The idiots in charge of education in Washington, DC Public Schools should be ashamed of how low they have sunk the education of DC’s youngsters. It’s really a travesty.

This type of question is why tests must be field-tested before they are used for any type of assessment. It takes a long time to get a bunch of good questions that actually test what we want students to know. All experienced teachers have thrown some clunkers into the mix and wound up wasting time.

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But the funny thing is at first teachers were allowed to read these tests but NEVER for the big’un lest they cheat. In elementary and the number of second language kids I worked with, I anguished along with them over the PIA that was given 4 times a year. (Plus the NAEP and the CAS and often another random one squeezed in there). I couldn’t get over the ineptitude of the reading test, as well. There were often several questions on a PIA that the teachers couldn’t decide what the answer should be. I am all about questions that make you think too, but as you pointed out, ones that make you stop and wonder “what on earth…?” on a timed test!? (actually they get all day if they need it, but what 3 or 4th grader has the stamina to sit and take a test, all day???) If the average citizenry had a look at the testing calendar for a year, everyone would get the same idea that teachers have, “When are they suppose to learn for these tests?” http://dcps.dc.gov/DCPS/In+the+Classroom/How+Students+Are+Assessed/Assessment+Calendar/DCPS+Assessment+Calendar+for+2014-2015

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That first one is a real ring-tailed doozy. Surely, as you say, the only thing you can do to make it an actual problem is to assume the typo: they meant angle 3.

Fine, but how do you get a two-column proof out of that? I mean, more than one line. Because the result is itself a perfectly valid version of the famous Fifth Postulate. And a not uncommon one. Or, if you please, it’s a valid *definition* of parallel; also common enough.

Maybe it’s highly unreasonable to expect tests for innocent children to be written by someone who knows mathematics beyond the high school level. Or reveiwed by someone with expertise in what you might call the elements of geometry After all, the kids don’t know nuthin of this high-level stuff. And if they studied some geometry from the wrong textbook, they deserve to fail.

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very nice

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