Some students’ problems are beyond anything a classroom teacher can solve. Here are two examples from “Brief Survey of Calculus”, a 100-level college course I once taught—but the same problems could occur at the secondary-school level.
(a) Problem with course content. “Colton” told me he always struggled with math, and he certainly did in my class. He spent as much time in my office as all the other students combined; that seemed to help some, but not that much. And he wasn’t at all stupid. Like so much mathematics, calculus requires a fair amount of algebra, and I already knew many of my students’ problems were more with algebra than with calculus. So I finally asked Colton a very basic question: How much is 3 × (5 × 4) ? I wasn’t too surprised that he tried to use the Distributive Law, as if the question was 3 × (5 + 4) ! Colton was a senior, and older than most—probably 23 or 24 years old, and the Distributive Law is generally taught by 6th or 7th grades (under the current Indiana standards, it’s taught in both). So he’d undoubtedly been confused about this for well over 10 years, and it takes a long time to unlearn something that deep-seated.
(b) Problem unrelated to course content. At the beginning of the semester, “Isolde” really seemed to want to do well, but she did several odd things that hurt her grades enormously. For example, she had a graphing calculator but not a non-graphing one. I didn’t allow graphing calculators on quizzes/exams, so she started the first quiz/exam without any calculator until I noticed and loaned her one. Exactly the same thing happened on every other quiz/exam! She kept missing classes and even exams, and she never came to my office hours; she blamed all of that on transportation problems. And she repeatedly forgot important things. Perhaps she had tremendous family responsibilities, or she might have had ADD, or both. But she never told me what was going on, and, sadly, I couldn’t find a way to help her.
Example (b) is clearly related to my What I Learned item #1, “students really are responsible for their own learning”; but example (a) is something else.