Who did Rand copy that one from? Can we not quote a serial plagiarist in an education blog?

For one, he gets it wrong: it will be five or fifty excellent calculus teachers, because learners vary. But what do plagiarists know? They just crib over the smart kid’s shoulder.

There is a good conversation to be had on the power of ed tech to leverage the best educators, but there is a reason (left as an exercise) we do not mention politicians in the workplace, military ward rooms, and bars.

I realize that Senator Paul hasn’t gotten this far into the logical reasoning process, but… there’s no community in America that is going to accept a 1:2,000,000 teacher-student ratio for any course, much less for calculus.

Love,
me
(@cheesemonkeysf)

If Rand Paul’s idea is correct, then, Khan Academy should hire him to teach it for all the world to learn it (calculus).

Silly Rand Paul. As if there is “one person” who is “the best” at teaching calculus. No such animal. As a reputedly excellent calculus instructor myself, I cannot help but be aware that some students still don’t “get” calculus when I teach it, perhaps in part because they don’t “get” me. There is no one ideal math professor who is all things to all people. Different students require different styles.

Something comforting in the consistency of Paul’s predictably shallow “analysis” of yet another issue about which he clearly knows nothing. But therein lies his appeal to many: the ability to articulate perfectly the wrong ideas that they, too, assume are “common sense.” In a nation obsessed with rank-ordering everyone and everything (“Top Ten Hemorrhoids of All Time”; “The One Hundred Cleanest Fast-Food Rest Rooms You Must Visit Before You Die!”), the notion that there would be a “best” calculus teacher whom we could, of course, readily identify and agree upon, is perfectly sensible. And then, naturally, everyone should be taught by her. Because human interaction among teachers and students, students and students, etc., is in no way essential to learning mathematics (or anything else). Rugged individualism means never having to share or struggle with your own or other folks’ speculations and inklings about challenging ideas.

@Kenneth Tilton wrote in part: “Perhaps the one thing we all agree on is that the single most important factor in the classroom is the teacher.”

Where was that agreed upon? And in what is the teacher “the single most important factor” exactly? That claim gets bandied about a great deal, most frequently as a misstatement about closing ethnic learning/achievement gaps. And it simply isn’t so that either teachers or schools are the biggest factors in that regard. I’ll grant that I’ll take a solid teacher with sound content knowledge, basic pedagogical skills, and deep pedagogical content knowledge over lots of tech, a “great” textbook, etc., as I’ve seen the former work wonders with bad books and other disadvantages, while I’ve seen some teachers that could screw up any and all other positive resources available to them.

But that’s about as far as I’ll go, lest someone quote me out of context to support the notion that “great” classroom teachers are the key to curing all our social ills, particularly those so obviously grounded in economic and social inequity. I have no doubt that Mr. Paul would be comfortable with that notion, however.

That said, there are actually an increasing number of free or relatively-affordable online resources, including some damned good videos (not from Khan Academy) that really do get at some meaty K12 math issues intriguingly. If you’ve not looked at the free video minicourses James Tanton has up on gdaymath.com for solving quadratic equations and dealing with “combinations and permutations” (a distinction he neatly rejects and obviates), they’re one place to start. No, they’re not revolutionary in terms of “how to teach mathematics in a classroom,” since they are not teacher-student or student-student interactive, for starters. But they beat all other presentation of the ideas I’ve encountered (your mileage, of course, may vary on that score).

While I know from corresponding with Prof. Tanton that he plans to cover the full range of K-12 math in this courses, at least through calculus, I believe), building on his THINKING MATH textbook series among other sources, I can’t claim that this “solves” the issue of how to guarantee that all kids have access IN A CLASSROOM to a great math teacher. No one can realistically guarantee that, and many of those who use that rhetoric in the education deform movement are alarmingly hypocritical, in that they would never approve the costs involved in trying to make that happen.

If I were king of the universe, AND if I actually had at my disposal the necessary cadre of fine mathematics teachers to stock our K12 classrooms (not to mention our university classrooms), I’d wave my hands and do it without hesitation. But that cadre doesn’t exist, isn’t on the horizon, is actively undermined by parents, politicians, pundits, publishers, professors, pupils, and other pedagogues, not to mention the likes of Rand Paul and his daddy. As America by and large doesn’t know what mathematics is or what quality mathematics teaching looks like, it fights against many instances of such teaching and attempts to nurture more of it. Green’s article in the NYT Magazine gets at some this pretty accurately.

So while we try to improve our practices and those of colleagues who are willing to share, take risks, think, reflect, and so forth, we need to recognize the limitations of getting good math teachers into many, let alone most or all, classrooms. We simply can’t wait for that to happen because if it does, it will take, at the very least, decades. I’ve been looking at mathematics teaching professionally for over 25 years. I turned 64 yesterday. While I’m thrilled by all the thoughtful, reflective, talented, insightful, and gifted young (and a few not so young) math teachers who are actively sharing their thinking and practices in various communities on the Internet and in other contexts, there just aren’t enough to go around or to counter all the dead wood. And the scary part is that there is plenty of NEW dead wood being produced and ushered into classrooms every year. Some of them are salvageable, but many will be as bad or worse than some of the horror shows most of us have experienced in one or more capacities – as students, colleagues, coaches, supervisors, parents, etc.

So as hypothetical King of the Universe, I might be able to “get rid of” the bottom 5, 10, 25, 50 or even 90% of the “bad” math teachers out there (and let’s pretend that we had some accurate and meaningful way to determine such things), thus satisfying the deformers’ fondest dreams. But then what?

Dan, the point you made about a teacher doing Math Night to help parents understand is key. None of these reforms about math education can happen in a vacuum. There’s always a political side to what happens to people’s children, and if the way you help children learn math is important then the way you communicate with parents is also important.
So many bad educational ideas, like “value-added measures” and “cubicle warehouse with math software” get packaged & sold to parents–and that builds distrust toward teachers (deserved or not). Paying attention to the political facet of better math learning is just something you have to do if you want better math learning to propagate.

“there are a lot of teachers out there who are ineffective. It seems easier and more efficient to make the effective teacher’s strategies more accessible…it is very good that Paul has a focus on effective teachers.”

I want to point out something about word choice, Jon. It’s the use of “effective teachers” or “ineffective teachers” which implies that the teacher is like replacing old guitar strings with new strings to get better music. I’m the same teacher that I was in 1995 when I started, and I started teaching with lots of great explanations for math & physics, but my effectiveness has improved with better methods of teaching/learning in the classroom (my students do more of the explaining than I do). Therefore that is why the Japanese lesson study forbids using personal terms in the critiques to keep the lesson as the subject.
We need to push back on politicians, editorial boards, pundits, and school administrators who talk about “effective teachers” because they lose focus on the one thing every teacher can use: methods of learning that build curiosity.

The myth of “the one best teacher” is compounded with the “one ideal solution” illusion. As a result, education is unduly fad driven. Right now there’s a boomlet for “accelerated curriculum” such as Statway. You know what? At my college it works great! But it’s not for every student who needs algebra and statistics. Ditto with our self-paced drop-in learning center. Some students need more structure. Years ago we introduced “splits” which take a one-semester class and slow it down into a two-semester sequence. Some slow-learners like it.

I hope we’re finally taking seriously the problem of properly pacing students in the learning environment that best suits them, whether standard lecture classroom, accelerated or decelerated program, self-paced, on-line, etc., etc. Of course, we’re hobbled by limited resources from offering every learning mode for every course, but the emphasis on proper placement is one trend I heartily support.

Less than 5% of American high school students graduate with calculus behind them, and my bet is that he’s one of them. So he’s not the idiot people on this forum want to make him out to be. Clearly he will never intend to take away math teaching jobs (if there ARE any in the US), but I’m 100% behind ONE calculus expert documenting what it’s really all about.

Our calculus text books contradict each other so much that even Americans who take calculus in high school really do NOT know which version is correct, much less how to explain it.

At least give Rand Paul that much credit, even if he is dead wrong (and contrary to his father) regarding illegal aliens.

It bothers me when I hear parents saying they wish they’d been taught like that (especially based on a one-off lesson). I bet their teacher from back in the day wishes they’d always turned up as a motivated, focused student eager to learn?

John–um, when I read this:
“Our calculus text books contradict each other so much that even Americans who take calculus in high school really do NOT know which version is correct, much less how to explain it.”
I’m not sure ‘contradict’ the accurate word for this. Every Calculus book I’ve seen has the same definitions for the derivative, and same set of integral tables, same infinite series for sin(x) and cos(x). Some develop ideas in a different order, some use different proofs for the FTC, but they are all pretty much factually correct.
Why not let the different textbooks coexist and give teachers the time to compare the differences for themselves to decide what’s best for the students they have?