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.

  1. 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.
  2. 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.

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    $\begingroup$ @StasK, this REALLY struck a chord with me as an American undergraduate math major who recently escaped the horror of high school education. I remember being penalized for leaving radicals in the denominators of fractions, taking otherwise perfect tests or quizzes in pen, and being forced to complete massive homework assignments full of mindless, tedious rote computation. I wish people could've told me from an early age that this is NOT what math is all about, and I feel like I'm still trying to rekindle my curiousity and creativity that was crushed from my 12 years in public education. $\endgroup$ – Kaj_H Apr 22 '14 at 20:08
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    $\begingroup$ @dtldarek, this is definitely way out of scope for Academia.SE -- they don't even take questions about undergraduate research. I can reasonably expect math educators to start pointing fingers at me saying that I don't respect the work of a high school teacher, so the question will endi up with -15 score (which is already happening here -- I am getting as many upvotes as downvotes on my question) and no usable answers. Well... if you think it does not belong here, flag it :). $\endgroup$ – StasK Apr 22 '14 at 21:28
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    $\begingroup$ @StasK I agree that this would be a better fit for MathEd.SE, and I doubt you'll get downvoted. In fact, given the general culture here and on MathEd.SE (which is an offshoot of this site), you might even get upvoted just for badmouthing high school education (just look at how popular Lockart's Lament is around these parts...). I wouldn't always suggest moving a question about learning math, but this is a very in depth and very education-specific question. $\endgroup$ – Jack M Apr 23 '14 at 0:52
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    $\begingroup$ Again, what prevents you from taking the active role, without having to pull someone out of school? I know this sounds demanding, but I think you're expecting too much from High School teachers. I would contend that very few people with good Math/Science skills would take a High School teaching job. Why didn't you take such a job? As for standardized testing, few High School teachers have any choice but to teach for those tests--that's dictated from up above. In fact, most teachers have very little latitude in what they teach any more. Even a good teacher has almost no freedom. $\endgroup$ – T.A.E. Apr 23 '14 at 2:05
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    $\begingroup$ "I can reasonably expect math educators to start pointing fingers at me saying that I don't respect the work of a high school teacher, so the question will end up with -15 score" -- ha. I'm sorry that your opinion of educators has reached such a low level! Obviously your tone is a bit nonconstructive, but your question is excellent! Welcome to ME:SE. $\endgroup$ – Chris Cunningham Apr 23 '14 at 14:57

Talk to math teachers as you would talk to any other professional with whom you share a common interest (the education of your son).

Note, I have addressed this to respond to you specifically in some areas, and I have had to make some assumptions in some places. I did this, in part, to try to make this answer more generally helpful (because the title is so general). So, please don't take some of my later assumptions as me presuming your thought processes.

  • Be clear about what you want

A lot of the response you've gotten so far is sympathetic, agreeing with your concerns about school math, or focused on suggestions for what to do with your son's education. That's because the question itself has a bit of a "blowing off steam" quality to it rather than a "focused on a specific outcome" quality. In a way, that's good. Better that you do that here, because your son's math teacher does not want to be a sounding board for you blowing off steam.

In parts, your question seems to want working groups chosen differently, though you don't entirely agree with your son. You also seem to want the teacher not give certain information at a certain time. You also talk about pulling your son out of school. And wanting a letter written to attest to his math knowledge. Is it all of the above?

  • Want something realistic

The question is vague on what you expect the teacher to do as a result of your interaction, so I can only guess at what it is you hope will change. The list of things I was able to discern from your question had items that were in conflict with each other, so right off the top I would say to make sure what you want is something the teacher is able to provide.

As I tell my kids, always ask the person who can actually help you. Likewise, ask for things a person can actually provide.

  • Frame your question in a efficient way

Here I am assuming your goal is to address what the teacher is teaching. Whatever class your son is in, there are learning outcomes defined for that class. This is part of what is guiding the teacher. Some of that may be dictated by standards, but an advanced class may go well beyond state standards. Whatever the situation is, you won't know until you talk to the principal or perhaps even the teacher to get some idea of what the end-goal is for the class. If the class goals are different from what you would prefer, it may not entirely be in the teacher's hands.

But my point here is that a better understanding of what you want will help you then seek information to help you frame your question (i.e. in the context of these learning goals for the class, you may be concerned that what your son is currently doing will not help him reach those goals.) Frame the question in a way that helps the teacher respond to you constructively.

  • Don't talk about your PhD

Credentials aren't a prerequisite for talking to your son's math teacher. In reality, what does mentioning that actually establish? In some contexts we might mention our credentials to establish a basis for our expertise. But your concern here is as a parent. Your experience and knowledge is certainly helpful, but it's helpful to you and not to the teacher. If the fear is that you will not be taken seriously, your authority is in your status as a parent, not a mathematician.

My point is, examine how you position yourself so that it is focused on smooth communication, a sense of common purpose, and how the teacher can help with the goals you are interested in. If your intention is not to intimidate the teacher, then you want to make certain you are not doing so inadvertently.

  • Assume professional expertise / plan for a conversation

Teachers are constantly challenged as professionals. Their sense of profession is under siege from both parents and policy makers. Be aware of this, because if you say things that indicate you are essentially there to add to the chorus, you'll just sound like the chorus. You want to be someone who has a concern you both can address together constructively. You don't want to be part of a chorus.

As an accomplished math learner, you may underestimate the role of pedagogical content knowledge (Shulman, 1986) in teaching. The teacher may know quite a bit about teaching math that you do not. Hopefully, the teacher also has some understanding of your son's math learning that you do not have. If you're not ready to accept this, then you are going in ready to dictate rather than to have a conversation. Communication is not one way. As you titled your question, you are seeking to interact with the teacher. You want to tell the teacher something, but the teacher may also have something to tell you. Approach the teacher with your goals, but recognize that the teacher may have suggestions you have not yet considered.

And finally, I hope your son has a great high school experience and a smooth transition toward who it is he wants to be.

Best of luck to you.


Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4.

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    $\begingroup$ Thanks, JPBUrke. This is very good answer for a very vague question. $\endgroup$ – StasK Apr 23 '14 at 15:41
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    $\begingroup$ Thanks, @BenjaminDickman - I wanted to put something in there to note that I didn't want any of my assumptions to imply I thought I knew how the asker was thinking. $\endgroup$ – JPBurke Apr 23 '14 at 16:47

Ah, yes. My sympathies... maybe the question should be moved to another site, but, pending that... and/but the U.S. environment will not change significantly any time soon, for many reasons. I have my own acquaintance through my kids with better-quality [sic] U.S. education, at the supposed high end.

In that context: first, also I am acquainted (through colleagues and general awareness) of other countries' education systems and, especially, mathematics. The "former Soviet" system, as well as many "Soviet bloc" countries, but also to a lesser degree Western European countries, compelled students to take mathematics seriously. The point is ... "or be left behind".

Not only does the current U.S. system honorably emphasize "breadth", but it does also not judge so harshly. For some decades, and, even now, in the U.S. people have many further chances after earlier failures. There is no nation-wide stigma/reward. This is a good thing in many ways, but it is bad in that it allows a certain fraction of people to not try hard, to think that there will always be one more chance, etc.

In that context... :) ... there is simply no one to turn to for high-school tutoring at the level of the old Soviet and eastern-bloc mathematical establishment. At the same time, ... did it ever really matter? To the extent that "mathematical prowess" was a low-overhead proof of machismo or value-to-the-state, or to corporate entities, aggressive orthodox low-level mathematics (which includes Olympiads, btw) was only of interest as a demonstration of aggression and quickness, not of wisdom about structure of the universe, to say the least.

So, as in my own childhood, hoping that a kid has access to books (or, ... the internet?), there is no lack of opportunities to learn many things, including much mathematics. The question of learning to feel an obligation to learn such things is different. This sense of obligation is not currently available in the U.S. Not clear to me that it should be...

I do explain to my own daughter that the "standards" promulgated by k-12 schools, and even good universities, and even graduate schools, are ... sub-minimal. The current culture makes understanding such things an abrupt transition. No easy way, I fear. But, in her early 20s, my daughter does seem ever-more able to understand my point to her (for almost 20 years!) that she (and anyone) should embrace their studies, not thinking first about what's on the exam, and how to minimize effort (as game-theoretically rational as that surely is!), and view "school" as an annoying side-effect or incidental. I tell the same to my grad students.

So, to paraphrase, it's not about the school curriculum at all... which should be only some formality like a driver's license test... but what one (=the kid) wants.

(And, of course, kids have a hard time understanding such a message, given the ambient culture.)

Best wishes! :)

Oop, and the operative advice about how to approach the H.S. teachers to get them on a better track... is... don't. They are not equipped to understand the mathematics, and will at best be alienated by your raising the issue. Srsly. I've been there... offering my advice to my local high school, and been rebuffed on the grounds that, while I have a Ph.D. in math from a fancy school, I do not have a license for teaching H.S. math in Minnesota. That kind of thing. Better not to make yourself crazy, and not irritate the locals.

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    $\begingroup$ +1 for "it's not about the school curriculum at all... which should be only some formality like a driver's license test... but what one (=the kid) wants" Also, regarding your comment "Srsly. I've been there... offering my advice to my local high school, and been rebuffed ...", my comments in this 12 May 2006 math-teach post at Math Forum may be of interest. $\endgroup$ – Dave L Renfro Apr 23 '14 at 13:50

how do I approach high school math department without completely pissing them off?

If this is really the question, then I suggest you don't approach them at all...

What exactly are you expecting? Chances are that the high school teacher who does the Calc class will be ok/not great. You might luck out and get an awesome teacher, but don't bet on it. If your son really wants to start learning math on his own, then he should just learn math on his own. There are a plethora of online resources you could use, and many state universities run enrichment programs for advanced math students.

If you simply explain to your high school that your son would like to enroll in such a program, I'm sure they would be more than happy to accommodate him. My experience has been that your typical high school is not very capable of handling "off the charts" students, but they get quite excited when they can help to arrange for such students to pursue their studies elsewhere. I think your son's teachers want him to succeed, even if they may not be able to mediate that progress themselves.


The teacher may be doing better than you can imagine, teaching a large (likely) group of students, very few of whom have any interest in math. I think it is silly that you blame the teacher. (Sure, the teacher might be bad, but you give me no evidence to think so.) Yes, the American system has problems. (I am very impressed with the math skills of the people I meet from Russia.) But that is not the fault of one teacher.

I heard very little in your question about what your son desires. Have you been trying to hold him to Russian standards? Does he enjoy this?

I love math. But no one pushed me. (And I do not like working at the pace required by elite universities. Because of that I don't have a PhD, just a masters' degree. I teach at a community college, where we have a number of great teachers. My guess is that you would not judge us as great, because we don't do things the way you think is best.)

You might be trying to feed his hunger for interesting math. That's great. You could homeschool him. You can sign him up for classes with Art of Problem Solving. You might be able to get him excused from his high school math classes, while he stays in school for the rest. Find creative ways to solve the problem, without blaming the teacher.

I do agree that it's silly to teach partial fraction decomposition in precalc, but I can't imagine a teacher who would choose that. Someone higher up made that terrible decision. The teacher would be taking a risk to leave it out. And, as you said, it would be pretty hard to do right by the topic at that level. If you get past your bad attitude about the teacher, there's one topic the two of you would probably agree on.

What you might have to offer is not your knowledge of math, but your knowledge of a different system of teaching. If you can be patient, and think about building connections, you might be able to help with the math team at some point. You might be able to make a positive difference for a number of kids at the school - if you learn to respect the hard job every one of the teachers there is required to do.

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    $\begingroup$ Thanks, Sue, good answer. I have done some math team topics in his middle school, which was private, smaller, and more receptive to my inputs (primarily because the math department head was a real mathematician, cared about learning math properly, and we were on the common wavelength). I taught in college. I have some idea about the ratio of the prep time to the class time. My son picks some of the educational battles (clubs and courses outside STEM -- he trusts my judgement there), while I have been handling the big picture and the domains of my expertise like mathematics. $\endgroup$ – StasK Apr 24 '14 at 13:44

Here is an analogy:

I mailed some ice cream last week through UPS, but they took almost a week to deliver the package and the ice cream melted. This is ridiculous, because I was only mailing it to my next-door neighbor.

Can you believe that they picked up the package, took it to their local delivery center, processed it for an entire day, and then claimed that they could not deliver the package because my neighbor was not home? They didn't deliver it until my neighbor answered his doorbell to accept the package.

I could have just taken the package over to my neighbor and it would have been no problem. UPS is terrible. How can I talk to them without completely pissing them off?

If you are in a unique situation to deliver mathematics to your son, then you should not angrily bust into the school offices. That is not their fault.

They have a system in place that works, on average, pretty well considering that it teaches everyone in an entire country. The system that works on average, pretty well is almost by design not very good at dealing with certain side cases.

Teaching mathematics to the son of a mathematician and delivering ice cream to your next-door neighbor are side cases that should not be handled using the general method.

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    $\begingroup$ Chris, the system makes a rumbling noise and apparently has moving parts, but on average, it puts American high school graduates roughly three years behind their international peers. For nearly every case that I know of a good math student, it is either the product of the gigantic parents' efforts outside the school, sustained basically throughout K-12, or the extreme motivation of the students him/herself, at least through the middle and high school. The system per se simply does not produce. $\endgroup$ – StasK Apr 23 '14 at 15:40
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    $\begingroup$ @StasK, are you interested in the average US high school student or in one particular student? $\endgroup$ – jwg Apr 23 '14 at 15:44
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    $\begingroup$ @jwg, Chris' claim is that the system works for an average student. My response is, "I don't think it does". But either of these are side-tracking from the central question that I have, which is indeed about one particular student. $\endgroup$ – StasK Apr 23 '14 at 15:49
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    $\begingroup$ @StasK My point is not that it works for an average student, but that it is only even intended to work for an average student. The idea that it should work for your son seems outlandish to me (but maybe spending my entire life living in America has shaped this opinion??). $\endgroup$ – Chris Cunningham Apr 23 '14 at 20:51

Sorry, you don't get to decide how the teacher breaks down the class into groups, or at what point they deal with partial fractions. Nor does your son.

If your son is capable of much more, and you and your wife have advanced degrees in mathematics, the two of you should be teaching him math. At least what $\sin(x+y)$ is, and potentially the Extreme Value Theorem.

At this point your son's only problem is that he has to spend some time in a class where he already understands everything (not too much if you make sure that you add depth and rigor to the topics his teacher is teaching, rather than work ahead too far) and he has to spend a small amount of time doing very boring homework. He should be able to cope with this, and certainly won't be the first person to have done so.

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    $\begingroup$ So you are saying, he has to waste ~6-8 hours a week sitting in a poorly run class, and then add some other time learning math in the family? Do YOU have 6-8 hours a week to waste? Also, the problem with the current class is that he does not understand everything, since it is taken so far from the context of whatever field of math it actually comes from and applicable to. Most of my explanations are, "If you were doing this properly, you would have first learned [two months of linear algebra], and only then you would do Gaussian elimination. Now, since you only have one homework, let's...". $\endgroup$ – StasK Apr 23 '14 at 16:01
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    $\begingroup$ I don't have 6-8 hours a week to waste. But I did when I was a high school student. The predicament you describe seems to be your belated realization that you should have started teaching him linear algebra (or whatever) two months ago, and then you could help him now. If you start today, in two months you won't have to make excuses about why he is struggling anymore. $\endgroup$ – jwg Apr 23 '14 at 19:36
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    $\begingroup$ Two months ago they were doing some resemblance of limits. For him to understand that, I should have started teaching limits four months ago. Four months ago, they were doing trigonometry, all of which can be taught in one hour if you know complex analysis. So I should have started complex analysis a year ago, because it does take some time to develop. And no, he does not have 6 hours a week to waste: school + extracurricular stuff do make up ~60 hours a week. He has better work ethics than I do. $\endgroup$ – StasK Apr 24 '14 at 3:37
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    $\begingroup$ If he is going to learn complex analysis at some point in his life, why not now (or a yar ago), assuming that he's ready? $\endgroup$ – jwg Apr 24 '14 at 5:23
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    $\begingroup$ The 6-8 hours he's going to spend in class (which he might be able to spend quietly doing his own work, or helping others) are because you don't want to piss the teacher or the high school off. If you did want to piss them off, I would say go ahead and withdraw him. Again, the problem is that you didn't already teach him this stuff. If he knew $sin(x+y)$ and how to derive it from complex analysis you could make a valid case for him having advanced courses or skipping classes. As it is all you can say is "He could have learnt this easily, but hasn't". $\endgroup$ – jwg Apr 24 '14 at 5:31
  1. I don't think approaching the teacher is the answer to your problem. Sure, the teacher may be mediocre. But still your boy should know how to do sin(x+y). He could have gotten that from books, from drilling himself, etc. Just take any book and work all the problems and you will learn. Also, a kid who is sooper smart in math complaining about the teacher not explaining stuff is not the answer. He should be able to nuke it out from books. I suspect that he is either not as bright as you, not putting in as much effort, or is just too accelerated.

  2. There is a world of gap between can't remember sin (x+y) and those theorems you mentioned.

  3. As someone else mentioned, what is the point of talking to the teacher? Are you going to change them into something they are not? Really?

These two things show me you are not really thinking strategically and shrewdly about what you want to do and how to get there. Go back and think a little more about what you want and how to get it. Even think on downsides. I think you are putting a little too much of what you want, what you would want into what your son does. Based on the remarks about your Ph.D. and the super theorems. I mean who cares in the grand scheme? This is about him, not you.

Oh and you don't need to learn linear algebra before trigonometry. I didn't, Feynman didn't, Lisa Randall didn't, etc. etc. The answer to this kid learning his chops is not that he has not been doing enough theory. He has not even learned things in the bag of tricks sense. And he could. Just grab some decent (old) books and do it.

Probably even the books now that he has are fine. One VERY practical tip that I have for him is to do all the homework problems. I mean ALL. Not just the assigned ones. But everything in the book.

I was a bright kid but struggled in school as I did not do all the HW. Going from doing now HW to doing assigned homework took me from a C to a low A. Doing all the homework took me to a very high A and outperforming students smarter than I. It actually got me super interested in the subject as well, not just drill. I ended up sort of self teaching myself AP calculus working each section ahead of time before class. and then the classes were literally (and not like a millennial says it) review, for me

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    $\begingroup$ If you want to be able to update your answers, register an account. The way you use the site starts to be disrupting. $\endgroup$ – quid Jun 11 '17 at 13:20
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    $\begingroup$ Stop adding new answers to this thread. $\endgroup$ – quid Jun 11 '17 at 13:25

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