The Progression of a Weak Student

Every semester, there is a clear track that some students seem to fall into, which is roughly as follows:

After the first homework is graded: "I had a really bad time on this assignment, but I'm going to work really hard and I'm going to bring my grade up."

After Test 1: "I'm going to study hard and do really well on my other tests, so doing so badly on this test won't hurt me so much."

After Test 2: "I'm going to do really, REALLY well on the third test and final, and then those will bring up my scores on my first two tests."

At some point in the semester: "You drop the lowest lab/homework/quiz/whatever score, right?"

After Test 3: "Does the final exam grade replace your lowest test grade if you do better?" (I can guarantee I will get this question from at least one student as a test is being turned in. It does not bode well for the student's performance on that test.)

After the Final: "Is there anything else I can do to bring my grade up?" (Hint to my students: There's a reason we use the word "Final".)

Of course, all of this is complicated by the fact that the weakest students in my classes are those who are really bad at math, and therefore can't correctly average their grades. A friend of mine had a student who got an 80 on the first test, failed the second test miserably, and didn't come to the third test at all. My friend was startled when the student (who hadn't been coming to class or turning in homework either) showed up to a review session for the final exam. She took the student aside and asked, "You do realize you can't pass the class, right?" The student was shocked: "I thought I had a B!"