The first day of class, I have a room full of students that I know nothing about. Some of them don’t belong in the course. Rarely, they don’t belong because they know too much. More often they don’t belong because they don’t know the prerequisite material.
I don’t start teaching from scratch. I assume calculus students know how to solve quadratic equations and Intermediate Algebra students can solve linear equations. I do a certain amount of review, but I can’t review everything. When students make too many mistakes on the prerequisite material, I know they have almost no chance of passing the course.
Recently I had Intermediate Algebra students who could not solve
– 8 – x = 0.
This is a prealgebra problem which is taught in middle school to most students. I knew the three students who were stuck on this problem had little chance of passing Intermediate Algebra.
A single problem may be just a brief mental block, but these students repeatedly made mistakes on material they should have known.
The second problem is with students who do not work. In Intermediate Algebra the homework is online. They have at least a week to do every assignment and can do it as many times as they like to get credit. I can see how long each assignment is open, and the students who do all the assignments with at least 75% correct, average less than 2 hours a week. This is not excessive for a four credit course.
Last semester I had a class with the worst pass rate I have ever had, but all of the students who failed either did not do their homework or did not know the prerequisite material, usually both.
 In high school it is Algebra II