http://www.nytimes.com/2012/07/29/opinion/sunday/is-algebra-necessary.html
Is Algebra Necessary?
By ANDREW HACKER
New York Times
July 28, 2012

A TYPICAL American school day finds some six million high school students and two million college freshmen struggling with algebra. In both high school and college, all too many students are expected to fail. Why do we subject American students to this ordeal? I’ve found myself moving toward the strong view that we shouldn’t.

My question extends beyond algebra and applies more broadly to the usual mathematics sequence, from geometry through calculus. State regents and legislators — and much of the public — take it as self-evident that every young person should be made to master polynomial functions and parametric equations.

There are many defenses of algebra and the virtue of learning it. Most of them sound reasonable on first hearing; many of them I once accepted. But the more I examine them, the clearer it seems that they are largely or wholly wrong — unsupported by research or evidence, or based on wishful logic. (I’m not talking about quantitative skills, critical for informed citizenship and personal finance, but a very different ballgame.)

This debate matters. Making mathematics mandatory prevents us from discovering and developing young talent. In the interest of maintaining rigor, we’re actually depleting our pool of brainpower. I say this as a writer and social scientist whose work relies heavily on the use of numbers. My aim is not to spare students from a difficult subject, but to call attention to the real problems we are causing by misdirecting precious resources.

The toll mathematics takes begins early. To our nation’s shame, one in four ninth graders fail to finish high school. In South Carolina, 34 percent fell away in 2008-9, according to national data released last year; for Nevada, it was 45 percent. Most of the educators I’ve talked with cite algebra as the major academic reason.

Shirley Bagwell, a longtime Tennessee teacher, warns that “to expect all students to master algebra will cause more students to drop out.” For those who stay in school, there are often “exit exams,” almost all of which contain an algebra component. In Oklahoma, 33 percent failed to pass last year, as did 35 percent in West Virginia.

Algebra is an onerous stumbling block for all kinds of students: disadvantaged and affluent, black and white. In New Mexico, 43 percent of white students fell below “proficient,” along with 39 percent in Tennessee. Even well-endowed schools have otherwise talented students who are impeded by algebra, to say nothing of calculus and trigonometry.

California’s two university systems, for instance, consider applications only from students who have taken three years of mathematics and in that way exclude many applicants who might excel in fields like art or history. Community college students face an equally prohibitive mathematics wall. A study of two-year schools found that fewer than a quarter of their entrants passed the algebra classes they were required to take.

“There are students taking these courses three, four, five times,” says Barbara Bonham of Appalachian State University. While some ultimately pass, she adds, “many drop out.”

Another dropout statistic should cause equal chagrin. Of all who embark on higher education, only 58 percent end up with bachelor’s degrees. The main impediment to graduation: freshman math. The City University of New York, where I have taught since 1971, found that 57 percent of its students didn’t pass its mandated algebra course. The depressing conclusion of a faculty report: “failing math at all levels affects retention more than any other academic factor.” A national sample of transcripts found mathematics had twice as many F’s and D’s compared as other subjects.

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A related discussion here is at http://giftedissues.davidsongifted....sing_the_achievement_gap.html#Post118807 . I think it is reasonable to expect high school graduates to know Algebra I (for example finding the equation of a line given two points) and for college graduates to know Algebra II, but since I think a large fraction (maybe 50% or more) of the population cannot learn algebra, that means that lots of people are not smart enough to get a real high school education, much less a college one. The idea that a bachelor's degree is for the (at least mildly) gifted, not for everyone, is "elitist", but I think it is true.

That article appears to conflate "mastering algebra" with passing an Algebra 1 course (or passing an Algebra 2 course, in places). Is that a reasonable conflation, in the US system? In the UK, a student needs to get grade A-C at GCSE mathematics (exam taken age 16) in order to be counted in certain "success" statistics for the school, and in order to go to university (any subject). The GCSE syllabus includes a lot of what you call Algebra 1 or Geometry e.g. solve quadratics, do stuff with the equation of a straight line, work with exponents, calculate volumes and areas of various 3D shapes, prove simple things using circle theorems, etc. However, getting a C at GCSE is a pretty low hurdle, and by no means proves that you've "mastered" all that material.

I don't think it's unreasonable to expect high school kids to take Algebra. Algebra is not that difficult, frankly. I do think the bar is set super low in math in the USA. My son is doing a beginning alegebra boook at home, and he just finished third grade.
I think the USA needs to really wake up in math and science. I'm sure other countries have their high schoolers take Algebra, and they can do it. OK, I don't think everyone needs to take Calclus, but Algebra???

LOL! And what talent would this be?

With higher education collapsing, the non-productive degree departments will be reduced or eliminated. Art and most of the hyphenated departments will be gone. Only the ones requiring math will be left.

Many vocational programs like surveying, welding, machining, etc etc have a very high math component. Algebra and working knowledge of geometry are REQUIRED.

Maybe hair dressing and truck driving will allow someone to function without numerical literacy, but the higher certs in trucking do REQUIRE math skills.

The author of this article has no knowledge of how the real world works or any interest in providing a productive future for kids.

Based on my experience working with less conceptually intelligent people (and by this I mean those who are generally not able to deal with theoretical aspects of math in any classroom environment), many people seem to develop enough math skills to do the jobs they want to do.

So, for example, if you have a person who really, really wants to learn how to do machining, such a person will apply themselves and eventually learn enough math to perform their job well.

Remember, everyone is generally able to learn specific mathematical skills, it just might take them a long time.

And by long time, I mean 5 years to grasp something that I could grasp in about 10 minutes.

Often being on the job for years is an excellent way to obtain sufficient vocational training to perform jobs rather than any kind of more formal vocational training.

If someone knows what kind of job they like to do, they will generally find a way to work around or deal with any intellectual limitations.

Yup. I agree... 100%

It's like anything else - you get out of it what you put in to it. Gifted kids may be ready to learn it younger, but it's certainly not beyond the average student, assuming they're willing to pay attention and apply themselves (which they'll have to do with anything in life if they want any kind of success).

I don't think it's unreasonable to ask high school students to master an algebra class. BUT...

In my state, graduation requirements include passing Algebra 1, Geometry, then Algebra 2. Which is fine...for some kids. But we have to be reasonable and understand that not all kids are college material, not all kids are particularly bright, and that there simply *are* kids who will become cable installers, welders, and plumbers (and at the rates our plumber charges, I fail to believe I'm condemning these kids to a life of penury by saying so). Holding these kids to that particular standard is an exercise in failure, and to no real purpose. It hurts them, and it hurts their classmates, who must wait while the teacher tries to drag them along.
We need to go back to a multi-path secondary school program. It would mean more appropriate education for the students, a better use of the teachers' time, and be a more efficient use of our tax dollars.

You probably don't want to know, Austin, how very little math is required of the average health care degree program.

Indeed. Everything that eldertree just said, including the high school graduation requirements imposed by the state BoE, and the relative insanity of doing so.


I taught chemistry to pre-nursing majors (year-long survey course, otherwise known in the trade as the G-O-B course, for 'general-organic-biochem') and most of those students could not:

a) turn a simple real-world problem into a mathematical expression of any kind,

b) solve VERY simple equations, even those previously set up for them, of the variety; 3x = 21,

c) recognize the words "quadratic equation,"

d) correctly use simple proportions to solve for scaled quantities, or

e) work with metric units using dimensional analysis to perform unit conversions correctly.

My child could do most of those things by the time she was in second grade, and could do them with mastery by the time she was in 6th grade.


These were college students, recall. People who were studying to become nurses.

I weep for the future...

----------------------

My major comment re: the article is that, well, DUH-- maybe this just suggests that not everyone is that bright. Maybe not everyone is "college material" to start with.

Now, what I ultimately mean by that statement is-- maybe that's actually just reality and it's fine that not everyone can become proficient in everything.

Also unspoken is that not everyone gets what they want. Very few people (relatively) who want to become brain surgeons are capable of doing the job to begin with. It's not very nice to delude those students well into college-- better to let them get over their disappointment early and make other plans. At least that's my opinion.

Same thing goes for college in general. Maybe if you can't handle basic algebra, a university isn't the place for you, if you see my point. I hardly think that the reasonable thing to do is to lower the standards to make college more inclusive. Lowering barriers to access, I'm all for, make no mistake-- but lowering expectations, I'm dead set against.

The world needs skilled tradespeople, too-- and not everyone can learn to be highly skilled there, either. The difference is that nobody is trying to suggest that I should feel like a failure for my lack of ability every time I take my car to my mechanic.

Kind of makes me grumpy that we seem to have lost our minds completely in the past generation, at least re: what constitutes "success" educationally.

I'd even go so far as to argue that "making math mandatory" doesn't prevent us from discovering talent as much as removing the mandate does.

Because look, even if it were possible to 'remove' math requirements from fields like medicine, geology, or fashion design (hint: it isn't, because reality doesn't care about anyone's fantasies), maybe allowing people to call themselves professionals in those domains without actually, you know-- being competent at them--

gets in the way of those people discovering just where their talents actually lie.

Maybe they DO have talents. But maybe a high school or university/college classroom isn't where they're going to find them. If we participate in the fallacy, we are tacitly discouraging those people from doing the kind of exploration necessary for finding out where they ARE competent.

Sorry-- the article is just stupid. The logic there is abysmal.

::scuffing toe::
When I first got my RN (AD program), chemistry wasn't required at all. Math was the same class, essentially, that they taught the 9th graders who couldn't pass algebra.


::applause::

The problem is that more and more jobs are requiring skills that are best acquired in post-high school programs. If kids can't even get through high school--and Algebra 1 is determined to be the barrier course--they can't move on to an Associate's degree in an area they CAN complete studies for.

I don't think anyone is talking about changing Ivy League institutions (or their peers outside the Ivies) to lower their academic entrance requirements. However, if a student who has studied plumbing at his local vo-tech program and wants to get the next stage of certification so he can get a higher paying plumbing job drops out of high school because of Algebra 1, there might be a better solution from adjusting high school graduation requirements rather than adding to the roles of drop outs who already can't get the higher paying plumbing jobs.

I forget what the statistics were on state university students and how many were rquired to take remedial courses on entry. I'll go with the scientific term "boatloads".
Purely anecdotally, I will say that our local junior college has a higher percentage of students taking remedial math on entry (a course preparatory to college-lite algebra) than not taking it. With that in mind, I think the goal aimed for by making geometry and algebra 2 mandatory is probably not so much mastery as statistical sleight-of-hand in the School Grading arena.

Maybe the real problem is that most of those higher paying jobs actually require the skills learned in Algebra 1. My question is-- if being a highly paid plumber doesn't require a basic high school education, then why would anyone insist that candidates for journeyman programs have a diploma?

Math-phobic or not, I think that JonLaw's point is a good one-- most people are capable of learning (up to some point, at least) what they are highly motivated to learn.

There is an alternate route to Vo/Tech education at community colleges, and in many cases, work experience will stand in for educational ones. A G.E.D. has no particular course requirements, so there is an alternative minimum.

Algebra 1 isn't that hard. In all of my years of teaching, I really only ran into a couple of students who truly weren't capable of going there. (Those were some sad, sad, sad office visits involving a lot of kleenex, by the way; those kids really didn't belong in college at all.)

It would have been better for those few kids to have known how limited they were before leaving high school, honestly.

I'm trying to think of an occupation that does NOT require the knowledge of basic Algebra 1, and I can't think of one. Basically even being an adult homemaker, childcare provider, or anything else as an independent adult requires some basic algebra and applied consumer math.

There's no other way to understand pricing, critically evaluate credit-card or loan agreements, comparison shop, or understand government spending/budgeting. (Well, okay... understanding government spending may be a reach. Nobody understands it. LOL)

Being able to calculate expenses and determine ordering quantities or make estimates on a job are all algebra skills. Now, should we be teaching "calculus-track" algebra and also "vo-tech track" algebra? OF COURSE.

My point is that basic citizen-level numeracy has moved to be more demanding, though. I do not think that the barrier is a single class. The real barrier is the knowledge.

I'll just briefly mention that I believe it's important to keep Algebra 1 as a requirement for high school graduation, as well as (jmo) I believe it's a level of math that the majority of people *can* succeed at. I won't go any deeper into philosophy or debate

I did want to add one thing that I think hasn't been mentioned, in support of requiring all students to take Algebra. There are kids who don't get excited or turned on by math in elementary school that *do* discover math is interesting and fun once they get to Algebra - I've known a few kids who went into Algebra kicking and screaming and truly believing they weren't "math-brains" who all of a sudden started to "get math". Even in my own school experience, I was always good at math but never really thought much about it until I took Algebra, started seeing the real-world connections, and that's where my love of math took off.

polarbear

While I don't think it's unreasonable for the majority of HS students to take and pass the classes that have been discussed, as with most subjects related to public education there is a one size fits all thought pattern that all too often holds back many be they low ability, average, or high ability.

Perhaps the solution is in taking a page out of the college notebook and offering diplomas with different requirements (majors) or a HS diploma (basic), another with honors, another with honors and distinction.

Yes, other countries do that. It makes sense.

It would also be reasonable to offer different math courses: basic algebra and honors algebra, basic geometry and honors geometry, etc., as is often done with English classes.

I don't believe you need to be particularly smart to be able to do algebra. The fact that so many students cannot reach this very low bar is a big problem, in my opinion. I think the problem starts in elementary school. My kids did virtually no math at all from Pre-K until 2nd grade - yet in the same time they were required to read, write and have a very basic grasp of spelling. Starting in second grade they did 40 minutes of math three times per week (no homework given). One of those days was spent doing "math based games", which included checkers, chess, knot games etc. The remainder of the academic time was spent on literacy based activities. Kids are just not doing enough math in the early years to set them up for success later.

I am also a University professor. We are having a discussion about dropping the calculus requirement for the same reason. Kids just cannot pass it.

I think there are parts of algebra I that are tough forthe uninitiated. The different varieties of rate*time=distance word problems aren't trivial. Related rates problems also aren't trivial. Nor is multiplying or dividing long polynomials/polynomial fractions. Etc. The basics are easy enough, though.

College students should be able to pass calculus, though.

New York state has long offered a Regents Diploma. Quoting Wikipedia,

"Regents Examinations are statewide standardized examinations in core high school subjects required for a Regents Diploma in New York State. In the past, Regents Diplomas were optional and typically offered for college bound students. In recent years graduation requirements have been made more stringent, and currently all students are required to receive a Regents Diploma, and therefore most students, with some limited exceptions, are required to take the Regents Examinations. To graduate, students are required to have earned appropriate credits in a number of specific subjects by passing year-long or half-year courses, after which they must pass Regents Examinations in some of the subject areas. For higher achieving students, a Regents with Advanced Designation and Honors designations are also offered."

Barron's publishes many study guides for the Regents exams, which can be found on Amazon by searching (for example) "regents algebra". They are inexpensive either new or used and get mostly good reviews.

Here is an interesting follow up on the Algebra for All initiatives:

http://blogs.edweek.org/edweek/curr..._algebra-for-all_p.html?cmp=ENL-EU-NEWS2

Thanks. It refers to the following paper.

http://epa.sagepub.com/content/early/2012/07/30/0162373712453869.abstract
The Unintended Consequences of an Algebra-for-All Policy on High-Skill Students: Effects on Instructional Organization and Students’ Academic Outcomes
Takako Nomi
Abstract
In 1997, Chicago implemented a policy that required algebra for all ninth-grade students, eliminating all remedial coursework. This policy increased opportunities to take algebra for low-skill students who had previously enrolled in remedial math. However, little is known about how schools respond to the policy in terms of organizing math classrooms to accommodate curricular changes. The policy unintentionally affected high-skill students who were not targeted by the policy—those who would enroll in algebra in its absence. Using an interrupted time-series design combined with within-cohort comparisons, this study shows that schools created more mixed-ability classrooms when eliminating remedial math classes, and peer skill levels declined for high-skill students. Consequently, their test scores also declined.

The report is at http://www.eric.ed.gov/PDFS/ED512659.pdf . A related thread was "Effects of almost universal 8th grade algebra"
http://giftedissues.davidsongifted....2180/Effects_of_almost_universal_8t.html

I do not wish for all high school students to take Algebra. This dumbs down the classes. Students are usually passed through these courses (here anyway). They are appalled when they are placed in a basic math course in community college. "I passed Algebra; Why am I here again?".

My daughter's Algebra II course did not finish the book (or even the curriculum) due to the lower abilities of students in the course. Most of the class failed the placement test for College Algebra. College Algebra seems like a wasted class as it is just taking Algebra II again - just faster. We did not take College Algebra if we successfully pass Algebra II.

Personally, I think the biggest issue with kids and Algebra is that we spend all those years beforehand teaching various methods of computation without really explaining why we bother in the first place. We give them occasional hints with word problems, but 8 cookies plus 2 cookies really isn't sophisticated enough for them to get the central idea, that math is essentially another language that we use primarily to express relationships, and that the numbers in and of themselves are essentially meaningless, unless given meaning through context. Because up to the point where they enter a Pre-algebra class, math is ALL ABOUT THE NUMBERS... so how can you suddenly say they're meaningless?

In the face of a giant paradigm shift, some embrace the new and go on to success. And some are so stuck in the old mindset that they can't get out. Education is filled with such examples, where advancement to higher levels involves a teacher saying, "Everything you think you know about this subject is wrong." Algebra is just one example, but it also happens to be one nearly everyone experiences.

I recently asked why my daughter was already seeing simple computation represented as Algebra problems in the first grade, and I think I just answered my own question.

Because students who fail placement tests at the community college graduate at much lower rates than those who pass, some advocate using high school GPAs instead for placement. But what does a passing grade in high school algebra
signify if one cannot pass an algebra test?

http://www.nytimes.com/2012/02/29/e...ny-to-remedial-classes-studies-find.html
Colleges Misassign Many to Remedial Classes, Studies Find
By TAMAR LEWIN
New York Times
February 28, 2012
Two new studies from the Community College Research Center at Columbia University’s Teachers College have found that community colleges unnecessarily place tens of thousands of entering students in remedial classes — and that their placement decisions would be just as good if they relied on high school grade-point averages instead of standardized placement tests.

...

I agree Bostonian. Many (or most) of the students in my daughter's class were just there to pass. They are always passed anymore.

Yes! I've been re-teaching long division and fractions to one of my kids this summer because the algorithms used in school are merely methods that work, with no real thinking required. I was amazed to see that his math book teaches long division the way I learned it in the 70s. All these years later, and no one has figured out that "2 goes into 2 once, bring down the 5" in 25/2 is a bad idea? My kids learn that 2 goes into 20 10 times, and 2*10 =20. Great! You've divided up 20 out of 25. Subtract, and you have 5 left to divide. And we do exercises with Cuisinaire rods to demonstrate what's happening in long division.

I've shown him the relationships that exist in and between different arithmetic operations, and a kid who detested mathematics is now telling people that he likes math. The other day, he complained that "I was really looking forward to learning something new, and it's over already."

The article seems to say that many kids go into the placement test with no prior study / review, and with no particular reason to attempt to do well. If you plunked me in front of an algebra test today, and said it would make no difference in anything how I did on it, you'd probably conclude that I needed remedial coursework. What I really need is a half-hour review of whatever I've forgotten in the 25 years since I last took an algebra class, and an understanding of the consequences of the test results.

I didn't use any math beyond basic algebra in jobs like cost accountant and executive assistant. I haven't worked outside the home since my son was born and now as a homeschool mom, I am now relearning the algebra that I have had many years to forget. I noticed some things several things on IXL that I don't remember ever learning and I know I never used.

My husband is a manager and works for a university. He says he has only used basic algebra skills in the jobs he has had and was not taught some of the skills that are on IXL's algebra. He says he never needed them.

I have not had a chance to talk to my sister who took every math class she could get in high school and is a highly paid manager working for the federal government. I doubt that she uses all of the algebra she learned.

I am guessing my relatives who were engineers used a lot of algebra, but the rest of us would have been just fine with just the very easy basics.

My son knows he probably won't use some of what he is learning but he is willing to learn as much as he can so that he will do well on the ACT-- if we can get accommodations for his dysgraphia. If not, he will try to learn enough to pass the algebra CLEP test at some point.

I am a homeschool mom. Although I could relearn algebra and show my son how to do something using the one and only algorithm that I was taught, that was never enough for him. This and dysgraphia has been a challenge for both of us.

When we race to find the answers to algebra word problems, he almost always finds the answers faster than I do because he can do so much of it in his head. I can't. Years ago I was taught to write out every little step and not question how it was done. I am older and stuck in my ways and my mind is just not as flexible as his.

My son has always had the freedom to try different ways to find the answer and then use whatever algorithm works the best for him.

On his own, he figured out an alternate subtraction algorithm using negative numbers that I had never heard of. He did this right before he turned five. Older friends in his acting class had told him about negative numbers but not how to do this subtraction method.

He found it easier to use algorithm for mental math and asked me why he couldn't do it this way. At first I told him it wouldn't work and that he had to do it the traditional school way but I went into another room and tried it and it worked. For so many years I thought the way I had been taught was the only way. I showed it to my husband. My husband and I talked to the kindergarten teacher about this method that our son was using for subtraction before he started kindergarten not knowing that all they thought was important for him to learn was to color in the lines, even though he has a disability that makes it difficult for him to do this.

We really had no choice but to homeschool.

I mostly just lurk on this board looking for good information, but felt that I must make a comment here or bust in frustration :-)

I think some of the comments regarding math and whether or not a child should go to college if they can't do algebra have been a bit elitist.

I have a master's and my husband is working on a PhD and is a senior administrator at a small local LAC and neither of us were very strong in math. I would have given up years ago if someone had told me I didn't belong in college because I wasn't good at math. And by not very good I mean I started in basic college algebra and almost failed.

I think one thing that is being overlooked a great deal of the time on boards such as this one is the fact that not all gifted children are gifted in every area. And I'm not talking about the my child is a gifted athlete or my child is gifted in interpersonal skills (I did have classes on Howard Gardner's theories in graduate school.) But, that some children are gifted verbally and some children are gifted mathematically.

I have a daughter who in years past I would have said was generally gifted in both areas. She just turned 15 and until she hit algebra she was/is gifted in both areas. But as years have passed and she has grown, she is much more gifted verbally. I do not have an IQ score on her but with subtests and SAT's from when she was 11 and her recent ACT score and other evaluations over the years she would probably hit in the HG to low PG range. Never applied to Davidson, (did Duke Tip instead) but I could take her current scores and she would qualify as a Davidson scholar. But math is not her thing. She started taking classes at our state flagship university at 14, but not in math or science subjects. I would hate for someone to tell my child who is off the charts on the verbal side that she is not college material because she struggles in math.

Now, she can do it and will pass with more than a C, but it is not easy, we have had to slow down, we have had to back up and review and this is a child who has never had to review anything. We do not do repetition. She usually is a tell me once I've got it kind of person. Now part of it is that she doesn't like math and in her teenage state of mind sees no need for it in her future career as a writer. If she applied herself more she would probably do even better, but math does not come easy as it did when she was younger and it's not because she didn't learn the basics well.

There is another thread talking about written expression disorder. Should we not send those kids to college? Never mind they may excel at math, they may struggle to write their college papers.

I try to be careful of saying that "I don't understand what's so hard about writing a research paper, my child could write them in 2nd grade", and I think others should be careful to not say "what's so hard about Algebra my child could do it in 2nd grade". I have tried to teach my children that everyone learns at different rates and in different ways from the time she was 3 and 4 and reading chapter books when her friends barely knew the alphabet.

I'm not saying water down the curriculum or that basic Algebra skills are not necessary for higher education, they are. But does my daughter need Pre-Calculus and Calculus, maybe not? I just think we have to be careful of judging who's college material and who is not based solely on Algebra skills. And I did not fully blossom in education until I hit college and had some professors who believed in me and told me I could do it, and I did. I wondered why I had wasted my high school years, but I'm glad others did not give up on me before I even started.

So, just my little vent. Sorry so long.

Thanks for that RJED. Great explanation!

Thank you, RJED, for putting into words so eloquently what I've been struggling to say since this thread began. I am the parent of a verbally gifted daughter (2 actually, but the youngest is too young to start calling "gifted" yet) who really dislikes math. Her processing for basic arithmetic is pretty slow. While she reads on a 6th grade level, having just turned 7 years old, her math is pretty much on-level or just slightly above in a testing situation. The idea that she isn't gifted, or even further, isn't college material, because she struggles with math, is offensive.

To be honest, I see this a lot on the internet discussions of giftedness. There is a lot of information and support for parents of children who are mathematically gifted, and there are classes, camps, scholarships, and all for the students, but verbal giftedness seems to be a sideline--Oh, if they're reading early, then obviously all you need to do is give them more books. It's almost as if, for many, gifted = gifted-with-math.

On the one hand, I wouldn't want kids who could otherwise successfully attend and graduate from college not do that simply due to algebra. On the other hand, I can't help but think that this is yet another example of the dumbing down of our educational system.
After Algebra I comes Geometry, Algebra II, and Calculus. It doesn't seem too much to ask in 4 years of high school to have kids take Algebra I. Kids in most other countries do that and more. My son in his G/T class will take Algebra I in 7th grade.
There are lots of kids who are gifted verbally and not in math. Still, I personally think everyone, gifted or not, really should try to make it through Algebra I.

The dumbing down of our educational system is a major topic for me, being a public high school teacher. On the one hand (since we're using hands, LOL), I do worry about the dumbing down, as you said, and see it in my own subject area (English). On the other hand, as previous posters have mentioned, we're educating children at a higher level than ever before, where children who wouldn't have been to high school before are now required to attend, at least until age 16.

I consider the abstract thought required for Algebra, and wonder if that's the problem with forcing all students to take it in 8th or 9th grade. I teach 9th graders: I can tell you that a lot of them are still thinking very concretely. Perhaps the outcome would be better if they could take Algebra as an upperclassman? The problem, programmatically speaking, is that states require multiple years of math for graduation, and the math classes run sequentially. So, a student waiting until junior year to take Algebra 1 will not have enough time to complete the requirements and graduate on time.

I do agree with you- I hope that I didn't sound snarky saying, everyone should take Algebra. I see lots and lots of kids who just aren't "mathy" kids, when I've volunteered in my kids' classes, and they should still be able to go to college.
But it is a slippery slope.
Look at what, I'm sure, you see, with your English classes you teach. Probably often not as much writing, or the spelling is sloppy, or the grammar is poor- and you just go with it because all of the kids just about write like that.
It's like our state standards here in California, with our yearly STAR test. At the end of second grade, they tested things like- how to tell time. Lots and lots of kids didn't know that! I don't even think that is a gifted thing- I think that we just keep lowering the bar so everyone can pass and feel good instead of saying, let's set the bar higher and everyone tries harder.

My daughter is going into 10th grade this year. Unfortunately, setting the bar higher for everyone dumbs down the individual course. I get very tired of this since she needs to go through Calculus.

She is a very gifted math student - and really all around.

Maybe this is the problem, in that we're requiring too many units of math for graduation. For the non-college bound, it appears to me to involve too much needless repetition. When I was in HS I was that "ambassador" type who could move among social groups at will, and I had a number of friends who were, shall we say, less than diligent in their studies. I had a few conversations with individuals about their math difficulties, and they let me flip open their books, at which time I discovered that HS students were still working on decimals, fractions, and other skills I'd mastered in elementary school, in a class they required for graduation.

Unless the goal is to teach a child to hate math, what is the point?

I could see making Algebra I a graduation requirement, then making individual decisions for students on what it would take to get them to that level. If they need remedial math, fine. If not, I think they'd be better served taking the class when they're ready, getting it out of the way, and then making a decision about whether to pursue math further, or just take extra electives.

RJED...thanks for your excellent points.

I won't diatribe about my concerns with the expectation that EVERYONE needs a 4-year degree in order to be gainfully employed. But, I thought I would discuss the disconnect between higher math and our culture's incompetence at living out basic math principles (ie: if you pay for your $500 ipad with a credit card charging 22% interest AND you only pay the minimum fee each month...). Of course this sort of responsibilty starts in the home, but I think every high-schooler would benefit from life-math education. I have seen far too many young adults of late with ENORMOUS college debt and the skills to repay none of it. Maybe the students are offered this practical instruction...but I see little evidence if it.

A high school graduate should be able solve problems involving decimals and fractions. If they were having difficulties, as you state, the point was to bring them up to a certain level.

I'm getting off topic here, however, Evemomma just reminded me of my own convictions of HS students learning life skills math. When my DS was a Jr. (2 years ago) was the last year his HS offered such a course, it's now gone sadly. Teaching kids how money works and how to work with money. I would have loved them to include working with some financial software like Quickbooks too! I think most of us have either experienced or know someone who experienced the large lumps from not understanding how money works. If we're trying to prepare students for life after schooling, I can't think of a more important class.

Yea, work backwards from the life skills to the math...
Basis of not being taken by news statistics
Filling out taxes
Calculating gas mileage
Checkbook/using accounting software
Understanding APR
Using a spreadsheet
Creating a budget
How retirement funds work
Why the house always wins in Vegas
Calculating amount of tile needed to cover kitchen floor
etc.

Since my son has a disability that affects him physically I have made sure that he knows he will need a degree to get a good job. He learned practical math (things I learned in business math years ago) before he learned anything else. This was easy to do since we homeschool and had plenty of time to talk about budgeting and financial planning for the future. I have also made sure that he knows about debt and how it would affect his net worth and his ability to buy the things he wants and needs in the future.

I think maybe I did too good a job of teaching him about the pitfalls of student loan debt. He wonders if he will be able to go to college at all and if he can't he wants to know why he has to do more than the basic algebra that he agrees he needs.

He will not be able to joint the military to pay for college like his dad did. He would have difficulty working full time and going to school part time like I did because he will need to manage the fatigue and endurance issues that come with his disability. I think it might be more difficult for him to get scholarships because he is homeschooled. He knows he will increase his chances of getting a scholarship if he can find a way to take the ACT or SAT and make a good score. This will require a lot of math knowledge. For now all I know to do to motivate him to learn more math that he probably won't use in life is to have him work problems in an SAT prep book and remind him how important getting a good score will be for him and how important it is for him to find a way to work around his dysgraphia to get the answers quickly. We don't have time to worry about how his handwriting looks, as long as it is legible. He works on speed and accuracy while writing down only what is absolutely necessary to get the correct answer so that his hands don't get too tired to continue.

Luckily my son has always liked to take quizzes where he has to be the first to answer questions to make the highest score. He enjoys playing against other people doing online quizzes in anything but math. He says he thinks the reason he wins so often is because he reads and reacts faster than the other people taking the quizzes. I am hoping he will get to a point where he is comfortable doing math quizzes because I think it might be a good way to reinforce mental math skills and build confidence.

And the point that I'm making is that it seems the school is more interested in making the HS student show up for 3 years out of 4 to a math class, rather than prepare them for the real world.

Presumably, these students passed tests certifying they held the required skills many years before, yet there they are again, taking the same thing every year. Are they struggling in this class because they truly need remediation, or are they struggling because they've quit caring?

So sad! We're lucky here in NJ--they've actually added an econ and financial literacy course to the high school graduation requirements.

What we discovered when we went looking is that there is no textbook for a truly high-school-level Consumer Math/Financial Literacy course.

We were looking for a supplementary textbook since my daughter was taking the class at the time.

Her dad and I both regard that (at the time, required) course as possibly the single most valuble experience of our high school curricula.

It seems that there is abundant evidence that this course is needed more now than ever. How shortsighted to eliminate it. I'm appalled that the Core Curriculum (is this "common core?") doesn't see it as important.

Maybe financial literacy courses help students make better decisions, but I don't know of evidence for or against this hypothesis. The research cited at

Are Financial Literacy Programs Effective?
http://studentlendinganalytics.type...ancial-literacy-programs-effective-.html is inconclusive.

I am surprised at how little bright college students (many that I know are pre-meds) know about financial markets. They don't know the difference between a stock and a bond, for example.

When I was in college I read Beth Kobliner's book Get a Financial Life. It was very useful to me in reinforcing things I'd heard a hundred times at home, and making me independent in using those skills.

DeeDee

While efficacy is debatable, ignorance surely isn't a good idea, I think we can all agree.

I also saw that anecdotally with many college students; they really had no idea how loan repayment schedules worked, how a lease worked on an apartment, what a 401K was, or how credit card interest was calculated.

Knowing may not prevent people from making poor decisions, certainly. But not knowing virtually guarantees bad decisions, I think.

Personally, this is kind of a hobbyhorse of mine. I truly believe that kids at the lowest SES need the information the most, because they are least likely to be exposed to the information elsewhere.

Back onto the topic at hand; most of the basics of consumer mathematics and financial literacy require Algebra I skills. The only reason that my daughter's school offers this course is that the state requires three years of high school math, including and beyond Algebra I. Too many of them can't possibly pass Algebra II (which covers the entire textbook, trig subjects included)-- ergo, "Consumer Math."

It's a nice idea, even if the course itself wasn't very good; thus our search for a supporting text. Most of what we found was either a college-level or so basic that my DD could have managed it in 3rd or 4th grade.

We tried:

AGS Consumer Math (about fourth grade level in our opinion, and BADLY dated in places), but it did cover household budgeting and consumer purchasing in ways that the college texts did not.

Garman and Forgue's "Personal Finance" -- this is the lowest-level college text I could find. Bearing in mind that my DD had already taken high school Econ, she found this text to be quite enjoyable. It addressed the kinds of things that I think Bostonian has in mind-- markets, different financial products, etc. It did not address many of the more basic consumer mathematics ideas, however (renting vs. leasing vs. buying, price comparisons, calculating basic interest and compound interest, loan repayments, etc.).


Hopefully that helps someone else. It was quite frustrating to search for a text on this subject. I felt a bit like Goldilocks after a while.

Yes...why it is such a shame there is not more of an interface between algebraic concepts and real-life applications (and geometry/trig for that matter) .

....yet another consideration for homeschool should we get there.

Just something to consider though, with so many of the jobs in the highest demand these days being STEM related careers, even if it's difficult for your child, I'd encourage parents to help to find ways to help their child through any math classes. One of the most important things for GT kids to learn is how to work through highly challenging material. They're often used to things being "easy" and it isn't unusual for GT kids to not hit strong challenges until they get to college at which point it's like an axe between the eyes having never had to really WORK at a class before. Consider the high level challenge a blessing for the long haul.

One of my son's cousins recently graduated with an engineering degree and immediately got a high paying job plus a very nice sign on bonus when so many other college graduates can't even find jobs. After hearing this, my son said he is not interested in engineering and would not be motivated by the nice salary. He would rather live on less than have a career that he isn't interested in.

My son is convinced that he will need algebra for just about any degree he would be interested in. Because he was convinced that it was necessary, he was willing to work on algebra during the summer while everyone else was having fun. He knew he needed to make up the time he missed. He had to take a couple of months off from doing any math while getting used to the painful brace he wears from the time he gets up in the morning until the time he goes to bed, even when he has a migraine. His biggest challenges now are working around the pain and getting enough sleep so that he can think. Pain, lack of good quality sleep, inability to get enough exercise while getting required brace time, anxiety, isolation, and different learning style are our challenges and we haven't found anyone that really understands how difficult these challenges are. We will probably have another year of this and I don't know how we made it through last year. It is a challenge for me to fight off the anxiety and depression that sap my energy. It is really hard to see our "high challenge level" as a blessing.

Ah yes, one of the reasons I still suffer from college PTSD. I think I made it about three semesters before I started getting destroyed and ultimately collapsed into a puddle of C's, D's, and F's. I had about two college nightmares last week related to same.

I majored in chemical engineering without having any interest in engineering. I don't recommend that since you have no actual motivation to work on somewhat difficult material. No intrinsic motivation coupled with no study skills is a bad combination.

I also don't recommend law school. I got lucky in graduating into the dot com boom. It's just going to lard you up with debt unless you have significant pre-existing contacts with

So, in other words, don't be me.

Unless it's 1999. Then you can go to law school and be fine.

I rather doubt that I could pass it. I attended a very selective liberal arts college and graduated with an A- average, FWIW, and I tested as gifted. I have never taken calculus, though, and had to work pretty hard to complete trig (I did get a B+, I think?) in high school.

I do use basic algebra--as in, solve for x...but my math is rusty. It's never been a strength, though it's...fine. High average. I'm not terribly quantitative. I have very little recollection of much of what is being discussed in this thread, when it comes to nuts and bolts. (Why would I? I'm a writer and editor. I really don't use math at work, though these days a passing familiarity with statistics is helpful to me. When I do use it, it's generally in a homeowner/consumer context.)

I think high school students should pass algebra, but that there should be a vo-tech algebra track, as discussed upthread. I think financial and consumer literacy is FAR more important. I do not think you should have to pass Algebra 2 to graduate from HS.

I think there should be a quantitative requirement at colleges, but that math should not required in and of itself.

Let standardized test scores be your guide .

Students who scored between 61 and 65 on the PSAT math (multiply by 10 to get equivalent SAT math scores) had a 77% chance of scoring a 3 or higher (a passing score) on the AP Calculus AB exam, according to AP Potential http://www.collegeboard.com/counselors/app/expectancy.html?calcab . As a graduate of a "selective liberal arts college" you likely had a math SAT of 610 or higher.

Yes, I did, but not a lot higher. That's still only a 77% chance!

A new study finds that "Knowledge of Fractions and Long Division Predicts Long-Term Math Success" http://www.psychologicalscience.org...ion-predicts-long-term-math-success.html .

“We suspected that early knowledge in these areas was absolutely crucial to later learning of more advanced mathematics, but did not have any evidence until now,” said Siegler, the Teresa Heinz Professor of Cognitive Psychology at Carnegie Mellon. “The clear message is that we need to improve instruction in long division and fractions, which will require helping teachers to gain a deeper understanding of the concepts that underlie these mathematical operations. At present, many teachers lack this understanding. Because mastery of fractions, ratios and proportions is necessary in a high percentage of contemporary occupations, we need to start making these improvements now.”

The paper by Siegler et al. is

http://pss.sagepub.com/content/23/7/691
Early Predictors of High School Mathematics Achievement

Abstract

Identifying the types of mathematics content knowledge that are most predictive of students’ long-term learning is essential for improving both theories of mathematical development and mathematics education. To identify these types of knowledge, we examined long-term predictors of high school students’ knowledge of algebra and overall mathematics achievement. Analyses of large, nationally representative, longitudinal data sets from the United States and the United Kingdom revealed that elementary school students’ knowledge of fractions and of division uniquely predicts those students’ knowledge of algebra and overall mathematics achievement in high school, 5 or 6 years later, even after statistically controlling for other types of mathematical knowledge, general intellectual ability, working memory, and family income and education. Implications of these findings for understanding and improving mathematics learning are discussed.

And our school has just signed up for Everyday Math, whose curriculum is markedly deficient in . . . arrgh, fractions and long division. I keep telling myself that I can use a tutor and keep my kids up in math, but the elementary school math really does matter. This is just depressing. Good to know though. Thanks Bostonian.

I have a copy of the paper Bostonian mentioned today. If anyone wants it, PM me with your email address and I'll send it to you. It was a decent-sized study with ~4,300 kids from two countries (US and UK). The two cohorts were born in different decades (1970 in the UK and the mid-1980s in the US). Each group was tested twice (around ages 10-12 and as high school students).

From the Discussion:



Refs:

• Ma, L. (1999). Knowing and teaching elementary mathematics....
• Moseley, B. J., Okamoto, Y., & Ishida, J. (2007). Comparing U.S. and Japanese elementary school teachers’ facility for linking rational number representations. International Journal of Science and Mathematics Education, 5:165–185.

Oh, I'll be the first to say that we need better math instruction in schools, from people who understand it themselves. I just find that these studies that start with "there's a correlation between not understanding fractions and not being able to learn algebra" and go directly to "we need to teach fractions better" may be skipping an important logical step. (I haven't read the paper, so I don't know if it's guilty, but the major typo in the abstract you just posted doesn't make me hopeful.) Just because one thing is correlated with another does not mean that there is a causal chain where we can fix the other by fixing the first. It doesn't mean we independently shouldn't fix the first, because it is valuable in its own right. But the problem is that when you start fixing the antecedent, and then you don't get the results you wanted because they weren't actually causally linked in the first place, then the natural response is to stop bothering to fix the antecedent, even though it may have been good and worthwhile for other reasons that you're not paying attention to.

That's a fair point. The authors make this argument:


This argument makes sense to me. US elementary schools and math books generally teach kids how to do algorithms and don't go into depth about what's really happening when you do the algorithm, why it works, and how things in mathematics are inter-related. Fractions is a really good example of what I've said. Kids aren't taught about relationships between fractions and division, yet understanding these relationships is critical for doing algebra.

For all the vilification of Everyday Math that I've seen around here, I have to say that so far, it seems to be doing a good job of keeping fractions tied to division. My daughter has only completed third grade math, though, so there's plenty of time for it to go astray.

And like I said, I don't want anyone to think that I oppose better teaching of fractions. I just think it's valuable so the students will understand fractions better, whether or not it has anything to do with later study of algebra.

Being taught the material by someone who understands it well beyond the level covered by the class text/curriculum seems pretty crucial to me, too.

I think the fact that many primary teachers (and a few secondary ones) don't have a good grip on the underlying math themselves is probably a huge part of this problem.

I'm not really surprised by that observation, incidentally. My own mom was a terrible person to be teaching math beyond basic operations. Luckily, she taught K-2, so it was okay. But I had plenty of experience socially with her friends who were no more capable, and some of them were teaching 3-6.

We should stop expecting elementary school teachers to be experts at all subjects and have them specialize by subject, such as English, social studies, science, or math. The current system where students have a single teacher for all subjects makes sense if teachers are regarded as surrogate mothers and not just instructors. Since my eldest has more trouble remembering where his jacket is and putting it on than with fractions, I understand that elementary school teachers play a dual role .

I do hope it was Val, not the authors, who wrote exactly this...

The working paper version is at http://www.psy.cmu.edu/~siegler/Siegler-etal-inpressPsySci.pdf .

From the paper:

Marked individual and social class differences in mathematical knowledge are present
even in preschool and kindergarten (Case & Okamoto, 1996; Starkey, Klein, & Wakeley, 2004)
These differences are stable at least from kindergarten through fifth grade; children who start
ahead in mathematics generally stay ahead, and children who start behind generally stay behind.
((Duncan et al., 2007; Stevenson & Newman, 1986). Substantial correlations between early and
later knowledge are also present in other academic subjects, but differences among children in
mathematics knowledge are even more stable than in reading and other areas (Case, Griffin, &
Kelly, 1999; Duncan, et al., 2007).

*****************************************************

Fractions are worth teaching for their intrinsic importance, as ElizabethN wrote, but the paragraph above suggests a role for innate ability.

There is now a federally-funded Center for Improving Learning of Fractions (!) https://sites.google.com/a/udel.edu/fractions/home with some papers co-authored by Siegler , who also co-authored the paper I mentioned.

Ouch. Good catch.

I cut and pasted from the paper. I double-checked the final version and a preliminary version written by the authors that I just found.

The preliminary version doesn't have the faulty equation (it has no equation). It's possible that this was a mistake made by someone at the journal. I don't know; I wrote to the corresponding author to alert him to the error, and will report back if he replies to me.

Yes, that was the typo I mentioned (although I see that I was reading quickly and misidentified it as the abstract). I hope there's time to get it fixed.

Heard back from him already. He's going to ask the journal to fix it. They'll presumably make a new online version of the paper.

The president of the National Council of Teachers of Mathematics (NCTM) may agree in spirit with Hacker, having written

http://www.nctm.org/about/content.aspx?id=28195
Endless Algebra—the Deadly Pathway from High School Mathematics to College Mathematics
by NCTM President J. Michael Shaughnessy
NCTM Summing Up, February 2011

...

The NCTM/MAA Mutual Concerns panel presented four concrete, relevant, alternative mathematical transition paths for high schools and colleges to consider. One path emphasizes quantifying uncertainty and analyzing numerical trends. Its mathematical foci include data analysis, combinatorics, probability, and the use of data collection devices, interactive statistical software, and spreadsheet analyses of numerical trends. A second transition path concentrates entirely on the development of students’ statistical thinking, beginning in high school and continuing into the first year of college. Statistical thinking involves understanding the need for data, the importance of data production, the omnipresence of variability, and decision making under uncertainty. This path differs both in purpose and approach from an AP statistics course. A third path recommends building a transition grounded in linear algebra. Linear algebra integrates algebra and geometry through powerful vector methods. It offers an arena in which students can work with important multivariable problems and provides students with general-purpose matrix methods that will serve them well in many fields, including mathematics, science, engineering, computer science, and economics. Finally, a fourth transition path incorporates a suggestion that an alternative to calculus can be found in calculus itself—but a vastly different calculus from the traditional calculus I. This path concentrates on multivariate applications of both calculus and statistics, because today’s application problems rarely involve single-variable calculus or univariate statistics. We live in a multivariate world. Therefore, students’ mathematics experience in preparation for their transition to college should emphasize multivariate functions, partial derivatives, multivariate data sets, and analyzing covariance.

**************************************

I wonder where these "alternative mathematical transition paths" have been fleshed out, and whether students who have trouble with the current algebra-to-calculus curriculum will fare better in them.

I found this statement in that article:


Hmm. Honestly, I think that if colleges want to claim that their students are getting a real college education, they should ensure that everyone understands what differentiation and integration are. This would require a semester-long calculus course (AP in high school counts, IMO). Science and Engineering students have to take college-level English and other humanities courses. The vast majority won't analyze what motivated King Lear or Odysseus when they're programming in Scala or assessing flow cytometry results. So why do they have to take the humanities classes? Because they're considered to be an essential part of what it means to be "educated."

Given this, why should humanities students get a pass on calculus? Calculus is beautiful way of mathematical thinking that can change your philosophical perceptions about of mathematics and physics, and, by extension, the universe we inhabit. The idea that you don't have to study calculus (or algebra) because "you won't use it at work" is incredibly short-sighted. Calculus, algebra, and geometry teach a way of thinking as much as a way of calculating, just like great works of literature expose us to news ways of thought. When our educators push students away from mathematics, they cheat them and do them (and our society) a disservice.

I didn't understand the difference between "college algebra" and "algebra I" or "algebra II" and why college algebra precedes calculus (a high school or first-year college course). Does this mean that students are repeating courses they took in high school when they get to college?

The answer seems to be yes. I did a web search for "college algebra syllabus." I found that "college algebra" is really "high school algebra taught at a college."

I agree with the writer that the path is wasteful, but I disagree that learning algebra is out of date. If anything, understand the basic abstractions that algebra teaches will become more important as our civilization becomes increasingly technological. I think a big problem is that elementary schools teach algorithms instead of true numeracy. When kids hit algebra and suddenly have to apply concepts, they can't ---- how can they if they never really learned them adequately?

So could this be an important reason for what seems to be a revolving door of algebra classes? Not to mention why high school algebra classes have been watered down so much?

And of course, there is also the argument that when our education leaders recommend a course of action that no longer requires algebra or waters down high school math courses, we actually raise barriers for low-SES students. These kids should be learning numeracy and algebra in free public schools, not learning it via student loans in college. They should be taking each of these math courses once, and our schools have a responsibility to provide them with a foundation that will let this happen. My neighbor's daughter (a bright young woman) passed the state high school exit exam on her first attempt in tenth grade, and ended up taking "college algebra" and having trouble with it. This is just wrong, and it happens all the time.

Yes, our civilization is going to magically become more and more technological through the magic of technology.

Nope, we won't ever go into reverse.

Can't happen.

Not to us.

Yes, of course...and if we end up hunting cows with spears and using smoke signals to communicate, we definitely won't need people who understand math. Not us. It's better resign ourselves to things like polio and starvation.

We are getting close to this point so I'll have more info soon, but my dds' school system has the following path for Algebra, which seems to indicate that they view "college algebra" as distinct from algebra I or II and, presumably, more advanced:
Algebra I, Geometry, Algebra II, College Algebra, Trig, Calculus AB (or taken as two classes: Calc A and then Calc B).

Do all colleges and universities require everyone to take English? (I don't think so, though I'm not sure. It was required at my small liberal arts college, I think. I was an English major, though, so I wasn't paying attention to this.)

Anyway, I disagree that English/writing classes (I suspect what's really required are classes with a substantial writing component, just as schools also have "quantitative" requirements) are required because of some concept of what it means to be educated. I think they're required because we want to people to be able to communicate in written English.

Now, I've never taken calculus, as previously established. Perhaps it would alter my life view in some way. But then, would it be more important than taking statistics? (I also haven't taken that--and I really wish I had!) Or economics? (I actually did take this, but it certainly isn't required anywhere that I know of.) Or world history 101? (Also not required most places.) Or, heck, basic biology? I could think of a decent list of courses that arguably should be required for a student to be "well educated," but that's not the way it works nowadays. I myself wish I'd taken more of these broad, basic survey courses when I was in school, but you can't talk sense to a 19yo.

Most colleges have made a determination of what it means to them to be educated and fr public unvierities the state weighs in there as well. All colleges, except for a few, follow some sort of core, major, elective system. All students take a few English classes, math, science, etc whatever and how many the university deems to be of value. Universities adjust baed on feedback from employers, students, grad schools etc. 30 years ago Cornell engineering separated itself from the pack by offering writing for engineering majors, after hearing complains from employers that engineers couldn't write reports, CU made it a priority and it became a selling point. Similarly, why so many group projects, because employers have people working in groups! Colleges also have had to figure out what to do with a population who doesn't know certain things - if it's not getting taught in elem, middle or HS and colleges deem it important than remedial effort has to occur. Many colleges offer science and math for non science majors because so many say they aren't good at it or wouldn't take it or couldnt take it.

And as with all things, these are being decided by committee, often made up of people with a stake in it. Just like you can't make the tax code simpler without damaging the tax preparer industry, you will also have lots of less popular majors fighting to say their courses are "essential" to beng an educated person - and sometimes they are right.

DeHe

Articles such as

http://www.nytimes.com/2012/08/19/business/new-wave-of-adept-robots-is-changing-global-industry.html
Skilled Work, Without the Worker
By JOHN MARKOFF
New York Times
August 18, 2012

suggest that the future belongs to people who have the ability to do things such as program a robot, but I am not optimistic that a much larger fraction of people in the U.S. can be educated to this level than are currently.

That's because we're trying to create Robot Utopia where everything is completely automated and we no longer have to work with yucky things like dirt, dust, and automotive grease.

See the self-driving car for details.

I agree completely with everything you wrote here.

Old Glory Insurance.

For when the metal ones come for you.

Because they will.

http://www.hulu.com/watch/2340

>>SNORK<<

In all seriousness, I'm a professional physical scientist, and I'm deeply confused by the 'multiple emphasis paths' thingy in that article.

Frankly, I can't imagine being a scientist-- or really, even being scientifically literate-- without a rudimentary understanding of both statistics and of calculus. By rudimentary, I mean enough to recognize methodological flaws in sampling and analysis, and to know that 'integration' involves area under a curve, and that 'differentiation' is the other side of that coin.

So I'm very puzzled by the notion that only 'industrially' oriented folks would need to understand QA/QC statistical methods. That's simply not so.

:sigh: Physical science is a series of discussions about the natural world-- in the language of mathematics. Fluency is not just 'desirable' there. It's essential.

Do I get to continue to play the dumb monkey in this thread? Very well; carry on....

I do actually have a rudimentary understanding of stats, but it's really quite rudimentary. I need to have some basic comprehension of it for work. Fortunately, I live with a scientist, so he is called upon from time to time when I need help, although he doesn't always know the social science stats mumbo-jumbo I often encounter.

While I am certainly not a scientist, nor do I play one on TV, I consider myself more scientifically literate than 90% of the American public. That's a rough guess. Okay, maybe not WRT physics. But still.

I think we need to be rather wary of implying that it's necessary to pass calculus to be, what, worthy of basic intellectual respect?

Honestly, even if I had taken it, I doubt I would retain anything of value at this point. I took trig. Can I do trig? No. I haven't used it since I was 16.

I think precisely what HowlerMonkey was doing was avoiding that recall problem - that this is roughly what the words "integration" and "differentiation" mean is about what you would expect someone to retain if they took calculus decades ago and haven't used it since. And that level of knowledge is of value, I would argue; it helps someone to have a very rough idea of what kind of thing scientists might be doing when they make a model of climate change incorporating data and use it to make predictions, for example, which is one example of an idea a scientifically literate person needs to have these days.

On the "respect" question: "having passed calculus" is something with a lot of US-specific cultural baggage because of calculus's status as the peak of school maths education. There's no reason why everyone shouldn't have the basic ideas HK refers to, and in some countries everyone who has completed compulsory education will have - this is not a claim that in some countries the population is better educated, but a comment on sequencing within school syllabuses. I would hope that even people who don't take calculus in the US system come across the basic ideas HK refers to, later, if they are scientifically interested and want to be scientifically literate - don't they? If not, I do think that's a problem.

How is what HM said all that useful, though? I can't say that knowing that "'integration' involves area under a curve, and that 'differentiation' is the other side of that coin" does anything for my scientific literacy. It sounds like a Trivial Pursuit answer. I'd need to know a lot more than that for it to be meaningful to me.


I would certainly classify myself as scientifically interested. I'm married to a scientist and have edited many scientific journal articles. I have taken intro-level college biology and geology, intro- and mid-level ecology, and upper-level psych classes. I also worked as a biological research assistant in the field for many years. Calculus did not come up.

I'm trying not to take too much offense, but you know, I honestly don't think the people I went to HS with who took calculus are retaining some vast store of scientific literacy that I do not possess. I would never claim to have the background of someone *with a science degree*--but that's not what we're talking about here. I actually read scientific studies every day for work.

I'd agree with you that your background (which lacks calculus) is entirely appropriate and adequate to provide you with scientific literacy.

The problem is that the concepts taught in calculus all-too-commonly come as revelations which are presented solely in that venue. Similarly, statistical methods. Possessing a conceptual (as opposed to comprehensive or working) understanding of the concepts underlying calculus is exactly what I meant by "knowing the terms" at issue. I didn't mean verbal definitions, but conceptual ones. Honestly, that is a simple enough thing that I've taught middle schoolers what "integration" is in about twenty minutes; I find it horrifying that people can graduate from high school, much less college, without understanding that.

That would be akin to not understanding what a "subject" is in a sentence, or how a Democracy differs from a Republic. Is that merely a parlor trick or trivial pursuit answer? Well, maybe-- at least in isolation it is-- but it's still part of being literate in the relevent area.

Truly, statistics are probably more critical than calculus to the average person, and nothing more than algebra is actually required to understand the methodology of at least 80% of that. Oh, sure, you may not be able to follow the derivations completely, but that's fine if you know how to use the results and what they mean (or don't).

The fact that most people have no idea what a 95% confidence interval actually means is deeply distressing to me, because that means that while they may have access to peer-reviewed studies in journals, they lack the competence to actually understand them.

Even an auto mechanic ought to be capable of understanding the difference between quality assurance statements from two parts companies when they are made in statistically correct verbiage.

Does one have to acquire this understanding via formal instruction? Certainly not. I acquired my own linear algebra skill set via self-study in college. Colinsmum is absolutely correct about how oddly insular the view on this is in north America. Those who have taken calculus in the US tend to have a propensity to lord it over those who have not for some bizarre reason. I find that rather incomprehensible, too. Differential equations was ultimately far more interesting and useful. More to the point-- none of it is alchemy any more than German or Cantonese is. LOL.

Maybe we should stop teaching our elementary school-aged children about basic scientific principles, since they can't be "scientifically literate" until they take calculus.

The thing about statistics is that sure, you can sort of understand statistics, but without a lot more work and sweat, you don't REALLY understand statistics. I have some grasp of the basics. (I know what a confidence interval is, for instance.) This is unhelpful to me when trying to parse much of what happens in the Results sections of the papers I read for work. I can grasp whether the results look decent to some extent, but there's a lot of "And then a miracle occurred" handwaving going on that I suspect the authors don't even understand, having called in a stats expert and a fancy computer to do it for them.

With all respect, to me it is almost irrelevant whether or not one is gifted in a subject, or whether one finds it easy or not. I believe algebra e.g. is an important subject for every educated human being, and that if one finds it difficult, one should be especially encouraged to take it and master at least the basic tools. I am troubled by the idea that a student should not be required to take a subject he/she finds hard. I also firmly believe that college students do not generally fail freshman math because they are ungifted in math.

After 40+ years of teaching math, I have found that all that is needed in 99.9% of cases, to master a reasonable amount of any mathematical subject, is motivation and dedication, and hopefully a qualified teacher. My gifted students who tried to slide by by have regularly underperformed, even failed, while my less gifted ones who applied themselves have consistently over performed, even excelled.

Many people on this forum who admit they find math challenging seem to me like wonderful examples of motivated students who refuse to let their challenges in math shut them out from its benefits. I love to have such students. The gifted student who won't work is my frustration. I myself failed out of college before learning this lesson.

I was ungifted in English and maybe poorly taught in high school, but fortunately for me I went to a college where everyone was required to take expository writing and where every course (except math) emphasized essay writing on every test. Although math was my specialty, my greatest pride, after committing myself to working and studying and going to class, was in finally achieving an A- on a single English paper (about Portrait of the Artist as a young man) as a senior.

If we come out of college with skill in only the same subjects as before entering, I think we have somewhat wasted our tuition.

I agree wholeheartedly with Mathwonk. Is calculus beyond some otherwise well-educated people? Probably-- it includes certain abstract concepts that I think some people probably aren't hard-wired to grasp. But I don't think that algebra is in that category.




?? How does that follow from anything that anyone has thus far stated? If you look at my post, my statement was that any scientist needs a working understanding, and that any scientifically literate person needs to know-- well, basically they need to understand what it is that calculus does.

That's the difference between understanding how an internal combustion engine is put together versus the fact that it converts chemical fuel into useable mechanical work. A mechanic needs to know the former, and anyone that uses a car probably needs no more than the latter.

And yes, maybe we SHOULD stop teaching scientific "facts" without the context of the underlying scientific process, quite honestly. That's not what science is fundamentally, and it leads to no end of abysmal reporting and lawmaking that there is such confusion on this point.

A 95% confidence interval clearly means that the science has received an "A".

Maybe if scientists would study more and work harder, they could finally get to 100% and get that A+.

Fortunately, most people are just fine with getting an A and don't worry too much that it wasn't an A+. It's a good thing too, or few peer-reviewed studies would even be published.

Except for Tiger Moms.

They want the confidence interval to be 100% every single time.

I may be misunderstanding your position. Perhaps it would help if you explain what you mean by "scientifically literate."


So... you're saying we SHOULD stop teaching children science before calculus?

No. I'm saying that taking the math OUT of science leaves us with little but vague, hand-waving explanations and memorization. That's not good science education at all.

The scientific method isn't as 'glamorous' nor does it lend itself so well to flashy demonstrations or class projects to eat (a personal pet peeve, sorry)... but it's more authentic in terms of educational value than playing with liquid nitrogen or watching a thermite volcano. ::Sigh::

Absolutely not - if I get completely real! However, that is not to say that it is not nice to have that knowledge/skill. I speak from the perspective of someone whose part-time jobs as a sophomore, junior and senior in college were to grade homework (and sometimes tests) for classes in Calculus, Differntial Equations and Statistics. However, I don't use math (beyond arithmetic) in my professional life. To be (embarassingly) honest, I don't think that I remember all that much from Calculus, Differential Equations, Statistics or any of the math courses that I studied although it would be very easy for me to pick up the concepts if I see them again. In my professional life, I see lots of intelligent educated people who are math-phobic and probably unable to recall much of anything from Algebra.

here is my suggestion for one of the most basic ideas of calculus: if two plane figures are such that all horizontal slices have the same length, then they have the same area.

it follows that two triangles of the same base and height have the same area.

the next case of this principle is that two solids all of whose horizontal plane slices have the same area, have the same volume. archimedes used this cleverly to show that a sphere inscribed in a cylinder has 2/3 the volume of that cylinder.

in a calculus class they combine this with algebra to show how to compute a formula for the volume formula of a figure from the formula for the slice area.

by the way, a mathematician is not someone who knows a lot of math facts, but someone who knows how to deduce them. I.e. the prime compliment for a mathematician is that she "knows nothing but can do anything".

...and this is also generally true in the physical sciences. Oh, sure, there is a base of knowledge, but ideally, it's about using familiar tools to DO unfamiliar things. Or to find answers to questions, I suppose.

Math is a foreign language. Some people need to be fluent in some dialects (statistics, vector calculus) more than in others. What's really, really COOL, though, is that math is truly an international language throughout most of the world.

Not to rain on your parade, but the basic of idea of calculus is to sum up an infinitely small number of things to get a finite quantity, and then to do this in reverse, divide a finite quantity into an infinite number of small things. Once you can show that you can do this reliably, then the next trick is to extend this idea to where you can sum up across functions that produce an infinite number of small things. Historically, the basis of this approach had its root in addressing Zeno's Paradox.

http://en.wikipedia.org/wiki/Fundamental_theorem_of_calculus

http://en.wikipedia.org/wiki/Zeno%27s_paradoxes

As for your statement that a mathematician does not know a lot of facts. Its the exact opposite. Mathematicians know an enormous amount of facts and know how to operate a lot of intellectual tools, too. Its this combination of knowledge and operative ability that allows them to work a large set of problems and to attack unknown ones.

FWIW, I discussed this with my husband, who did take basic calculus, and he was bemused by the idea that calculus was necessary for basic scientific literacy. He felt that stats were much more important (I agree) and said that what little calc he remembers (not much) is not relevant to him on a daily basis.

Well, understand that I did qualify that statement-- significantly. I stand by it, but for the physical sciences, and with the understanding that "principles" there means methodology and conceptual understanding. I'm repeating that statement again, since it keeps getting oversimplified. Pretty sure that anyone who has taken Physics recalls "Newton's Laws" have something to do with motion and macroscopic objects, yes? That's what I mean by "literacy" in this context.

I was also very bemused by the notion of "vectors/calculus" being the STEM track, and not "statistics" instead.

My DH and I have both used our stats backgrounds far, far more than any other area of math we've ever learned-- including calculus. Diff-Eq and matrix methods are more useful when you get right down to daily use. If you don't use it, you do lose a lot of the nuance of the mechanics, however. I think that isn't a big surprise.

This essay supports Hacker's view that algebra is not necessary for most people (except to obtain necessary educational credentials).

http://econlog.econlib.org/archives/2012/10/does_high_schoo.html
Does High School Algebra Pass a Cost-Benefit Test?
Bryan Caplan
OCTOBER 17, 2012

"How much do students learn in school?" The question is harder than it seems. You get one answer if you measure their knowledge at the end of the school year or right before graduation. You'll probably get a very different answer, however, if you measure their knowledge a year, five years, or twenty years after graduation.

The latter measure is clearly more important. What good is "knowledge" that melts in your mouth like cotton candy? As you'd expect, however, we rarely measure long-term learning. Instead, we look for our keys under the streetlight because it's brighter there. Our obsession with student achievement ends with graduation.

Fortunately, there are a few noble exceptions. My favorite: Bahrick and Hall's "Lifetime Maintenance of High School Mathematics Content" (Journal of Experimental Psychology, 1991). The authors assembled a large sample of current students and adult (ages 19-84). They collected detailed information on their mathematics coursework, IQ, and other variables. And they reached some remarkable discoveries.

Here's how knowledge of algebra decays over a lifetime. The lines (top to bottom) show the fitted scores for (1) people who studied more than calculus, (2) people who studied calculus, (3) people who didn't study calculus but took another algebra course, and (4) people who didn't study calculus and only took one algebra course.

If you're a cheerleader for education, you'll fix your gaze on the top two lines. People who go beyond calculus don't just master algebra; they know algebra almost perfectly for the rest of their lives. People who stop with calculus do almost as well, their average score slowly declining from 90% to 75% over the course of fifty years. Wow!

If you're someone like me, however, you'll fix your gaze on the bottom two lines. After all, most students never take calculus. What benefit does this vast majority get out of higher mathematics? Not only is their proficiency low, but it decays fairly rapidly. Ten years roughly halves their edge over pre-algebra controls.

Non-economists will probably interpret this as an argument for making everyone take calculus. But what about the cost? Does it really make sense to torture everyone with four years of advanced mathematics to ensure that they don't forget their first year?

Before you answer, consider one more finding from the paper. Bahrick and Hall constructed a measure of how much subjects "rehearsed" - i.e., used - algebra in their daily lives:

The vast majority of subjects rarely use algebra no matter how proficient they are. Look at the fractions with rehearsal scores of 0 or 1: 89% for people who studied less than calculus, 91% for people who studied calculus, and 70% for people who studied more than calculus. If the students who already take calculus don't use it in real life, why on earth should we push weaker students to match their achievement?

Not that I took statistics (ha ha), but in looking at that article I notice that in their little study, the number of people who went past calculus is very small--makes me feel that the percentages are somewhat suspect.

Seems like there is an obvious confounding factor in this study: those who take calculus or beyond are most likely more math prone to begin with...setting up the argument -they would be the group most likely to remember/utilize advanced algebra even if they took home ec instead of calculus.

Personally, I see the lack of training in proper slip-stitching and flaky pie crust-making as it's own tragedy.

It seems self-evident that students who go to calculus or beyond would have significantly greater retention of algebra. In the process of performing advanced math, they're constantly referencing, reinforcing, and applying those algebraic principles. Whether they go on to use algebra "daily" or not, those neural pathways are well traveled.

I'm still unconvinced by the argument, "Students shouldn't have to take algebra because they won't use it in daily life." If we should only study what we'll use in daily life, why do we teach science? Why do our kids bother reading history books or classic novels? It's not like they're going to be debating the relative merits of Charlotte Bronte's writing style at the bank or in the lab or wherever.

Maybe they take these classes because of the connections they create in the mind and because knowing this stuff is just part of creating an educated population.

It's clear that the real problem here is that too many students are failing algebra. If they weren't, no one would be wringing their hands and asking if maybe we should cut it out of the curriculum. IMO, this is just a continuation of an established pattern in our schools: it's too hard, so excise it from the curriculum!

Given that students all over the world pass basic algebra, I wonder if our national problem is our dreadful math curricula. We've been discussing this idea recently on the Certainty among Educators thread. Perhaps our students' mathematical foundation is too poor to support algebra. It wouldn't surprise me a bit.

YES. Exactly. My retention of trigonometry is better than 99% of the population, as well, I'd guess. Why? Because I spent so many years doing statistics, advanced geometry, and calculus.

Besides, as MoN notes, how on earth are they defining "algebra"?? Because I can't imagine getting through a week without using a fair bit of what my daughter learned in Algebra I three years ago. I'm not talking about being a professional scientist-- I'm talking about figuring out consumer math challenges, budgeting, etc.

COLLEGE algebra? Well, sure-- I go longer in between using that stuff. But that is a straw man here, because this is about a push to remove Algebra I from Common Core graduation requirements. I vehemently disagree that such a thing is a good idea on any level.

If I student can't pass Algebra I (or, for that matter, four years of English composition), then perhaps that student needs a "modified diploma" instead. That's an option already for students with IEP's. I don't see a problem that needs fixing, here.

I wonder if the type of person who studies math beyond the calculus level would be able to answer algebra problems even if they had been cut off from schooling after arithmetic. You need not follow a particular approach in order to solve algebra problems, if you have an intuition for numbers.

My ds6 intuitively starting doing very basic algebraic equations around 4 years old. We never once discussed with him any of this...he just started doing it on his own. In fact, his favorite thing to do in math is to find multiple avenues to a solution. That was actually one of inklings that he was going to be a "mathy" kid.

Yes. Mathy kids are going to be fine this way without actual instruction.

I just think it is horrifying to conclude that ONLY mathy kids ought to be expected to learn it. I'm not a particularly mathy person... and Algebra I? Just not that hard-- but anyone who isn't mathy probably needs some instruction to learn it.

How much of Algebra I is regularly usable...?

Found this list of topics taught in Algebra I:
•Representing numbers with variables
•Addition, subtraction, multiplication, and division of real numbers
•Probability and odds
•Rates, ratios, and percents
•Exponents and powers
•Order of operations
•Functions
•The distributive property
•Linear equations
•Formulas and functions
•Quadratic equations and functions
•Polynomials and factoring
•Rational equations and functions
•Pythagorean Theorem

Do we really consider this high school algebra? My DD8 could figure this out now. It's a far cry from what I remember covering in high school algebra.

Actually, DD is learning basic algebraic concepts in 4th grade math right now. (If vase #1 has 4 flowers, and vase #2 has 8, and vase #3 has 12, construct an expression that represents the number of flowers in any vase...something like that).

I am a nonmathy person. I would classify myself as mildly mathphobic, in fact, although I am mature enough to recognize that my competency is okay, just not by any means stellar, and I don't think there is an actual LD. I have never held a job that required more than extremely rudimentary math (most of my jobs have been in the writing and editing fields). For the sake of comparison, my math SAT score was in the mid-600s.

So, on that list...here is my assessment of what I use.

Found this list of topics taught in Algebra I:
•Representing numbers with variables--Yes, I do this
•Addition, subtraction, multiplication, and division of real numbers--Of course
•Probability and odds--Yes
•Rates, ratios, and percents--Yes
•Exponents and powers--I don't feel like this comes up a lot but it's pretty simple
•Order of operations--Yes
•Functions--Hell to the no
•The distributive property--Yes
•Linear equations--I only vaguely remember what this is
•Formulas and functions--No
•Quadratic equations and functions--No
•Polynomials and factoring--No
•Rational equations and functions---No
•Pythagorean Theorem--I may have used it very rarely, but generally no

FWIW, I handle the family budget.

I do.

You can use simple arithmetic to figure out the first-year cost, but that's not the best question, because what if the first-year cost is greater for one option, but you plan to move out in six months? For optimum financial planning, you want to figure out how long you'd have to commit to the satellite service before it becomes the cheaper option.

So, in this specific example, 40m + 30 = 15m + 200, solve for m. That looks like Algebra I to me.


I think teaching the language of algebra at an early age is a good thing, because many kids who fail algebra do so because they can't make the conceptual shift of using letters to stand in for unknown or varying values. But let's not confuse language with understanding and applying the rules and concepts to solve problems.

42% is the answer.

Based on my single-malt unreliable pseudo-scientific survey of Algebraic topics used sometimes with n=1.

Well, it said "for a year."


What DD is doing is more complex than 9 + x = 10, which is introduced in grade 1 these days. (Although at that point, they don't teach them to solve it in the "algebraic" way.) FI, the answer to that question was not x + 4.

This is early pre-algebra in our school district.

polarbear

I am not sure where you got this list, but these topics are covered in Pre-Algebra. DS completed the ALEKS pre-algebra course this past summer so the topcis are fresh in my mind. He is also doing our District's Pre-Algebra course, which covers all these topics, but in more depth than ALKES.

Actually, the alegebraic modeling would be covered in a Pre-Algebra course. However, that's the type of basic problem that could be figured with just arithmatic. As the problem is stated, I would solve it in my head using arithmatic rather than algebraic modeling, not because I don't know algebra, but because it's quicker to do it in my head that way.

From a textbook site:
Houghton Mifflin - Algebra I Topics

Right-- thanks to spiraling in curricula, those same topics could also be said to be covered in Algebra II, by the way.

It's the level of detail and complexity involved that make them "pre" versus "algebra" versus "I/II" in the end.

That list is Houghton-Mifflin's, but Pearson's algebra offerings have a very similar scope and sequence at that top level of detail.

Exactly. About a decade ago, when my older DS got problems like these in first and second grade, I was surprised. Back then, there wasn't a name so I refer to them as kiddie algebra problems for lack of a better name. These days, my district has math units specifically labelled "elementary algebra" covering these easy as well as more difficult algebra-like problems as you proceed through the elementary math curriculum. These days, I am also seeing a significant extension of the coverage of geometry topics in elementary math curriculums.

Interesting. Our district does not use either of those textbooks. I do recall that Algebra II for older DS did review those toopics, but it also proceeded to more complex topics as well.

I just had to use algebra to solve a blood transfusion problem for some lab for some friend of my wife.

Apparently, I'm a general purpose help desk.

Maybe once the expression is written on paper, it's a simple Pre-Algebra problem. The process that came before it, of arriving at an expression where two linear equations intersect, was Algebra I in my district.

Indeed. And this is exactly why performing simple arithmetic is a poor substitute for Algebra. You can tap out the solution for one year on your calculator, but then you have to keep running other scenarios through it in order to gain a half-useful understanding.

How much for the first year? *tap* *tap* *tap*

But we're planning on leaving in April... *tap* *tap* *tap*

Grr... I hate math.

What if we end up being delayed a couple months? *tap* *tap* *tap*

Or, you can just write out one expression, and instantly have a full conceptual understanding of how the two solutions relate. As I said, it's not the best question.

And of course, these problems are never this simple, because we haven't even looked at annual contracts, relocation costs, or equipment rent.

This scenario illustrates why so many people fail at family finances. You need Algebra to do it right.

Our state has gone to Common Core so there is no more "algebra" class. Here is the content our state (NC) is using for High School Math 1:

Chapter 1: Solving Linear Equations
Chapter 2: Graphing and Writing Linear Equations
Chapter 3: Solving Linear Inequalities
Chapter 4: Solving Systems of Linear Equations
Chapter 5: Linear Functions
Chapter 6: Exponential Equations and Functions
Chapter 7: Polynomial Equations and Factoring
Chapter 8: Graphing Quadratic Functions
Chapter 9: Solving Quadratic Equations
Chapter 10: Square Root Functions and Geometry
Chapter 11: Rational Equations and Functions
Chapter 12: Data Analysis and Displays

As you can see the algebra is a tad lighter than most of us are used to in Algebra 1, more geometry is mixed in, and there's a bit on Data Analysis. Next year, there will be no more "geometry" class as we knew it -- that will also be a Common Core class (HS Math 2) and it will continue the algebra/geometry/and other stuff mix. This will continue through HS Math 3, after which point, the students will be set free to take more traditional higher level math classes and the Common Core requirements will have been fulfilled. That is the way our state is doing it. I am not sure whether all states are splitting the HS Common Core standards into 3 years, but my guess is most are. These classes replace algebra 1, geometry, algebra 2.

Remalew,

What is after HS Math 3 - Calc?

I'd guess pre-calc or Trig, depending on one's location.

That sequence is also intended to lead non-calc students to business math/econ and to stats.

Officially, our state says a "higher level math class to be aligned with student's post HS plans."

I've seen some graduation requirement lists that say pre-calc, some that say calc, some that say you can even take discrete math. Have to take 4 maths in HS though if you're in any of the college prep paths. I think it varies by county what they will allow for the 4th math and by school as to what is available.

Many kids start taking HS math 1 in middle school- crucial to do if you want to get to any AP math.

It will be interesting to see how other common core states deal with this.

Not sure what happens to Trig. I suspect it's included in the 3rd Common Core HS math. I haven't looked at the standards beyond the first math yet (our state hadn't had them published last I checked, but I'm sure they are now as they start going live with those next year).

Oh, that's interesting. In NC, we have a mandated by law end of course test for what used to be algebra (now the first HS level CC class), so that content in NC is going to be very standard in all 100 counties, as they'll all be teaching to the test. After that, there are no required EOGs for math, so I suppose it might vary from county to county. Though once the text books start coming out, I suppose that will cut down on some variation.

For MS and ES it is different-- they have EOGs (end of grade tests, different from the EOC for algebra / HS CC 1). Those will all teach from the state's list of Common core standards -- they will all teach to the test, so I suspect classes will be similar from county to county as they are now (we already had a standards and testing system in place, we've just swapped it for a different one, for the $). They are all (admins and teachers), in fact, freaking out a bit this year, because they don't know what the new tests look like.

From what I understand about what happened in NC, we got some federal money for implementing CC early and part of that was contingent on this testing system that we're implementing. But who knows. I live in a county where the BOE superintendent changes weekly and kids are zoned to different schools every year. At some point I just stopped paying attention and started signing my kid up for Art of Problem solving classes on the side.

I really don't like that in our state so much of what our kids do in school is legislated. But that's me.

This is all so interesting. My daughter took the normal AlgI, Geom, AlgII beginning in 7th grade. She is now taking College Algebra. I was worried this would be a total rehash, but the teacher has stepped it up quite a bit. She'll take Trig next semester and then College Calc I next year finishing with College Stats - and maybe College Calc II.

She loves math and learns it very easily. She is not representative of our population though. Most here struggle through math and barely finish Algebra.

kcab, your impressions of CC's actual mandates match mine. That is, that it does mandate certain algebra skills-- but doesn't mandate how/when they are taught other than "during the course of four years of high school mathematics instruction." That means, more or less, four years at or beyond the algebra I level (but, as noted, the devil is in the details there in terms of even defining what "at" means, nevermind what "algebra I" does).

I've been trying to keep up with that as it rolls out-- mostly because I have worried about it producing 'gotcha' moments for kids who are currently in their 10th-13th grade years (as mine is).

LOL... obviously, I meant "12th grade" there. That'll teach me to pay attention to my typing, won't it?