I volunteer a couple of times a week with a group that does after school tutoring for urban students in LA. My role is "math floater." I walk around the room and help the kids, and sometimes the tutors, with math problems. When the kids ask for help, it's usually just your basic math question, but when the tutors ask for help it's often less about the math and more about the unfamiliar approach the assignment takes to solving a familiar problem.
This is perhaps most exasperating for those tutors with math backgrounds. You can imagine what it must be like to have a degree in engineering and yet be stumped by an eighth-grader's pre-algebra homework. Of course, it's not the math that's throwing them; it's all the weird and arbitrary steps that have been layered onto the math.
After struggling a bit myself, I realized that the key was to approach these problems as bad translations of unknown texts. If I looked hard enough, I could usually find an antecedent, a good lesson (something I had read in Pólya or seen demonstrated by a master teacher or used with success in one of my classes) that had somehow devolved into the misshapen thing sitting in front of the student.
Recently, I ducked into the tutoring center when I wasn't scheduled to work. I just stepped in to use the bathroom but before I got across the room, I heard a couple of tutors calling my name. They were struggling with a third or fourth grade problem where the student had to perform a number of steps including filling out a three by three grid in order to find the product of two three-digit numbers. The answer kept coming out wrong and none of the tutors could figure out why since none of them were sure how the process was supposed to go.
The point of the question was to illustrate the distributive property. Handled properly, the general format could have made for a pretty good problem. As was it was a disaster. Developmentally inappropriate, badly explained, overly long (two-digit numbers would have made the point just as well), devoid of relevant context. Like a bad translation of a bad translation of a good problem. That got me wondering if perhaps the process for coming up these problems worked something like this...
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