Like just about every school, we have some students who struggle in our classes. For a small number of those students, we have a "credit recovery" system in place, where they work with an online learning platform to make up classes they have failed. I have a ton of problems with this, not the least of which is that it's completely designed around the idea of "recovering credit" and not around the idea of learning (or what the student even needs). But even with those concerns, I would be willing to give it a pass if it provided a viable way for these students to jump through the hoops, graduate and move on with their lives.
I haven't ever had any interaction with our system but, yesterday, I had the opportunity to help one of our students who was working on their Geometry class on the platform. I was a tad bit surprised when the problems I was helping her with involved the Law of Sines and the Law of Cosines. Back when I was a full-time math teacher we taught that in Trig, but I figured perhaps with the changes due to Common Core that too had moved down into Geometry.
When I had a chance to look later, however, I discovered that while it's an option in Geometry, it falls in the "+" category, which means it's "Additional mathematics that students should learn in order to take advanced courses such as calculus, advanced statistics, or discrete mathematics." That hardly seems appropriate for a student who is struggling in mathematics and is participating in our "credit recovery" option as sort of a last-chance.
But, again, I thought perhaps it was something we had decided as a school was to be included in our Geometry classes in which case, while I still didn't think it was appropriate for this student, it would at least be consistent with our regular classes. So I went and talked to our Math Department and we don't teach Law of Sines and Cosines in our Geometry classes. Which means this struggling student, who is in our online-only, credit recovery option, is being asked to do more than the students in our regular, teacher-led classes.
But it gets worse. Because after the relatively straightforward Law of Sines and Law of Cosines problems (assuming that's not an oxymoron), she was presented with a problem something like the following. (Because it's in the online platform, I don't have access to it to see exactly what it said but, for reasons that will become clear in a moment, I feel relatively confident that this is essentially it.)
Using the defects method, which relationship represents the Law of Cosines if the measure of the included angle between the sides a and b of ΔABC is less than 90°?Well, I read that a few times and was stumped. I had never heard of this "defects method." The student couldn't help me with what it was, so I asked her if we could go back and look at the "instruction" she had presumably had over this method previously on the platform. She said we couldn't because she was "locked out" now that she had finished that part. (I can't independently verify whether that is accurate, but she certainly thought it was.) So I googled "defects method Law of Cosines" . . . and found nothing.
Well, that's not entirely true. I found four or five links for it - all with various versions of that same problem that students had posted to various sites looking for answers (like this one). Unfortunately, I had a meeting to get to so I couldn't investigate further at that point, but later I spent more time googling and still came up with nothing. I did find something similar when talking about hyperbolic triangles (and I'm pretty sure even Common Core doesn't include that in high school Geometry), but nothing for 2D geometry. That night I asked on Twitter, and no one knew. And the next day I went in and asked our Geometry teachers, and they had never heard of it.
Now, none of that necessarily means it doesn't exist or that there perhaps wasn't some instruction in the online platform that would help explain it, but it does again make you wonder why it's being included in a credit recovery course for struggling math students. We don't cover it in our regular Geometry classes, none of the math teachers in the building (or who saw my tweet) have ever heard of it, and Google can't seem to find it either. Why in the world was this question there?
There are larger problems here, of course. How and why did my district select this platform? Who is overseeing the content and ensuring that students are actually getting content similar to the courses they are theoretically "recovering credit" for? Why do we think that students who struggled in a regular classroom, with a teacher and classmates to help them, is suddenly going to be successful as a learner in a learn-on-your-own online platform (even if the platform wasn't serving up the wrong content)?
Clearly, this "credit recovery" option is not at all about what the students need. It's not about what they want or need to learn to be successful in their future, it's not even about them being successful right now. It's just a desperate attempt by the adults in our system to somehow, some way, get these students to pass our required courses. As I said earlier, as horrible as that sounds, given our current system, if it actually accomplished that then I'd be okay with looking the other way (while still vigorously arguing to change the system). But it doesn't. We're taking these students that we've already failed and setting them up to fail again.
I still don't know what the "defect method" is in relation to triangles and geometry, but I have a pretty good idea what a defective method looks like in practice. If "defective method of instruction" was a standard, we would "exceed expectations."