I can only speak from my own experience, but out of all the various math teachers I've had, from elementary, to trade school, to 2-year, and four-year colleges, only one of the teachers I've ever had was actually good at teaching math. And that wasn't even the course I was taking. It was a computer science course. We have everyone from freshmen to seniors in the class. From the exceptionally bright (regardless of their class) to the slightly below average for the school. One day the teacher was talking about a program we had to write and he put a particularly complicated formula on the board that was going to be used by the program to accomplish the task. Everybody in the class looked at the formula and basically just screamed. None of us could grasp the formula, or how it should work. The teacher said, "Oh, this is easy" and proceeded to explain it to us. Everybody in the class, when he was done, sat there with their jaws on the floor because in less than 10 minutes, not only did we understand the formula, but we were shocked at how simple it was to understand. Almost in unison, we screeched out, "You should be teaching math here!" All of us got the formula, and we didn't feel the least bit stupid about the whole thing. The teacher laughed and said that he didn't want to teach math because he found it "boring." The guy wasn't some kind of genius, he just knew how to teach, and how to teach math in particular. Most people don't. IMHO, the way people think of math is completely wrong. They think that it is something like history, where you cover specific things, and they are as largely immutable as saying that on December 7th, 1941 Pearl Harbor was attacked. The reality is that math is the language in which the universe communicates (to put it in metaphorical terms) and it should be taught as such. I will never forget that I had a job where I was supposed to figure out an estimate at the beginning of my shift the kind of production numbers my team was to do that day. I quickly realized that the way they'd given us to figure out the number was far more complicated than it needed to be. Not all of the numbers that they gave us were actually important and that with a few minor tweaks to the formula you got the number corporate was really interested in. When I ignored those numbers and focused on the ones that really mattered, not only did I get the solution quicker but I got a more accurate number. Trying to explain that to the other leads in my department turned out to be a futile task. They didn't understand the formula at all, or why we were using it. Sure, they could plug the necessary figures into it and come up with a result, but it took them a long time. They also didn't get a really correct result. It was off by several percentage points. Try as I might, I could never get them to understand why my formula was better. Even after it turned out that not only was my team the only one to hit their actual production goals in the department, but also the only one to do it in the entire facility, the other leads didn't want to listen to me.
Funny. But it actually goes to something, a contradiction that I think is at the core of the issue on how to teach for success. In the US, there's a direct correlation between amount of time spent on homework and academic success, when broken down by demographics. Black kids spend the least amount of time on homework and get the lowest scores as a cohort, Asian kids spend the most. Whites don't have the most success. Of course, that doesn't include income disparities, as Asians also have among the most income in the US, and blacks the least. And while there is obvious anti-Asian racism in the US, it hasn't been as wide spread and devastating as the anti-black racism. There's no equivalent to the KKK targeting Asians, and while Japanese internment was horrific, there are numerous examples of destruction of black communities, often explicitly because they were garnering wealth and success. But when we compare US primary school education with international groups, we find that the Nordic countries excel, and their entire focus is on more organic play time and less homework. Perhaps that's what this study meant in its term of 'white supremacy' of the western model, but even that falls down in the face of the Nordic countries having disparate means and outcomes. Ultimately IMO it seems pretty obvious that traditional methods need to be re-evaluated for the 21st century, and countries like Finland seem to have a better model. Indeed, that model might be more useful to groups that have achievement gaps - focusing more on quality of educational time at school, and less on homework, works for several countries. Tying school quality to the wealth of the local community is an anvil around educational success among communities that have historically been denied wealth, not only due to the inferior quality of the schools, but also the traditional approach we continue to use that requires a stable homelife for most students to keep up with assessments.
I can balance a checkbook. Took Algebra 101 three times (twice in high school, once as a requirement in my liberal arts college), still don't get it. I was okay with x. But then the clowns tossed in y and z. Lost me. People have tried to tell me "algebra is really just math." Then WTF does it have letters in it? Is math racist? I dunno. But someone should do a study to determine whether it's biased against gingers.
You'll probably hate me for this, but I love math. I do it for fun and relaxation. Some of us are just weird, I guess.
FWIW when I saw this thread I read it as "Is Meth racist"? Think about it... Some random thoughts... Anyway, I heartily agree with Tuckerfan that the quality of math teaching in the U.S. generally sucks. My opinion is that it's a vicious cycle where because the teaching sucks, the only students who excel at math are the ones who have a natural talent for it. It figures that they would be the ones that go on to teach it. Those who do, who have a gift for teaching and a gift for math strikes me as vanishingly small. Aside: best math teacher I ever had was a high school geometry teacher who was a Korean War era Marine. He said he managed to make it through boot camp by just keeping his head down and doing what he was told whilst a lot of high school jock types washed out because it was the first time they'd ever been challenged. So he had a certain amount of empathy for kids who weren't gifted. If you didn't give up, he wouldn't either. I kept a copy of my last test in his class for many, many years. It was the only time I ever got a 100 on a math test. The next semester, for whatever bureaucratic reason I was shifted to a different teacher who was a good man, but not nearly as good a teacher I got a nice fat "F" for the grading period. I struggled mightily with algebra I and didn't qualify for algebra II, but I did get a "B" in my college freshman math class, so I guess something sunk in somewhere... Anyway, I've come to believe that instead of trying to force everyone to take STEM classes they may or may not have any aptitude for and wasting everyone's time, it would make a lot more sense emphasize consumer math. When I watch millenials try to make change at a fast food window, I never know whether to be amused, outraged or heartbroken. Oddly, I do quite well with basic arithmetic to this day, but any kind of higher math, forget it. We really need to be more realistic about what level of math kids need. I can see basic Algebra being a valuable way to identify kids with math aptitude, but it just seems like there's way too much shaming going on for kids who don't have any real talent for math and who won't ever need it anyway. If you want to get into the MBA program at the University of South Florida you have to have calculus. Once you get into the MBA program you won't need it and a professor told me some years ago that they're forbidden to use it in their course work. It's simply a gate keeping device. I also agree with Demiurge. The current model puts as much onus on parents as it does students when it comes to homework, even in elementary school. My Godson is struggling mightily to keep up even after being held back a year. His mother has neither the focus to help him sit down and get his work done (they both have bigtime attention deficit disorder) nor the overall reasoning ability (neither of them are stupid) to help him grasp the concepts they're trying to get across. The Asian "Tiger Mom" stereotype is in some ways unfair and somewhat ugly, but when there's no foundation at home, putting so many chips on homework seems like a self-fulfilling recipe for continued inequality. I've also come to believe that while we should make sure that bright, super achieving kids have no ceilings on how high they can go, what we really need to be working on is raising the floor for kids who have unstable homes and/or parents who don't appreciate the importance of education. A few years ago I was at a U-C/Irvine (AKA "University of Chinese Immigrants) basketball game where they had a draw prize of some kind. The winner was a student with an Oriental name. When she didn't claim her prize after her name was called several times, someone yelled out "She's at the library!"
Guess I'm a weirdo too. But, I always tell people who say "I haven't used algebra since high school", oh, yes you have. You just don't know it. Price comparison while grocery shopping? algebra. Calculating the distance from where you're standing with garbage in hand to the trashcan? algebra. How many spaghetti noodles do I need to feed 4 people? algebra. Every adult does algebra every day. They just don't know it. This is the issue I have with people who are adamantly against common core math. Every day people do math in their head. Understanding how to get from point A to point B has as many different paths as there are people. And, that's pretty much what common core is attempting to show that "old math" doesn't. When it comes to understanding math, one size doesn't fit all.
I've heard the idea floated that the stuff we currently assign as homework should actually be done in the classroom where the teacher(s) can help you with it, and the more basic instruction should be the homework - reading from the textbook, that sort of thing. Makes a kind of sense to me.
All I know is when my kids were in middle & high school they had a rucksack full of books/homework to carry around nearly every day. I don't remember having that much when I was a kid. And when I had to help them with their math? That was and for yours truly.
The system is fine when parents have the appreciation of education, emotional stability and the time to do it. Sounds like there's a built in bias toward failure for some people the way things are now. If teachers can't handle the load and parents have to be co-opted into the learning process then the system needs to be reevaluated. That's not a criticism of teachers (well maybe some teachers) but it does seem that parents are supposed to take up a lot of slack in the system.
I don't think the parents should take up the slack in the technical aspects of teaching, but providing a stable home environment and enforcing discipline and a good work ethic goes a long, long way in setting the stage for academic success.
Yes -- in education circles it's called a "flipped classroom." It's really how most of my English and history classes worked -- do the reading at home, then discuss it in class the next day -- but it is definitely a lot more effective when you have small class sizes. (In math, because smaller sizes make it easier for the teacher to give one-on-one help; in humanities and social sciences, because smaller groups lend themselves better to discussions where everyone gets to play an active role.)
I'm the same way, and I had a couple of "epiphany" moments in the last couple of years related to people's kvetching about Common Core. The first was when I was trying to do some math in my head while driving and realized that, like you said, the strategies I used were basically the way it's being taught now. The second was when I found a Tom Lehrer album that I hadn't listened to in a long time, put it on, and this song came on: In later verses he exaggerates for comic effect, but if you really listen to the first verse ... it's exactly the way I, and probably most people here, learned it in school. What people were deriding and bitching about in the '60s is exactly the method that makes perfect sense to me, because that's the way I learned. As for math teaching methods in general, I bet if you took a broad survey of American adults, most of them would say they never really liked math in school, that they found it hard, and that it was their least favorite subject. That alone should be enough to make us say "huh ... maybe the way we were taught wasn't the best way after all."
New Math makes dealing with base 2, 8, and 16 in computer science and engineering MUCH easier to grok. I don't know about common core math, but I'm quite glad I didn't learn old math.
As a construct used to organize things like dictionaries, encyclopedias, and libraries so that you can manually search for something alphabetically yes we do have many structures that would need another form of organization to make those searchable. As entertaining as that thought is for anarchists it becomes stupid if you think about it for more than a second in the context of reality. Also, when you even go as far as search engines and how they work in relating alphabetic symbols to numerical values for calculations the order of the alphabet becomes important for the organizational operations of the programs that sort words at a certain level. ASCII associations are transformed into numerical value which is how things are actually sorted by processors. If you started mixing up the order of the alphabet a computer would have to have some process to determine the new order of the letters. If the order of letters was randomized each time because you say it does not matter computers would cease to work. Blow your mind, the symbols of 0123456789 do not have to actually be in that order for math to work. However, we do need to associate them with units and agree on that association for math to work using those symbols. In other words sometimes you have to think inside the box or else you cannot communicate.
Actually, that's not entirely true. There's no particular reason it has to be in the order it is, but if it is not in any standard, recognized, universally accepted order, that is a major problem. I know a scout leader who can read and write just fine (in two languages), but who could never learn Morse Code because he doesn't know the order of the letters in the alphabet, so he can never organize the letters enough in his mind to assign Morse Code to them. He knows a lot of the letters (the ones we use the most), but he doesn't know them all, and can't even be sure which ones he doesn't know. And can you imagine a dictionary where the author put the words in there in random order, because there was no such thing as "alphabetical order"?
My mind is blown by all this stuff. Why is it ABC and not DFY? When two people see something red, are they seeing the same color? Why would anyone like anime? Mind. Blown.
We have pretty good reason to believe they are, or at least similar colors. a) we can tell colorblindness exists for some people, b) trichromats all report similar differences between pairs of colors.
There's a ton of good teaching ideas like flipped classrooms I never get to use because my group size is always 70+. Even "muddiest point" rarely works.
Well, in your day, we only had to count on our fingers because you couldn't kill more mammoths than that unless you were Sheena, Queen of the Jungle. And while I'm prepared to believe OF is a queen, he ain't no Sheena. Seriously, though, generational divides are a thang. I had to take a maths (yes, Americans, it's MATHS) module as part of my Open University degree and got on OK (I was taught most of it at GCSE-level), but it reminded me that my Mum's generation never dealt with negative numbers, or BODMAS/BIDMAS, or even powers/exponentials.
Okay I know what negative numbers are, and powers/exponents but BODMAS? Body mass calculation formula or something?
