I am a parent of a HS freshman who is taking precalc/trig now. His teacher is pretty much useless; my son has to come to me or my wife (let's just say that each of us has about 100+ college and graduate credits in math, and Ph.D.s in math intensive fields) to ask for explanations, and after almost a year of trig, his active formulae include mostly $\sin^2 x + \cos^2 x=1$ (which he knew anyway as Pythagorean theorem), and I am not sure he can do $\sin(x+y)$ without referring to his cheat sheet.
I am seriously considering going to the high school math department and asking to pull my son out to homeschool him for AP Calc BC using the materials that I trust (which would probably have to include the proofs of Lebesgue-Borel lemma and the extreme value Weierstrass theorem; I learned them when I was 15 or 16, so I don't see a big deal here). My big question is:
how do I approach high school math department without completely pissing them off?
My son still has to be there for three more years. His precalc teacher actually runs the school math team (although I think they missed organizing AMC 10 this year, partly because the school was closed due to snow on the primary competition day). Finally, I want somebody to write a ref letter to attest to my son's math skills when he graduates.
The specific complaint my son has about the teacher is that he does not explain things enough, and he does not explain things well. My understanding of a typical way the teacher interacts with the students is that he gives a bunch of definitions, and then gives assignments, many of which are defined as vaguely as "Well, here is a full set of 60 problems. Work about half of them; there will be 12 from this set on the test". All of the assignments are on the publisher's website. Technology is a blessing, of course: if a student cannot factor $2x^2-5x-3$, the system will hold student's hand, show calculations step by step, and then generate another $x^2 + 3x +2$ to let students show that they've learnt something. However, in my view, the technology should untie teacher's hands so that they are offer more explanations and examples worked through in class. The technology can be used to test the basic knowledge and afford a C grade; however, the grade of A should be earned by doing proofs and derivations.
The worst thing, though, is that I finally found out what the dreaded rote memorization is. I heard everybody talk about it as a problem in American math education; I now know what this phrase actually means. I don't think it hit my son as hard in any of the earlier classes as it did in this precalc. The most recent example from his precalc class is the partial fraction decomposition: $$ \frac{x^2 - 3x + 5}{x^3 - 2x^2 + x - 2} = \frac{\mbox{stuff}_1}{\mbox{linear binomial}} + \frac{\mbox{stuff}_2}{\mbox{quadratic polynomial}} + \mbox{may be more stuff like that} $$
The teacher then threw in the concepts of distinct linear factors, repeated linear factors, distinct quadratic factors, repeated quadratic factors -- my son had the terms in the notes, but not the definitions (OK, let's give the benefit of the doubt and assume that the teacher actually gave these definitions in class, and my son failed to copy them down properly; in the end, we had to Google them to make sure we got them right.) The teacher then said that this material is important because they will use this later in integration. Fine, I agree that it is useful when integrating rational functions; but why on earth throw this useless information at this stage, when integration is like a year ahead, and nobody in the class has any clue what the teachers just said? Why asking for these terms on the test? Knowing that $\frac{x+3}{(x^2+5)^2}$ is called repeated quadratic factor is not helping a student to do the calculation proficiently. I would introduce this decomposition when I would need it when we touch the integrals of $1/(x+a)$ and $1/(x^2+a^2)$. Without context, this information and computational method is going to be lost by the time the (next) class arrives at these integrals, so the (next) teacher would have to work through this, anyway.
A minor complaint that my son had was that the teacher did not break down the class efficiently into small groups when small group activities were offered. In my son's view, a better division would be to stratify the class by knowledge/ability, so that more advanced students would work on more complex problems. (In that partial fraction decomposition, what should stuff1 and stuff2 consist of? What degrees other irreducible polynomials could have? Can you create, and solve, a meaningful example with repeated irreducible factors of a sixth degree?). I hear my son here, although in my own teaching experience (a few years of undergraduate teaching in a couple of US universities), I would sometimes make sure that I have at least one strong student in each small group to really explain to other students what's going on. May be my son's teacher does the same; may be he does not really care how the knowledge is being transferred.
I can form two sorts of implications for the calculus class that is coming up next fall, and none of them is promising.
- The math department / district does not have a quality control system in place. My son said that he wanted to give his negative feedback the way college students do in their student evaluations (and, I believe, in evaluations he gave in some of his other educational institutions). If this is true, then there is no guarantee that the next teacher will be any better.
- The math department / district is simply fine with math being taught that way. If this is true, I don't want them to touch my son's math education, as I still hope he'd grow to love math.
Either way, I see my son better off taking his calc class off the grid -- with me using proper Russian books, or through AoPS, JHU CTY or Stanford EPGY or Coursera or whatever is going to both challenge him and provide better explanations than his school could.
My big plan for my son is that he takes AP Calc BC next year, and then takes stuff like Linear Algebra and Abstract Math online.
