("Tales from the Classroom" is a new feature posted occasionally here at this blog. All tales are true and present matters about which I have personal knowledge. The following tale relates the story of something that occurred in September 2013)
Upon helping Student B for a few minutes, Student A discerned that Student B's mathematics skills were woefully inadequate for embarking upon a study of precalculus.
Student A (frowning with dismay): What math courses did you take in high school?
Student B (cheerfully): I had a hard time with Algebra I. Next, I tried Algebra II, but I failed. I took a class in function and did okay with that. I'm taking calculus now because I heard that calculus was easier.
A few weeks later, the day of the midterm exam...
Student B (euphorically): I'm going to get an A on this exam. My fourth grade sister tutored me over the weekend.
A community-college adviser's signature was necessary for each student's admission to classes, and many courses have prerequisites. Nevertheless, the precalculus class in which Student A and Student B are enrolled contains many students clearly incompetent to undertake the study of mathematics at that level — nearly half the class mired in this predicament. Concepts which stump the students include exponents (what they are called and how to work with them) and substituting a value for a variable.
The professor, seasoned but not close to retirement, is at a loss as to what to do. If he fails half the class, he likely loses his job and all benefits connected thereto. If he doesn't fulfill the requirements for the course, none of the students in the class will have the tools they need for their later studies in mathematics.
Thus we see the state of American education today.