As I mentioned, my school runs a block semester schedule—we cover a year in a semester, four classes each semester. So Monday starts the new year.

I will be teaching Geometry and Algebra II again, although the geometry class will be 10-12 instead of the freshmen of my first semester. One Geometry, two Algebra IIs and, for the first time, **pre-calculus**.

Note that I am teaching four classes, which means no prep period, and 33% more pay. I am pumped. Okay, a little bit because of the pay, but mostly for two reasons.

First: Admins don’t give a teacher extra work unless they are happy with the teacher. I have now had two observations with notes so glowing that I keep checking back to see if the name is mine. I know I’m a good teacher. I’m just not used to the principal agreeing with me. More importantly, the administrators seem to like me for the right reasons. Both the principal, who did my observations, and the AVP of the master schedule (the one who reawakened my algebra terrors ) came to see me teach before making the decision. They liked my explanations. They like the fact that I pass most of my students. They like the fact that I engage kids with low abilities or incentives, a skill that that all previous administrators have used for their own purposes, but never acknowledged as rare or useful. It’s very nice, if unusual, to be appreciated.

Second: In my state, a math credential has two levels, basic and advanced. Advanced math teachers are much thinner on the ground. Yet in my first three years of teaching, administrators have on several occasions given advanced math classes colleagues who had *not* yet passed the tests necessary for advanced math, despite several attempts. They made this decision despite the fact a penalty is attached to using unqualified teachers, requiring a letter home to the students’ parents alerting them to the unqualified teacher. The administrators took this penalty instead of giving me classes that I was actually qualified to teach. Such madness as this is pretty normal, and it’s why teachers laugh hysterically when education reformers yammer on about giving principals complete control over hiring and firing.

As a result of these previous administrator decisions, I have never taught an advanced math class. Not once. Ever. I have no idea how to teach pre-calc. I have no idea how to talk to students who are taking a math class for some other reason than “I need it to graduate”. I have even less idea how to teach an entire class of people who–please, please, PLEASE god—know a positive slope from a negative one. I can’t wait.

I have a friend who is a professor at an elite public university, in a field that requires a lot of math. Back when I was first tutoring and learning math on the job, and got hired to teach a student pre-calc, I asked him “What topics are in pre-calc?” He sniffed, snootily, and said “Precalc isn’t a subject. It’s an administrative category.” I must have learned a lot of math in the intervening years, because I get the joke now.

I’ve got a book, so I’ll figure it out. But if any pre-calc teachers have broad topics to organize around, I’d love to hear about them.

In addition to teaching a full-schedule, no prep period, I start my yearly ACT class on Monday, and in a month I begin my AP US History review classes, two of them. I dropped my English enrichment class, though, so for the first time in seven years, my Saturday mornings are free. I love late winter/spring. But with all this extra money I may just take the summer off for the first time ever.

January 27th, 2013 at 12:23 pm

Dear Educationrealist !

I am fascinated by your work.

Send me e-mail. I have some family traditions to share,

which may (and may not) be useful in your work.

Your F.r.

January 27th, 2013 at 3:28 pm

I’ve taught precalc a number of times at a state college. I think of it as building up a vocabulary of functions you need before doing college math. Polynomials, rational functions, exponentials, logarithms, and trig functions don’t really have anything to do with each other, except that you need to know these functions to have examples for calc.

One of the big early conceptual things to do is to emphasize how to tell if a word problem is linear or exponential (things change by the same amount every year or by the same percent)

January 27th, 2013 at 3:43 pm

Thanks very much. So a lot of it is just building on what they learned on second year algebra and trig, deepening it? Then onto rational functions, particularly graphing them (which at my school, isn’t covered in earlier years). How important are polar coordinatees and vectors?

Thanks again!

January 28th, 2013 at 2:30 am

There’s an old supposition that if a student goes on in mathematics that they’ll be taking calculus. The calc professor will more or less assume the student knows the rules for all those functions and so that’s what precalc is seen as providing at the college level. Of course, in reality a lot of your students are more likely to take statistics and never see calculus so they’d be better served by spending more time on fitting equations to data.

Some precalc books do this weird thing where they try to over-motivate calculus concepts. For example, when introducing average rate of change for a function they’ll define the term “difference quotient” but it’s really ridiculous to have a special term for this if you’re not going to take it’s limit and call it the derivative. All of the books dance around the concept of limit since the rigorous treatment is too hard, but it’s necessary to talk about asymptotes which are important for understanding the rational functions.

Our college did cover polar coordinates in our precalc course, but the student wouldn’t see them again unless they took complex analysis as a senior. You’re probably safe de-emphasizing it or skipping it if you can get away with it.

We didn’t cover vectors and I think you’d be pretty safe not doing it. They’ll use vectors if they take linear algebra, multidimensional calc, or a serious engineering or physics course. But if they’re in that type of class, they’ll pick up what you’d teach them about vectors on their own.

January 28th, 2013 at 2:40 am

A friend of mine–a real mathematician–swears that polar coordinates must be covered in pre-calc, but I can’t understand why, since they aren’t a big part of the AP curriculum

Thanks again for the advice. The only thing I’m missing now is an incoming assessment test, but I think I’m just going to throw together some algebra II and trig questions, as well as some conceptual questions on various areas and see how they do..

January 28th, 2013 at 4:46 pm

A little bit of polar coordinates is useful is they are also taking physics. In physics they will have to add a horizontal and vertical vector to get a total vector, and resolve a total vector into horizontal and vertical components. The former is simply going from rectangular to polar coordinates without using the terms, while the latter is the reverse.

If you are thinking about doing anything like this, you should check with the physics teacher. This is usually done fairly early in a physics course.

January 28th, 2013 at 10:27 pm

“As I mentioned, my school runs a block semester schedule—we cover a year in a semester, four classes each semester. So Monday starts the new year.”

How wide-spread is this calendar in CA? Math apps started really moving this weekend and I’m trying to figure out why. 🙂 Thx.

January 29th, 2013 at 3:42 am

Not very. I only know of one other school that used to do it, and I’m not sure they do it anymore. It’s hell on test scores.

April 2nd, 2013 at 7:40 pm

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January 27th, 2014 at 11:44 pm

[…] they noticed the kids are doing well. I know the first decision to put me in pre-calc last year was deliberate, a decision to give me more advanced classes because they wanted a higher pass rate. But I honestly […]

January 3rd, 2016 at 3:56 pm

[…] then met with the AVP in charge of the master schedule to insist I wasn’t qualified to teach a newly scheduled precalculus class. The AVP went to the principal, the principal advised him to watch me teach, something none of the […]

February 14th, 2016 at 11:40 pm

[…] High schools determine staffing requirements based on the number of sections the district gives them. The administrators divide the sections by the contractual class load—very often five, for six-period days. In our school, it’s three. (Yes, we teach three 90 minute classes and one 90 minute prep, and then we start all over again mid-year.) […]

May 27th, 2016 at 3:48 pm

I would definitely cover vectors. They are so common in physics. Especially if your algebra 2 classes blow them off–in that case we can say “it was as if they were never taught”.

Yes, physics covers vectors too, but physics is that much harder when all the math has to be developed as part of the course on top of the physics. The duplication is actually nice to drive things home. In physics class, you can think “I know this is a math thing from math”. In math, you can think “this is like velocity and acceleration”. The little bit of switching back and forth really makes the ideas stick better and be easier.

I had same insight when I took (basic) fluids and (basic) circuits. Adding resistances or head loss in series or parallel. It just helps to be able to think in EE, oh…that’s just plumbing, not fancy ‘trons. And then in fluids, heck that is just the resistor law we have seen already.

If it is part of the curriculum, I would cover polar coordinates. Actually in general, little worried that your properly expedient methods in the lower level courses to kids that won’t go further will not serve kids right higher up. but who knows.

May 27th, 2016 at 3:56 pm

I’m actually not really sure what precalc is.

My school, after trig or alg2/trig, had a full semester of “functions”, which included complicated inequalities (number line hell, manipulations of inequalities, etc.), and simple derivatives/antiderivatives (no integration by parts, product rule, volumes, centroids, etc…..but the basic derivative and antiderivative of common functions. Max/min/inflection points were covered.

After functions, was a full semester of analytic geometry. Lots of graphing functions. The baby calculus from functions is useful here for critical points. Also covered were polar coordinates and transformations/rotations. The latter I just remember being algebra bookkeeping hell, but it is what it is.

Year after that was used for a full year of Calc BC or Calc AB. Almost no students took one and then the other because acclerated seniors were the main audience for calculus. Any hyperaccelerated kid would take BC of course. AB was full year, just an easier senior class option than BC. Little artier kids took it or those who got by but struggled a lot in precalc. Or just wanted to enjoy senior year!