# College Math Teaching

## September 20, 2013

### Only a narrow view of the students on a campus

Filed under: basic algebra, editorial — Tags: — collegemathteaching @ 4:52 pm

My recent experiences on teaching college mathematics has shielded me from a significant segment of the student population. While I have taught across the curriculum, mostly I’ve taught courses designed for science and engineering majors.

Today, I sat in a so-called “college algebra” course (remedial) to evaluate a new faculty member. This faculty member was getting excellent class participation; I was favorably impressed.

He was teaching them how to graph a polynomial that has been factored; example: $p(x) = (x+1)(x-1)(x-2)$. He wanted them too see if the graph of the polynomial was above or below the $x$ axis; in particular he was interested in the graph of $p$ between $x = 1$ and $x = 2$. So he chose the test point $x = \frac{3}{2}$ and asked the question “is $\frac{3}{2} - 1$ positive or negative?

Many sang out “positive”; a few said “negative” (seriously) but……one student said “$\frac{3}{2} - 1$ can be positive or negative.”

I started to laugh out loud but had to work to stifle it.

Later, when talking to this faculty member, I asked if the person who said “it can be either positive or negative” was making a joke. The faculty member looked down and said “uh….no.”.

So, what is going through the mind of a student who says such a thing? I don’t know for sure, but I think that it might be something like this:

At Cal, he was among the hardest workers in the dorm, but he could barely keep afloat.

Seeking help, he went at least once a week to the office of his writing instructor, Verda Delp.

The more she saw him, the more she worried. His writing often didn’t make sense. He struggled to comprehend the readings for her class and think critically about the text.

“It took awhile for him to understand there was a problem,” Delp said. “He could not believe that he needed more skills. He would revise his papers and each time he would turn his work back in having complicated it. The paper would be full of words he thought were academic, writing the way he thought a college student should write, using big words he didn’t have command of.

Sometimes students are so lost, they don’t realize that they are lost; they don’t understand that the material WOULD be clear to them if they understood it. They don’t see that there IS something to understand; it is almost as if the responses that they hear the other students given are random phrases with certain key words and key phrases in them. That these key words and key phrases actually have meaning is lost on them.

As far as whether these students should even be admitted to begin with is beyond the scope of this blog; personally, I am a fan of the “prep school” approach that the service academies use (a year to address a student’s academic deficiencies prior to being admitted to the main campus) but I haven’t studied the data there.

The issue to me: what does one do with these students? Some MIGHT reach the point where they realize that there is a point to it all, but many won’t.