It would probably be worth looking at the methods and techniques used by (for example) advanced flight training or similar instruction during World War II. Huge classes were routine, and a lot of effort was placed on getting people to understand what they needed to know. This would hold true for many fields outside math as well. They certainly weren’t interested at all in the latest fashion trends or fairy tales with regard to education techniques, just getting the job done in the least amount of time for the greatest number of people…
What, specifically, do you think those instructors were doing that a) isn’t currently a common practice and b) is applicable to a 9th grade classroom?
I’m not sure, that’s why I suggested it should probably be looked at. It’s a good question, isn’t it?
There seem to be a few assumptions, here… First, you assume that schools aren’t interested in getting the job done. Second, you assume that military instructors are immune to “fairy tales”. Third, you assume that their attempts to “get things done” were particularly effective. I see no justification for any of these assumptions.
It is not, for the reasons Chronos outlined, and about a dozen more.
You’re not the first person to assume that teachers are helplessly waiting for somebody smart to come along and show them the ‘one weird trick’ that will suddenly make the job easy.
To be fair, there are a lot of newbie teachers desperately looking for that one weird trick, and a whole industry devoted to selling them hope. But there’s no trick.
I had good algebra, geometry (I loved doing geometric constructions), and trigonometry teachers. I had awful teachers for calculus, who wanted us to use rote memorization to do this step, then this step, etc., with no explanation for why any of it worked or what it was for. If we asked questions, the answer was “It’s in the book!”
Did she teach statistical correlations?
Don’t ever put words in my mouth.
There is no suggestion of “one weird trick”, Good try, though.
That’s certainly a discussion that could be had for its own thread. I would suggest however that Education in general has had various “fads” for lack of a better term, with respect to both Reading and Arithmetic instruction over the years that were in retrospect were proven to be counterproductive, albeit well meaning, perhaps. (As an aside, I had a professor once tell me that if he was required to go back in time to kill someone to make the world a better place, it would be John Dewey).
That’s why when students came in with AP math, we put them in what was virtually Calc 101.
I had a good friend who was a terrible teacher. He was so bad that one class of students who survived his class made up T-shirts that said “Miller’s Survivors” (not his real name). He knew it too, but couldn’t do anything about it.
My best teacher, the one who got me in to math, was generally a disaster for the poorer students. I can see why too, but for me he was brilliant.
And one of my PhD students spent his career teaching in a community college (CEGEP if you know the Quebec system). He won teaching awards year after year and his students (some of whom I taught when they came to McGill) just worshipped him. He must have been doing something right. So yes, there is a lot of variation in effectiveness.
I’m not sure what point you’re making. Of course there have been various fads in education. That’s precisely because schools care about doing a good job. And so, when someone comes along and tells the schools “You can do a better job by doing this”, they do it.
That sounds like teaching pre-selected adults a skill that they are going to have to use in the near future and thus they are highly motivated to learn, which IMHO is just about the easiest kind of teaching there is.
The only problem with that is that when a flight training student didn’t grasp the fundamentals quickly enough, they took him out of flight training class, gave him a rifle and put him in the infantry.
When I was in 11th grade and we were moving out of basic algebra and geometry and into higher levels of math, I started struggling more and falling farther behind the rest of the class, despite her patience and efforts to get me up to speed.
It so happens that the half-dozen or so math geeks in the class loved the teacher and to this day still say she was the best teacher they had inn high school. They were the ones who went on to demanding jobs requiring high math skills. Was she effective because she both educated and inspired the best students, or not effective because an admittedly mediocre student (me) fell further behind the pack?
The highest level of certification is from the National Board for Professional Teaching Standards. Here are the standards for those teaching ages 11+.
Quite. Which raises two different points.
First, the students were highly motivated to succeed.*
But secondarily, the system had a solution to folks who failed. Wash them out. If the public school system had the right to tell any kid at at any age: “Sorry kiddo, you’re not hacking the program. Pack your things and don’t come back.” our school system would be very different and the tasks of teachers would be too.
* Although truth be told, the loss rate of USAAC bomber crew in Europe was higher than that of US Army infantrymen in Europe. You didn’t have to sleep in the mud, but coming back to that warm bed in England was far from guaranteed.
You’re right and I apologize. I should have said instead that your presumption echoes the sentiments of such people.
And third, i suspect they were training a skill (or set of skills) more than they were teaching understanding. That’s different, and usually easier.
In fact, one neat trick to teaching some aspects of math is to turn it into training discrete skills. “How do you solve this kind of problem?”, rather than “how do you manipulate equations?” The benefit is that it makes that piece easier for a large fraction of students. The cost is that it can make it harder for some students to generalize to solve related problems.
'Zactly.
Knowing and understanding are two very different things. Knowing lasts only as long as you’re actively using [whatever]. Understanding is much harder to teach, much harder to “get”, but is potentially almost life-long.
My very subjective view of mathematics teachers is biased well in favour of all my teachers. From age 13, when our teacher taught me what an icosododecahedron (and what a tesselated one is), and topology (how to make a “flexigon”) on to differential equations at senior level, I was very fortunate to have excellent math teachers.
I wish I had shown the teacher who taught us trignometry an inverse kinematics engine I wrote on paper in Flash Actionscript during a hospital stint, and when I transcribed it into real code, it worked perfectly.
I remember the fad for education when I was in school - whole word and “new math”. My impression was that the concepts came from places like OISE (Ontario Institute for Studies in Education) where the eggheads dreamed up new ideas. They then persuaded departments of education to adopt these, to the detriment of students.
Nobody gets brownie points or recognition for saying “you’re doing it right. Just emphasize these bits…” They get professional recognition, distinction, and prestige from saying “You’re doing it all wrong. Drop what you are doing now and change to my way!”
And then it will be almost a decade before people realize “Hey! This isn’t working!”
I blieve that’s what’s called a “private school”. I recall the conversationin the hallway outside our class the first day…
“I’ve got a surprise for. Freddy’s going to do much better this year!”
“I’ve got a surprise for you, Mrs. Smith. Freddy’s not coming back this year.”
Freddy had flunked his grade and was going to repeat for the second time, back in the day when kids actually flunked. However, not at this school. This wasn’t Nob Hill. No set of parents was so important that the school would slow the whole class for them.