# College Math Teaching

## March 5, 2014

### Comparing calculus exams…..and university students

Filed under: academia, calculus, pedagogy — Tags: — collegemathteaching @ 2:04 am

Some people tried to argue with me about calculus; they seemed to think that calculus at one institution is the same as at another one.

Hardly.

Not only can courses vary in terms of topic and difficulty, but so can exams…and the difference might be very subtle to those who are unfamiliar with giving and grading exams.

Here is one example: suppose you want to examine the students on the Mean Value Theorem. How might you do this?

1. State the Mean Value Theorem (yes, the bad students usually can’t even do this).

2. State and prove the Mean Value Theorem (prove using what?)

3. Let $0 < x < y < 1$. Show that there exists a $c$ between $x$ and $y$ so that $y^2 - x^2 = 2c(y-x)$.

4. Use the Mean Value Theorem to show that $|cos(x) - cos(y)| \leq |x - y |$

5. Show that for all real $x, y, |cos(x) - cos(y) | \leq | x-y|$

Not only do these questions vary in difficulty, they may or may not have been covered directly in class prior to the exam; that makes a big difference.

Now about the students
We are doing a job search. We have someone who is interviewing; he currently teaches at a school whose student population has a median ACT that is about 3 points higher than ours. BUT his institution is “technical majors only”; they don’t have much (any) of a humanities, communication or education program. So, if you compared their calculus student ACT to our “engineering/science calculus” ACT, the difference shrinks considerably, if it remains at all. But our department does teach the “business calculus”, “baby stats” and “math for poets” courses…and he will NOT be used to that type of student.