I was reminded of what my daughter’s first grade teacher said to my wife and me, when I read that Massachusetts has been given the go-ahead to test math teacher competency. There’s quite a bit of opposition to the testing plan.
OTOH proponents argue
then I suggest that they attempt to demonstrate how testing of the teachers ability to know something will give any appreciable data on the best method to teach the subject.
december: *“I’m well-qualified to teach arithmetic, because I had so much trouble learning it” *
Just a side note: you seem to be quoting this remark (by, presumably, your daughter’s first-grade teacher) as patently ridiculous, but it may make more sense than you think.
Naturally, anybody who’s teaching math of any sort should have arrived at the stage of understanding the subject well, no matter how difficult they may have found it when they first encountered it. However, it is in fact true—it’s certainly been true in my twenty-nine years of studying and teaching mathematics and working with mathematicians—that people who initially struggled with math concepts often turn out to be more effective math teachers than the naturally mathematically gifted types to whom those concepts seem intuitively apparent and simple.
The difficulties most students have with learning math are based not so much in simple stupidity or inattention as in crucial mistaken assumptions about the concepts. As you know, the logical structure of mathematics is very hierarchical: if you make one mistake in your fundamental notion of what some mathematical definition means, none of the subsequent statements based on that definition are going to make any sense at all. Unfortunately, many mathematically gifted people are often completely mystified how somebody else can not immediately grasp the idea that seems so obvious to them, and so they have a very hard time figuring out what it is that their students aren’t “getting.”
Whereas somebody who has a clear recollection of going through similar struggles themselves will often respond immediately with something like “Oh! I think I see the confusion. You’re assuming that (this triangle has to be equilateral, the result of the subtraction has to be positive, whatever wrong conclusion the student has jumped to). I can see how you might think that, but in fact we specified earlier that…” And so the student’s confusion is cleared up.
Now, many people who are gifted at mathematics and to whom math thinking comes very naturally are capable of the necessary imagination to understand where the confused student is coming from, but alas, many others are simply not very good at “seeing how somebody else might think” anything that is so blatantly incorrect. So their math teaching is often much more frustrating, both for them and the students, than learning math from a less mathematically brilliant person would be. That’s why I don’t necessarily agree that it’s absurd for someone to think that having struggled with learning arithmetic made them better at teaching it—assuming, of course, that they actually did learn it successfully and now understand it well.
End of side note. As for the point of the OP (which actually seems mostly unrelated to the thread title), I agree with wring that the people who are advocating testing only math teachers, only in underperforming schools, should explain more clearly why they think that is a good use of resources in improving the students’ math education.
Given how many times december has been proven wrong whenever he starts Yet Another “Insightful” GD Thread, does that mean he’s the smartest of us all?
(Ooooh, there’s a scary thought…)
Just wanted to comment that I agree with Kimstu. I think one of the most frustrating things out there is to try and learn from a “Natural.” This applies to anything, even sports.
In my experience “naturals” have no idea how they achieved proficiency so they have difficultly helping others achieve proficiency.
I am with Hello Again. I taught a graduate statistics lab for two years, and I agreed to do it for this very reason. I had a lot of trouble wrapping my mind around stats, but in teaching myself I figured out some good ways to teach others. Incidentally, I was teaching the lab for a professor who himself was no stats whiz. He was an excellent teacher.
I am possibly the first stats teacher in existence to demonstrate the central limit theorem to doctoral students with a zoo-themed example and animal crackers, but a lot of my students loved me.
Another kudo for kimstu here. One of the worst professors I had was a (physics) professor in grad school who had been a child prodigy…you know, PhD at age 20 or some such. And, he was completely incapable of explaining things!
As for myself, I would have no qualms at all about teaching calculus but I wouldn’t know how the hell to go about teaching arithmetic! I think this would be true of many, if not most, people who have gone up through say upper-level undergraduate mathematics unless they had also had some specific education training.
So, yeah, my vote would be that someone who teaches arithmetic should have a good grounding in education and know and understand math enough that they are not phobic or ignorant of it … But, it may well be better if they weren’t gifted at it either.
I can relate to that too. I discovered this issue when, as a student, I was giving individual maths lessons. I plainly couldn’t figure out what the less gifted of the kids didn’t understand.
It’s at this time I figured I shouldn’t try to become a science teacher (also because I discovered the gifted ones were failing because they wouldn’t bother actually working a little bit. I understood that this career would be extremely frustrating)
Not to hijack, but as this plane seems headed to Cuba anyway…I’m going to go even further than Kimstu and state that “naturally gifted” people (as math teachers) are generally much worse at teaching math to students of ordinary or lesser ability. Neither I, nor my son, are naturally gifted in mathematics but my daughter is.
I am procedurally adept at the (often complex) financial mathematics used in my line of work, but in terms of having to grok complex (for me) abstract, multi-level algebraic relationships I can only approach these types of problems in a plodding mechanistic fashion with the exception of geometry which is (usually) easy.
It always drove me crazy in the higher level high school and college math courses, that I knew I could understand how to do a problem and the number relationships involved, if only someone would explain it to me in a mechanistic and structured way. By the time we got to the more complex equations I was at sea and had to basically ape the more basic problem solving procedures in the book, which only caught about 60-70% of the solvable problems but foundered on the more creative and complex problems which usually squeaked me by with a C.
It is not part of normal human nature to be patient with those who are lagging behind and holding the group up. People who are confused usually just lapse into a resigned silence (or drop out) rather than suffer continued humiliation and importations that they are “not really trying”. IMO there is a early transition point between basic math and more complex algebraic variable math where you’re either on the train or you’re not and if you’re not you are SOL. Standing at the station is not an option and chasing the train is no fun.
Having said this, I realize my type of problem and request is frustrating for those who are math adept. I am not a paragon of virtue with respect to patience in this respect. People have different strengths and weaknesses. As an example I have tried to teach some sales skills to professionals with accountancy and engineering backgrounds, and the light is just not on in there, with respect to how to handle complex interpersonal representations and move smoothly and effectively through the various stages of initiating, handling and completing (successfully) a complex sales transaction. I often felt like I was dealing with people who were brain damaged and wanted to scream (but didn’t) “Christ why don’t you get this. It’s so simple!” I can well understand how the math adept can be frustrated with slow learners.
I know there are at least a few people like myself in this respect and always thought that there was a pirate’s ransom of book sales for the person who could develop a series of instruction guides explaining more complex math as a series of basic mathematical concepts and conceptual building blocks, in a basic but non-insulting way to otherwise, reasonably intelligent people trying to help their children understand basic and complex algebraic math. I have never seen this book or it’s like but if I did it I would pay a significant sum for it and so would millions of other people.
I would agree that teaching skill is different from technical skill. (Although the best teacher of elementary and high school math that I ever met, Julius Hlavaty, did have a Ph.D.)
I was struck by the intensity of the opposition to the test. Presumably these teachers won’t be tested on calculus or the central limit theorem. They will be tested on whatever arithmetic or mathemtics they teach (I assume.)
The huge opposition to the testing makes me suspect that a goodly number of these teachers may not be able to do whatever level of math they’re teaching. 
I hope I’m wrong…
did it ever occur to you that it may be demeaning?
Teachers have at least a bachelors degree (that’s my understanding for a reg teacher, subs may be able to be near graduation or something). Many go on to get Masters and PhD’s. IN my state (MI) they’re required to continue taking college classes to maintain their certification.
and these folks want to spend $$ and time having the teachers prove they know how to divide 346 by 43.
It’s a great way to get teachers to leave the profession.
You’re an acuary, right? How would you feel if you had to take tests to demonstrate that you still remember how to solve an algebraic equation or diagram a sentence?
and, of course, you’ve not been able to suggest how this test would indicate in any way the persons’ ability to teach.
So, they see “gee, students aren’t doing well in math” what to do?
- Determine by reseach the best method of teaching the subject so the students learn (by researching other successful systems for example). Spend the time and money to determine the best method and insure that the teachers are using these methods.
or:
- Spend $$ to develop tests for the teachers. NOt to test how they teach the subject, but to determine that the teachers know the subject. Pay for the teachers time to take these tests, so they can demonstrate they know how to add, subtract, divide and multiply.
which method do you really feel is the best, most cost efficient method of addressing the underlying issue “our students aren’t learning basic math skills to our satisfaction”