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In response to a Tennessee proposal to requires four years of math for graduation, an algebra teacher writes that not everybody can learn algebra or needs to know.
It was totally crazy to ever require algebra -- let alone the geometry all must now take. When will the out of touch realize that some are left brained and most are right brained?
... Here is an algebra problem that any Algebra I student will be taught. Factor 8Xsquared -95X -96 I will bet that very few of your staff or even the state school board could do it.
I do not know anyone who has ever factored anything outside of a classroom. Have you ever rationalized a denominator?
Why is this man a math teacher?
Colby Cosh links to a discussion on whether math has progressive uses. It starts with this post:
I've come to realize that probably one reason I struggled with algebra, geometry et.al., was that it seemed to me that these were basically reactionary academic disciplines, useful for designing weaponry or potentially repressive computer technology, but not with any obvious humanistic or social positive uses.Read it for the philosophy joke.
If I'm wrong about this, I'd appreciate it if people could show me how this discipline can have progressive uses.
I also feel this could be useful in developing better ways of teaching higher mathematics if such uses could be found.
25 comments:
You know, when I originally saw that thread a while ago and the argument struck me as bizarre.
Then I read Hardy's "A Mathematician's Apology" where he
distances himself from applied math because of its utility in war.
Hardy has to resort to redefining math in order to make his profession a peaceful one in his own mind.
I'll give you a fun quote but before you read it bear in mind that Hardy's sidekick Littlewood served in WWI. Hardy was NOT into applied math and you should take what he says about "real" math with a grain of salt. He doesn't mean to be humorous but his attempt to distance himself from that part of mathematics is comical.
Here is the text in full, it's about 50 pages. You should read the whole thing for no other reason than because this book is a "classic."
http://www.math.ualberta.ca/~mss/books/A%20Mathematician's%20Apology.pdf
Here is the quote:
(see pg. 48)
"Real mathematics has no effects on war. No one has yet discovered any warlike purpose served by the theory of numbers or relativity, and it seems unlikely that anyone will do so for many years. It is true that there are many branches of applied math, such as ballistics and aerodynamics, which have been developed deliberately for war and demand quite an elaborate technique: it is perhaps hard to call them trivial, but none of them has any claim to rank as being 'real.' They are indeed repulsively ugly and intolerably dull; even Littlewood could not make ballistics respectible, and if he could not, who can? So a real mathematician has his conscience clear..."
"When will the out of touch realize that some are left brained and most are right brained?"
He forgot to say that some -- including math teachers -- are harebrained.
Some of the comments were quite funny.
We've talked about the politicization of education before, and how a lot of ed-school ideology is the sort of leftism that makes lifelong social democrats cringe (in the way that so many conservatives cringe at creationism). What strikes me about those comments is the way that it funnels everything through the lens of politics - 'the personal is the political' carried to its illogical end:
1. Radical progressivism is self-evidently The Truth.
2. Therefore, any deviants from radical progressivism must be reactionaries.
3. Therefore, any deviation from radical progressivism must be malicious in intent.
It's at this point that it stops being a policy debate, and becomes a religious crusade. Lifelong leftists who don't believe are not merely wrong, but apostates. As for non-leftists... I remember reading a quote once by a liberal voucher supporter who said that Milton Friedman set the cause of school choice backwards fifty years - not on account of his arguments, which he came to agree with, but on account of him being Milton Friedman. Friedman:Satan::Vouchers:Necronomicon.
Tedious full disclosure: I'm an admitted right-leaner, so take the above with a grain of salt if you wish. I'm trying my best to be fair here, and certainly don't wish to imply that my own 'side' doesn't do the same thing (or worse).
I love this one:
I think that the use of our brains beyond the limbic system and the basic sensory, motor, and association cortices is elitist and should be stopped. Using our frontal lobes has let to racism, war, and mathematics, and clearly we would have been better off without using those particular neurons. Let's make stop using our frontal lobes the last logical decision that we make, people, and reclaim a simpler time, before it's too late for everyone.
Now that I can't remember things like "isolate the variable" and "inverse operations" I'm well on my way to taking this guy's advice.
He forgot to say that some -- including math teachers -- are harebrained.
LOL!
The question is what should students know before we allow them to choose their own path. Up through 8th grade, schools should try their hardest not to close doors. For math, this means algebra in 8th grade. One could argue that this is overly optimistic for some students, but the alternative should not be real world or checkbook math. It should be real algebra in 9th grade.
Many won't need algebra as adults. They won't need lots of things they learned. So what? That was the basis of my "smoking gun" comment about EM. Here they are deciding 5th grade math content on the low probability the students will need the skill as an adult. Of course, their assumption will guarantee the result. As I found with the comments on the YouTube (Professor's video) site, some teachers base their whole philosophy on these assumptions.
The commentor said that dissenters had a "narrow" and "monolithic" view of math. Actually, my view of K-8 math education is all about not closing doors. You do that with a proper course in algebra by 8th or 9th grade. The problem is that once you're off the algebra in 8th grade track, it's unlikely that you will receive proper math courses in high school.
I'm all for 4 years of English and math in high school, no matter what your track. The goal doesn't have to be calc or trig, but it should be more than playtime learning.
Educators talk about "deeper understanding", but they don't have the knowledge to even know what they're talking about.
It's not so much the crazies who want to get rid of algebra that you have to worry about, it's the others who have hijacked math by changing content, meanings, and expectations. It's one thing to have an opinion, but it's another thing to not know that it's an opinion. And, it's quite another to force that opinion on others.
I think they really know it's an opinion, but they want to hide it. They have to make it into something more. They don't want to tell you that everything is based on lower expectations, so they come up with talk of higher-order thinking, deeper understanding, and students taking ownership of their learning.
Perhaps they think that good intentions are all it takes to prove your rightness (or leftness).
It should be the student's choice whether they want to pursue academic courses, as opposed to trade-like courses, in high school. This means that kids need to have been taught all the skills and knowledge they need by the 8th grade in order to have this choice available to them. What typically happens is that the choice is foreclosed to most kids because they were never adequately taught the basic k-8 skills they needed to know by 8th grade. Educators now make the decisions that kids whouls be making by not teaching properly.
Since I finished my formal education I have not:
critically analyzed a poem
written a book report
boiled anything in a beaker
turned on a bunson burner
calculated the chemical reaction of combining any two items
read anything included in an anthology
run a relay race
Was my entire school career a waste of time? Apparently, I learned a lot of totally useless skills with no real world application.
Yet somehow I've managed to become a highly successful professional.
a lot of ed-school ideology is the sort of leftism that makes lifelong social democrats cringe (in the way that so many conservatives cringe at creationism
You know, that's a pretty good analogy.
I wish I knew more about intellectual history...
The question is what should students know before we allow them to choose their own path. Up through 8th grade, schools should try their hardest not to close doors. For math, this means algebra in 8th grade.
absolutely
very difficult to get this message across
Educators now make the decisions that kids should be making by not teaching properly.
Exactly.
This is what brings the pushy parent onto the scene as well.
The pushy parent is the one who doesn't accept the school's verdict on his child's ability to learn advanced material.
Was my entire school career a waste of time? Apparently, I learned a lot of totally useless skills with no real world application.
The terrific thing about cognitive science is that it explains the pragmatic reason for acquiring a high-quality broad liberal arts education.
Business leaders constantly tell professors that they're looking for liberal arts majors, not business majors.
They've been saying this for years; Ed hears it in every conversation.
I've always assumed they knew what they were talking about, but I never understood it.
Cognitive science explains it.
A high-quality liberal arts education gives you broad background knowledge.
Broad background knowledge, well-learned, makes you a much faster learner any time you have to pick up a new skill or concept.
The constructivist argument that the economy now requires so much adaptation and produces so much new knowledge that it's a waste of time to learn "old facts" has it exactly backwards.
The more you know the faster you can learn new things.
The question is what should students know before we allow them to choose their own path. Up through 8th grade, schools should try their hardest not to close doors.
And even well past 8th grade, I suspect.
If you look at any discrete subject area, and the number of people that go into that area, you could justify giving up on teaching anything in high school at all.
I didn't even know that my eventual career choice existed when I was in high school, let alone 8th grade. The same is true for many others, I suspect.
A broad liberal arts background is the best education for the vast majority of students. Thanks, Catherine, for putting it so well!
this means algebra in 8th grade.
"absolutely"
"very difficult to get this message across"
The problem is that they've redefined it. Most schools have algebra in 8th grade. Our neighboring town even has "Advanced Algebra". It could be that advanced algebra really means regular algebra for those students who get help at home or with tutors. Nobody is crazy enough to say that algebra isn't important. They just redefine it.
They argue with generalities and you never get the chance to argue details. There is no process for that.
If you look at any discrete subject area, and the number of people that go into that area, you could justify giving up on teaching anything in high school at all.
Exactly.
I didn't even know that my eventual career choice existed when I was in high school, let alone 8th grade. The same is true for many others, I suspect.
What IS your career??
I didn't even know that my eventual career choice existed when I was in high school, let alone 8th grade. The same is true for many others, I suspect.
Another great point.
Cognitive science put it all together for me.
We all sort of intuit that a high-quality, broad liberal arts education is good....
But we can't say why on any grounds other than core values (i.e. we value a broad liberal arts education).
Values ought to be enough; we shouldn't have to be constantly fending off attacks on the liberal arts launched by ed schools.
But since we do have to fend off these attacks, it was incredibly useful for me finally to piece together these various findings and observations.....
The irony is that a high-quality broad liberal arts education gives you far more flexibility than any other kind of education.
The problem is that they've redefined it. Most schools have algebra in 8th grade.
Actually that's not the problem here.
The problem here is Darwinian gatekeeping.
The district simply does not feel it's important in any way for our students to be on par with their peers in Europe and Asia.
Until just a couple of months ago the administration openly rejected the very idea that it would be possible for Irvington schools to put Irvington students on par with their peers in Europe and Asia.
Shortly before Christmas the math chair flatly denied that algebra-in-8th-grade is the international standard.
Suggest to the math chair that he talk with members of the National Math Advisory Panel, namely Sandra Sstotsky, Vern Williams, Wilfried Schmid, Hung-Hsi Wu, Liping Ma, Diane Jones and Tom Loveless.
Suggest to the math chair that he talk with members of the National Math Advisory Panel, namely Sandra Sstotsky, Vern Williams, Wilfried Schmid, Hung-Hsi Wu, Liping Ma, Diane Jones and Tom Loveless.
Wish I'd thought of that.
The great thing there was that the very next day the principal, assistant principal, and math chair attended a conference at which they were told that algebra in the 8th grade is the international standard.
heh
Shortly before Christmas the math chair flatly denied that algebra-in-8th-grade is the international standard.
The math chair is correct. In Singapore and Russia Algebra is taught in 7th grade, not 8th.
-Mark Roulo
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