That’s because there’s no “right” that applies to every student. Trying to devise a curriculum and method of instruction to achieve the greatest improvement with the greatest number of students is a matter of continuous improvement that we expect in every other field of human endeavor.
Do we refer to people who make circuits smaller, computers faster, or vehicles more crash-proof as “eggheads” who are only doing it for professional recognition?
Wholesale expulsion of young people struggling with a subject is not a solution to the problem.
I can’t speak to whole word reading, but “new math” stuck around, because it did, in fact, work better than what came before, and was a benefit to the students. Except that it’s not particularly new any more: We’ve been teaching “new math” for over fifty years now. Most of the folks nowadays complaining about “Why do we have to do new math, instead of the way we did it when I was a kid” were, in fact, taught new math themselves.
Largely, yes, but it’s still the same complaints about the same old math pedagogy repackaged. Into a box that they don’t even fit in, because common core doesn’t even say anything about how to teach math (or any other subject): It just covers which concepts should be covered, and when. Which, of course, goes along with all of the other completely counterfactual complaints about common core.
I remember moving state here in Oz, when I was 8. I left a state system that had been teaching old maths, and entered a state where new maths was taught. It was a bit bewildering at first. What the hell was a Cardinal number? And why are we playing with attribute blocks and Venn diagrams? Some of this I didn’t hit again until university.
In reality it was a melange of old and new. We still did multiplication drills, long division and such like. I think the intent to teach some elements of the underlying mathematics clicked with me. So that was good.
One of the tales of new maths goes:
Little Johnny comes home from school. His parents ask him what he learned at school.
“Multiplication”, says he.
“Ok, what is four times five?”
“Hmm” says Johnny, “I don’t know. But I do know it is the same as five times four. “
I’m not the smartest guy in the room, but as a teacher, I guarantee that any system based on attempting to create a methodology for teaching math or reading to children with a wide range of ages, abilities and backgrounds based on the experience of the military teaching specific skills to a group of prescreened, (generally) highly motivated 18 to 20ish-year-olds, at their level of maturity, education and abilities would be nothing more than a fad, that would prove “counterproductive, albeit well meaning, perhaps.”
Ironically, this is the sort of reasoning which leads to various education (or management) fads. Someone sees something which worked in one particular set in a specific set of circumstances while willfully ignoring the material differences and the absurdity of attempting to apply what works in that specific setting to a general situation.
(My interest in WWII aviation training stems from my interest in the Pacific War, and the difference in training programs was a contribution to Japan’s defeat, and I’ve looked into this from before.)
First, one of the greatest differences was the elite nature of the cadets for flight training compared to the general population. That in itself means that it’s almost certain that any program based on a teaching methodology for elite students simply won’t work in a generalized student population.
Of the over 8 million members of the armed service, a few hundred thousand pilots, navigators and bombardiers were trained, so less than 5% of the total. The majority of the graduates became officers, which again is an elite status. There was a high school graduation requirement, back when less than 24% of Americans had that diploma.
There were strict aptitude tests (starting from 1942 after the change from qualification tests because of the lack of candidates). At one stage, about 70% of the cadets were getting washed out in the year-long process it was taking from start to finish.
As has been pointed out, so much of the education process is dependent on the student, and it’s simply impossible to generalize an educational process a group designed for elites, and take it to the masses.
Math and physics were only a tiny fraction of the preflight curriculum, which lasted nine to 10 weeks and these gradually became increasingly focused away from theory and more towards specific applications in aviation.
The cadets were a captive audience, generally motivated to pass the subjects, years older and more mature than elementary or middle school students, and facing intensive short-term courses designed specifically for practical applications which their lives would literally depend upon.
Frankly, it wouldn’t matter how these courses were designed. Attempting to apply lessons learned the WWII pilot training to a math program for six- to 18-year olds across the entire spectrum of backgrounds, abilities and interests would be a fool’s errand.
Teaching at university level, there is no doubt that only a few years of maturity and a desire to be there makes for a significant difference in student engagement and results. Some of this is clearly down to self selection, someone coming back into the tertiary system from a job, and not dropping straight in there from high school tends to be much more motivated. But your average 18 year old student is still a few years short of attaining their full potential as a mature adult. That makes for younger students that can have a harder time engaging and performing. Focus needed to get your head around your linear algebra course can take a backseat to ruminations about how cute the girl two rows in front of you is.
Nothing against your link, but I find it interesting that the column is dated 1969, when the column didn’t get going until 1973. I guess we’re broadening the meaning of, “it’s taking longer than we thought.”
At any rate, thanks for that. It explains why my parents, who wanted to help with homework, couldn’t. I was a victim of “new math,” so I was talking about “sets,” like I was learning at school, and they were asking, “What’s 3 + 4?” I couldn’t understand them and they couldn’t understand me. Thankfully, later, I had a teacher who taught to the curriculum, but who also made sure we knew our addition tables and our multiplication tables thoroughly; and by extension, our subtraction and division tables. Unbeknownst to the Powers-That-Be, I guess, but I’m grateful. To this day, I can still do the mental arithmetic necessary to calculate sales taxes, put together my client invoices, and figure out a 20% tip at the sports bar. I don’t really need math for anything else.
I was a beneficiary of new math. I loved it. I learned a lot of math from it. I went on to be an actuary, which is a pretty good gig, but you need to be good at math to do it.
As someone who taught for ten years and got out, I strongly agree. Teachers are very much like coaches. You are as good as your players. Mozart could give a person piano lessons but, if they really don’t care and don’t practice on their own, they are not going to be any good at it.
Another element that bears on the effectiveness of math teachers is the framework imposed by the particular school system involved. Some public school districts require that every classroom in the district align precisely with regard to topics and activities (every Algebra II class introduces imaginary numbers on Tuesday, assigns the same problem set from the same text, quiz on Friday, etc.).
Such rigidity offers some administrative advantages (such as comparing performance) and some teachers are able to make the most of it, but it’s pretty brutal for students.
After a few years working in a number of such districts I eventually landed a position in a small private middle school where my marching orders were simply to get as many students as possible through Algebra 1 and ready for high school Geometry. I had complete freedom to do what I thought was best for the students. It was WAY more work than before, but WAY more satisfying and I was able to be far more effective. Retired after nine years there, truly my dream job.
It’s interesting that I, whose progress in math stalled out midway through high school, can calculate a tip in my head - and not just 20%, but also 17.5% and 22.5% - while my son, with a Ph.D in biochemistry - has to use a calculator.
Same here. I don’t remember any math teacher teaching the why of it, or how it applied to life skills, although admittedly I wasn’t always paying attention. When I got into electrician school, trig suddenly made sense, and I also realized the importance of algebra. Calculus still doesn’t make sense to me.
That’s very sad. I know there’s a sort of “divide” among math teachers about teaching “pure” math vs. applied math, but until kids are engaged it doesn’t matter what you’re trying to teach. I discovered that even in middle school at twelve years old, some kids had already concluded that they were “bad at math” and were difficult to turn around.
I had them build a model railroad. Every year the next class added to it, until it ran all the way around the perimeter of the classroom. As a project, it offered something for just about everyone: electricity, geology and geography, engineering, physics, commerce, law, even storytelling. It didn’t suck it every single kid, but darn near.
It is if you leave it to someone else to deal with them. And when parents are paying for the privilege of putting their kids in a class that is not held back significantly by a bottom 20%. All the comments here seem to revolve around “depends on the students” so segregating students by ability so as to group those who need assorted levels of attention or intensity of teaching makes sense. But… where it fails is when it morphs into segregating the students by financial class or ethnicity based on false assumptions.
Regardless, I received a better-than-average education, and I am amazed at how many of my fellow students, who I would have considered mediocre, did quite well in life professionally. However, when I dropped out of university and got a blue-collar job I found out what those at the lower end of the IQ scale were like, and it was an eye-opener.
I encountered “new math” toward the end of high school. Obviously, the teachers were confused too, and the applicability of set, rings, etc. was not immediately apparent. It became more obvious once I got into computer science, and obviously computer math - where for example floating point calculations only sort of maps to real mathematics, made good use of such concepts.
Also, students are usually not as passionate about math as we math teachers are. Yes it may be really cool (to us) what happens when you divide all of those numbers by 3 but for 90%+ more of the students it’s a digression that confuses them more.
The first time I used trig to calculate a string of conduit bends, the guys working with me just laughed. After I lifted it into place and it fit perfectly, all the jaws were hanging open.
I had some teachers who were basically checked out and awaiting retirement. Yes, having a teacher who actually teaches is better, though tracking students earlier and progressing faster would have made more of a difference.
