I am teaching a calculus class for business this summer (6 students) and all of them do not have the math background needed for the class. We are supposed to cover derivatives and integrals, but they don't even know how to evaluate functions. For example, I gave them $f(x)=x^2+x$ and the following happened:
- 4 of them had no idea what $f(2+h)$ was supposed to be. They tried $f(2+h)=2^2+h$, or $2^2+x$ or similar incorrect expressions.
- 2 of them had no idea what $f(2)$ was supposed to be. They tried $f(2)=(x^2+x)\cdot 2$ (yes, $x^2+x$ times 2), or $2x^2+2$ or $f(2)=fx^2+x2$, or similar incorrect expressions. After spending nearly the whole class explaining how evaluation works, they understood how to compute $f(2)$ and had some idea of $f(2+h)$. Then, I changed to another function $g(x)=-x^2+1$ and they were stuck again.
- The example above is just an example. Please do not give suggestions about how to explain evaluation to a student.
- I have taught the course before, but this problem has been getting worse and worse over the years
- I have no idea how they passed previous classes
- This is the last math class the students will take
- My chair and dean verbally told me students are getting worse (math-background-wise) and that nobody cares what I do with this particular class. They won't say that in writing, of course.
My questions are:
- How to deal with the problem of ALL students having a very poor background?
- Do I just teach the required topics and likely fail all students?
- Do I spend time making sure some students understand even if I only cover 50% of the material?
- Do I just curve the grades even if they do not understand the material?