When I read this article, it made my blood boil! Amazing that this junk makes it into print!
(Since it's Monday, you may want to put reading this one on hold...)
Is Algebra Necessary?
NYTimes Sunday Review, Opinion Pages
I agree with
rknop that
"the core of his argument is the
ultimate in anti-intellectualism"
The problem with Algebra is not that it's too hard or not useful; it's that students are poorly prepared for it. And they haven't learned the habits of persistence that would get them through it.
ReplyDeleteDaniel Willingham also has a nice rebuttal to this editorial:
ReplyDeletehttp://www.danielwillingham.com/1/post/2012/07/yes-algebra-is-necessary.html
In the editorial, Hacker dismisses nations like Finland and South Korea that do well in algebra, crediting it to the perseverance of their students.
Their success could point the way for us to solve this problem. Their curriculum is designed so that the transition from arithmetic to algebra is not as abrupt as it is in the U.S. Their teachers also have much better "pedagogical content knowledge" which is one of the most important teacher characteristic for student success.
We could solve this problem. But Hacker would rather throw in the towel. Yuck.
We can also get rid of teaching fractions!
ReplyDeletehttp://www.usatoday.com/tech/science/mathscience/2008-01-23-fractions_N.htm
-Mark Roulo
And in 1989, the National Council of Teachers of Mathematics released a standards document that recommends 'Decreased Attention' to (among other things):
ReplyDeleteFrom p21,
*) Complex paper-and-pencil computations
*) Addition and subtraction without renaming
*) Long division
*) Written practice
The document also explains that, "Programs that ... emphasize
symbol manipulation and computational rules, and that rely
heavily on paper-and-pencil worksheets do not fit he natural
learning patterns of children and do not contribute to
important aspects of children's mathematics development." (p15)
NCTM1989 then lists grade 5-8 content that should get
more attention and less attention. From the less attention
list we get:
"Algebra
 - Manipulating symbols" (p71)
The war on mathematics (and even simple mathematics like arithmetic) is nothing new :-(
-Mark Roulo
George Orwell had a great quote: "There are some things so stupid only an intellectual could believe them."
ReplyDeleteYet another dingbat runs straight into Chesterton's Fence.
Catherine, I got a link to this article this morning from a teacher in a (science!) teacher's listserv. Presumably, she agreed with the author (and I base this on other opinions expressed by this person).
ReplyDeleteJohn Allen Paulos pointed out that learning algebra makes you fluent in the lower mathematics that it requires. So, even though a 45-y.o. florist may not know how to factor a polynomial, she will be able to quickly and accurately tally the cost of a bouquet, thanks to that "useless" algebra class.
The article's dismissal of STEM is simply breathtaking.
ReplyDeleteSince "a mere 5 percent of entry-level workers will need to be proficient in algebra or above"....we can just jettison the subject completely!! Who needs it?! Those 5% can just go become service workers and fetch me my skinny double caramel macchiato every morning. We don't really need their future inventions, cures, scientific breakthroughs, and insights. Good riddance!
The next sentence is a gem too:
"And if there is a shortage of STEM graduates, an equally crucial issue is how many available positions there are for men and women with these skills. A January 2012 analysis from the Georgetown center found 7.5 percent unemployment for engineering graduates and 8.2 percent among computer scientists. "
So, there's a shortage, but it's really a surplus, so....we don't really need any more people in the workforce who are competent in math. I suppose we can just import what we need from India and China, anyway.
The author seems to be saying: since I and other non-math people suck at algebra, no one should be forced--or better: have an opportunity--to do it.
The biggest problem I have with math in America in general, and which this article demonstrates in spades, is the fact that by the time our kids are in 5th, 6th, or 7th grade, the doors are already being closed and locked to STEM careers. So many kids are so far behind, that is is impossible for them--even those with high mathematical aptitude--to make up for the years of poor curriculum and lack of emphasis on mastery of basic skills. By the time many kids face algebra, they can't hack it, because they haven't the underlying skills to deal with it.
How are you supposed to guess which 12 year old will turn out to be turned on by chemistry or number theory? How are you supposed to know which 13 year old could make a major technology breakthrough as an adult? This is essentially tracking on steroids, with the system deciding which pre-teen will be allowed to try to be a high-achiever.
I agree that the higher levels of a subject firm up knowledge of the lower levels. (I have basically no algebra left at this point, but I can do anything you like with a fraction.) In addition, there's the factor of confidence. I remember barely anything of my high school algebra and trigonometry (geometry I feel a bit more comfortable with), but 20 years later, I have a lot of confidence that I've been there before, and if I need to, I can do it again. This isn't just a matter of feelings, because my post-SAHM dream job is to do something with taxes, an option that would never have occurred to me if I hadn't had good high school math (and a math MA dad) and some confidence in my ability to deal with that material.
ReplyDeleteAnn,
ReplyDeleteit's 4th grade. Kids fall off the capable-of-SAT-math track by 4th grade. they do not get back on. they aren't just shut out of STEM majors--they are shut out of median scores on the SAT general math exam, unable to compete against hteir international competition even to get into liberal arts schools.
the bright American students that ace the high school math in the US can't hack it as STEM majors--even when they were supposedly in the right track. They have no depth, and don't understand why math works as it does. their international competitors do.
I need to post about this, but I started MSMI because of what I saw as the tremendous failing in our middle schools. but the more i try to teach fractions to teachers and parents, the more i see teachers and parents who do not understand arithmetic at all.
ReplyDeletethese are people with careers in stem fields who do not know how to regroup 98 + 13 into 98 +2 + 11 to regroup into 100 and 11. they are adults with masters degrees in fields where they supposedly do stats who have never seen the area model of multiplication--and didn't ever derive it for themselves.
I can start to teach them fractions, but they don't understand why the standard algorithms for multiplication and division with remainder work.
they can't teach what they don't know. it will be a long while before there is a cohort of people who know again can be passing that information on.
I used to read sci fi about cultures where war had wiped out cultural knowledge in one generation. Edmund Husserl, the philosopher worried the same thing could happen, and tried to invent a philosophy to prevent it. but i never foresaw that the knowledge could fail to be transmitted in a culture that had not had such trauma. but we are now systematically getting dumber, failing to pass on what was previously known.
at least the prof is consistent: the elite have been championing ideas that have been terrible for the lower classes for 50+ years now, ones they themselves won't adopt. this is just another in that line that they will espouse yet not allow their own children to act on.
it's 4th grade. Kids fall off the capable-of-SAT-math track by 4th grade. they do not get back on. they aren't just shut out of STEM majors--they are shut out of median scores on the SAT general math exam, unable to compete against hteir international competition even to get into liberal arts schools.
ReplyDeleteThe problem is that you can't tell people this.
I mean, you can, and I have, but if you look back at the unschooling thread, you'll see exactly what happens: "I know someone who decided at the last minute to become a [random STEM career], they taught themselves what they needed to know, and they were just fine!"
End of story.
I don't even know what to say to that -- because, yeah, sure, it does happen. But I fear that there is a pretty serious Jeanne Dixon effect that people are not taking into account.
How many folks switch out of STEM tracks or just don't even try to go that way due to their bad math experience? And what is the reason they tell you that they switched? I suspect there's a lot of the politician-equivalent of "I wanted to spend more time with my family" rather than "I couldn't hack the math."
"How many folks switch out of STEM tracks or just don't even try to go that way due to their bad math experience? And what is the reason they tell you that they switched?"
ReplyDeleteWhen I was in college (late triassic ...), the kids were pretty rational about why people dropped out of STEM fields and switched to psychology or sociology or whatever. The answer was usually that "major X was too hard." I suspect that most college age kids these days are equally clear about this.
Now ... how many of them can be specific enough that the problem was the math? That I don't know. But there wasn't much fooling around with stuff like "I like psych better" than difficult-STEM-major.
The kids who don't even start with a STEM major probably have a slightly different story. They will claim that they *like* their field better than a STEM field. And they are probably correct, too. We tend not to like stuff we aren't good at, and the STEM stuff can be quite difficult.
But I wouldn't want to guess how much of this is/was math specific versus being better at humanities-type fields.
-Mark Roulo
To really enjoy a STEM field, the easy stuff has to be easy, so you can focus on the cool, tough stuff and not get bogged down. If you are struggling over the algebra or calc, you can't get any enjoyment out of the rest.
ReplyDeleteSo, saying someone doesn't like a field of study doesn't really help. Yes, they may not be predisposed towards that field, or they may not have the prerequisites to enjoy it fully.
But I wouldn't want to guess how much of this is/was math specific versus being better at humanities-type fields.
ReplyDeleteNo one's asking you to.
they learn to hate math in grade 4, too. For the kids who had been inclined, the incoherence and shallowness followed by incredibly stupid math appreciation assignments is enough to swear it off. For the kids not naturally inclined, being taught it so poorly means they simply can't make any sense of it, and can't reason or compute.
ReplyDeleteMath is fundamentally different than reading or the disciplines dependent on reading or writing. Order matters. You can't come at it from a variety of directions to improve a fundamental deficiency.
Terri, you're right. the people willing to hear me when I say "fourth grade" are those who already believe or at least suspect it. when they don't, they tie themselves in knots to deny it. A friend of MSMI is on Mpls' school board subcommittee for C & I. She also taught math enrichment at one of the schools in mps. whenever she would make a comment to the cmte about how kids there were fundamentally misunderstanding arithmetic, fractions, etc. the board would respond with "what is wrong with that school!" as if it were the anomaly, not the typical case.
I don't know how we say it so the rest hear.
Our kid had a fifth grade teacher who began her unit on fractions by saying that she hated doing them when she was a kid and found them hard.
ReplyDeleteGreat way begin! Blah.
I mean, you can, and I have, but if you look back at the unschooling thread, you'll see exactly what happens: "I know someone who decided at the last minute to become a [random STEM career], they taught themselves what they needed to know, and they were just fine!"
ReplyDeleteIn unschooling, you might have the time and flexibility necessary to put the intense focus you'd need to make up for earlier deficits. But in school you still have to keep up with homework for your other six subjects. That makes it less likely. Assuming a typical school environment, catching up becomes less likely by the year. If you're dealing with the time and resource constraints of school (actual face time with an adult in minutes per day; multiple subjects on a strict schedule), the kids really do have to keep in step all the way or they will fall off.
Thinking back to my own math education, I found that the worst part was, as others have mentioned, the lack of interest, understanding, or enthusiasm among the teachers. I had, to my memory, a single good math teacher - and if I think back on it, he mostly let me sit in the back of the class and work on special projects.
Most of the rest were, like social studies teachers, just football coaches chosen to teach it because someone thought math was for men.
I didn't take a single math class after tenth grade, and not a single math class in college. This was not because math was boring, or because I didn't get it, but because my teachers were boring and turned me off for years.
I think the biggest gap to be breached is the gap of interest and enthusiasm. When I work with my son on math, I try to communicate where I see math going for him, and what I find fascinating about it. It would be great if more kids didn't have to suffer through the tedium of unqualified, unenthusiastic teachers.
(And for those who doubt my qualifications, it's true my doctorate is in literature, but my GRE math was 750 and I worked professionally with stats and big data analysis).
There is a lot of anti-intellectualism out there and a lot of animus against those at the top of the ability/motivation curve; you know, the nerds, the grinds etc. Doubters should read the ed section of the WaPo; there's a whine about the "elitism" and "lack of diversity" at TJ math/sci magnet HS almost every month. Some of the comments are supportive but most fall into the "no resources for the able and motivated" category. For lots of people, it's unfair to allow the kids who have worked hard and done well to be challenged. Due to community presssure, the admit process was changed so that now 1/3 of entering freshmen need remedial (for TJ) math.
ReplyDelete