### We All Could Have Guessed It

Since the university is paying me $7000 (+ benefits)* to teach the Calculus Circus, I spent part of this afternoon observing my TAs (part of my job description) instead of devoting the entire afternoon to fixing my computer science homework.**

Today my students were working on increasing and decreasing functions. Finding critical points, determining over what intervals functions were increasing and decreasing.

One TA asked the students to consider the function

What my students couldn't do:

For

Needless to say, they are completely unable to find the domain of any functions.

With a simpler problem they had 6

I'd have a lot easier time teaching calculus if my students knew algebra.

*My TAs' workload adds up to two full-year FTEs, so the TAs are the expensive part of running the class. Costs the university two full-year grad tuition waivers, two full-year grad assistantship-salaries, and whatever else a grad student costs. Add that to what they pay me, the cost of replacing the batteries in the wireless mic (and all the other room and technology costs). When you compare that to what the class brings in in tuition, the university probably nets almost $100,000 on the course.

**It now grades at 89/100 as I clean up the annoyances of output-matching. More worrisome, my program in its current state reveals the sort of wanton disregard for efficiency or memory-management that you would expect from me, considering my background. Fortunately I have almost a week to fix it.

Today my students were working on increasing and decreasing functions. Finding critical points, determining over what intervals functions were increasing and decreasing.

One TA asked the students to consider the function

*y*= 2*x*+ 3. Instead of blinding taking the derivative and trying to set it equal to zero, the students knew that it was a line and that since it had positive slope that it was always increasing.What my students couldn't do:

For

*f*(*x*) = 5/(*x*-2), they could find*f*'(*x*) = -5(*x*-2)^{-2}. They could not not follow when the TA rewrote it as -5/(*x*- 2)^{2}. Similarly, with a more complicated function, they didn't see why (1/2)(*x*^{2}-1)^{-1/2}(2*x*) was*x*/sqrt(*x*^{2}- 1). And with all these expressions they couldn't figure out how to find the*x*values where the expression equalled zero or the*x*values that made the expression undefined.Needless to say, they are completely unable to find the domain of any functions.

With a simpler problem they had 6

*x*^{2}+ 12*x*= 0. They factored it as (6)(*x*)(*x*+ 2) = 0. They then declared the roots to be 6, 0, and -2.I'd have a lot easier time teaching calculus if my students knew algebra.

**Update:**Eek! It's not just the students! One of the TAs (a section I didn't visit today) just emailed the students in that section correcting a very alarming algebra mistake.*My TAs' workload adds up to two full-year FTEs, so the TAs are the expensive part of running the class. Costs the university two full-year grad tuition waivers, two full-year grad assistantship-salaries, and whatever else a grad student costs. Add that to what they pay me, the cost of replacing the batteries in the wireless mic (and all the other room and technology costs). When you compare that to what the class brings in in tuition, the university probably nets almost $100,000 on the course.

**It now grades at 89/100 as I clean up the annoyances of output-matching. More worrisome, my program in its current state reveals the sort of wanton disregard for efficiency or memory-management that you would expect from me, considering my background. Fortunately I have almost a week to fix it.