This week I was teaching yet another review topic in my Pre Calculus class. I realize that the first weeks of this class are not exciting to teach because it’s like re-teaching everything that they learned in their prior math classes. All of the topics are ones that I know are taught in the earlier classes. But you’d think it was the first time some of them had ever seen it.
So we work our way through Real Numbers, Exponents and Radicals, Polynomials and Factoring, Rational Expressions, Solving Equations, Solving Inequalities, etc. We started Rational Expressions on Wednesday. Fractions. Everybody’s favorite topic.
After I taught my lesson and had time to think about all of the thoughts running through my head while I was teaching it, I decided that as a teacher you have to be the ultimate multi-tasker.
Here’s what was coming out of my mouth:
When you’re simplifying rational expressions, the key to your success lies in your ability to factor. You must factor the expression on the top and the bottom of your fraction completely before you start reducing. For example, let’s look at this problem: x cubed minus 4x over x squared plus x minus 2.
I continue to go through the example. I’m not going to write out every word I said because I think you get the idea that it’s technical and not extremely exciting.
Here’s what’s going on in my head:
What’s up with Sara and Jake? Are they dating? They’re sitting way too close and where are their hands? I try to shift so I can see underneath their desks. I can’t tell where her left and his right are. I can’t exactly say something right now.
Oh… Carrie’s not paying attention. Is she texting with her hand in her purse? Do they think I’m that stupid?
Is it hot in here? Do I need to open a window?
Scott isn’t taking notes. I wonder what’s up with that.
Uh oh… There goes another note between Jane and Bill.
Rose seems to be finishing up her homework instead of paying attention.
I know this is not exciting, but c’mon, let’s see you try to make a song and dance out of this material.
So the final answer is x(x-2) all over (x-1). Now, when you have a problem where it asks you to divide two rational expressions you have to remember to flip and multiply the second fraction. Here’s another example…
Ok… So I may be exaggerating a bit. But in order to be a good teacher, you have to be aware of everything going on in your classroom while you’re trying to actually teach. I’m lucky this semester because I don’t think I need to really worry about the possibility of a personality clash between two students escalating into a fight. But that’s a key observation that every teacher needs to make to avoid the horrible situation of a fight in your room. You also have to watch for cheating, how kids are treating each other, confused looks, light bulbs going on or off in their heads, and the list goes on. Of course you have to do this all while you have numerous interruptions of passes being delivered, students coming in late, phone calls from the office, sick kids needing a pass to the nurse, … And while noticing all of these things you have to decide when to confront the distracting behavior and when to ignore it and how you’ll approach each student who is not on task.
I have no idea if I had this talent prior to becoming a teacher. I’m guessing I did, somewhat. But I sure didn’t practice it like I do now. After 12 years I think I’m getting pretty good at it. And I must say that not everyone can do it. For everyone who thinks that teaching is just that: teaching. You’ve got another thing coming. Even though it’s a common opinion – not everyone can do this job.