Thursday, June 25, 2009
A Real Forehead-Slapper
In a discussion this week about the struggles we have with developmental math classes, someone mentioned that this state, like so many others, requires only two years of math in high school. That means that even many brand-new grads come to us not having done math in two years, and having stopped out before they even got to trig. Then everyone is shocked at low pass rates in developmental math.
We have anecdotal evidence that suggests that students who actually take math for all four years of high school do better in math here than those who don't. We also have anecdotal evidence that bears crap in the woods. Why the hell do the high schools only require two years of math?
My carefully considered (meaning 20 seconds of thought about other options) first answer would be Middle School Math. Epic fails at that level might lead educators to give up at the HS level.
My other answer would be NCLB and whatever passes for "math" on the evaluations used in your state, and when those evaluations are administered (10th grade). Any math after that will only reduce HS graduation rates.
However, I will tell you that four years of HS math will solve nothing. We have that system, and the last two years are usually something called "consumer math" that is more about meeting the graduation requirement than teaching math. It is also common to repackage Algebra I into a two-year course.
Finally, your comment about trig sounds hopelessly naive to me. I'd say the odds are very low that their second course in HS was the functional equivalent of Algebra II. Look at some transcripts and see for yourself, but keep in mind that course titles often lie. I advised a new student last month who was passing Algebra II and could not do algebra without a calculator on our placement test.
Think about that.
And so the bright students need only make minimal requirements, and many choose not to continue for a variety of reasons. Those include, but are not limited to, atrocious text books, atrocious curricula, and poorly trained (mathematics wise) teachers who think that pushing a graphing calculator in the hands of every student does them a favour.
I suspect that some of it comes down to the fact that most adults will say they don't use math beyond basic algebra and geometry. Other than interpreting statistics I don't use the vast majority of the math I learned.
I don't think that's a good argument. It certainly limits kids. I didn't really think I'd ever use calc as a teenager. However, I went on to take econometrics in grad school years later. So I appreaciate mom and dad insisting on high school calc.
My sister taught high school math for nearly 20 years (she transitioned to a university while in a doctoral program). Her experience was that it became increasingly difficult for her system to hire qualified math teachers, so the schools began to cut back on advanced math courses, offering (for example) trig once a year, calculus every other year, and so on.
While she also talked a lot about the students--their level of preparation, their willingness to work at math (which is, after all, at least at the advanced levels, even in high school, HARD)--she talked even more about the ability of the schools to offer advanced math.
- Math every semester grades K-12
- Science every semester grades K-12
- English every semester grades K-12
- Social Studies every semester grades K-12
- Phys Ed every semester grades K-12
Didn't have whole of room for "electives." But the rigor and preparation for advanced scholarship were fabulous.
Where are you going to find enough (qualified) high school calculus teachers?
Who is going to teach Algebra & Geometry to 5th graders?
Our schools of education should *require* two content areas for each graduate. My wife has bachelors & masters in education and never had to specialize in *anything.*
We need to have math-literate educators beginning at the grade school level. Instead, we have a lot of people who go to teacher's college, here in Canada, because it doesn't require math. (They love to combine a history and English background for the same reason.)
I would also like to hang the textbook writers out to dry. I suspect they pull together their volumes with the assumption they're being taught by educators who can add context to the brief and rigid sections that focus on solving question X with method Y. But since our teachers don't really have those tools, they don't understand the reasons behind such rules or when it might be better to put them aside.
I'm hoping that their HS math teachers will be better prepared for this. If not, I'm swotting up on the curriculum so I can lead her through. (Once she gets past Calculus II and Linear Algebra, though, all bets are off. My husband has some more math from his CS degree, but not a huge amount more!)
The situation is not going to change until the public understands that a high school degree is no longer a ticket to a family wage job. Students expecting to land jobs in the 'service sector' generally need to learn more than they get from high school so they need post-secondary education, which in turn requires better high school preparation than the minimum graduation requirements. I wish that school districts could offer two different diplomas; a 'meets minimum grad requirements' diploma, and a 'college-ready' diploma. At least in my state (WA) that would not be permissible.
A side issue is the move toward 'integrated math' curricula. I'll not digress into a pro-con debate on those curricula. Typically, a 3-year integrated math curriculum replaces the more traditional Algebra I - Geometry - Algebra II curriculum. The problem is that if a kid only completes two years from the traditional curriculum, it is pretty easy for us to place him/her into remedial Algebra II. On the other hand, every integrated math curriculum weaves the topics together differently, so when a kid shows up with only two years of integrated math, we have no idea what he/she ought to know. If a high school required 3 years of an integrated math curriculum, then we would have more confidence that grads could be expected to know up through intermediate algebra.
This is, for the record, both absolutely true and batshit insane. Thank you.
Math, like Foreign Languages, but unlike almost every other high school subject, builds. If you just scrape through Algebra I, you start Algebra II behind the eight-ball. Algebra II expects you to know the stuff from Algebra I. In contrast, if you barely scrape through Earth Science, you start Biology even.
Requiring more than two years of math for graduation is piling up opportunities to fail.
I agree- with one minor exception:
Requiring more than two years of math for graduation is piling up opportunities to fail at going to school.
Not requiring more than two years of math for graduation is piling up opportunities to fail at life.
The dumbing down of K-12 has been pernicious and ongoing for quite some time.
And it has caught up with post secondary ed big time.
The idea I always come back to is if private industry partnered with local high schools to make this happen. For instance, at my company many people have at least a BS and sometimes an MS. I always thought it would be nice if local high schools could somehow tap this talent pool. Obviously, every educated person does not a good teacher make. But amongst all the local companies and science/technical professionals you'd think there would be enough. Maybe an employee teaches one math class a year or one science class a year. Maybe there is an afterschool program that integrates math/science with industry projects and provides scholarships as incentive for students doing well and taking the math and the science.
In my personal experience, my math education was fine. The high school required 3 years but I took 4 knowing I would need that extra class at university anyways. However, my science education was terrible. Two years were required, and the knowledge you actually learned was a hodge podge of real science. If you compare that to foreign high schools we look really pathetic. Anyways, that was all a decade ago but I suspect similar to today's students. Maybe if I get to running my own company my industry/school partnership dream can take flight :)
Starting with the Class of 2005, the decision was made to have all NYS HS diplomas be Regents diplomas. There has been considerable slippage in this original goal: the current standard (according to NYSED) is that gen ed students in the Class of 2012 are now the ones who must pass the Regents or else. (Statewide, 16% of 2008 diplomas were "local".)
There are provisions for Advanced Regents diplomas now, which involves passing more tests, but the old line between college-prep and non-college-prep has been blurred.
The first math class where any rigorous learning happens is the first year that isn't required for graduation. It used to be algebra as the rest of the student were shunted into more "applied" tracks instead. Now it's trig in my state since everyone has to take 3 years of math starting with algebra. If we required everyone to take calculus, the first "real" class would be discrete math. As long as we have this idea that everyone should be socially promoted until high school and should then graduate in 4 years or the school will be at fault, requiring more years of math credit will do little to increase the amount of actual math learned.
Which state was this? I gotta get a look at those content standards.
There are literally thousands of entirely reasonable careers one can have without a calculus, or even serious algebra, background. Police detective. Information Technology manager. Lawyer. City planner. College dean.
This seems like a weird attempt to blame folks who aren't doing well for their troubles. It used to be that you could pretend that it was because they didn't have a sufficiently large number of diplomas tacked to a wall somewhere, but you could get yours and arrange them in the shape of a cross to defend yourself against our current exploitative economy. I think the idea was to have some kind of talisman against having to consider the fact that union solidarity -- or solidarity with fellow human beings of any type -- might be helpful in getting oneself a living wage. Maybe it's an excuse to union-bust or demonize people who vote for a government which can "promote the general welfare." I dunno. But it's just so . . . nonsensical. Absurd. Disconnected from any reality which could be useful to discuss.
*Yes, yes, discussing anything that takes place in the real world and not in a Dragonlance novel with a libertarian is wrestling with a pig. Bear with me.
Then I explain one of my philosophies about math classes. The fact of the matter is that most people don't retain all of the math that they've ever learned. For someone in a developmental math course it might be something like 50%. For a grad student, it might be something like 80% (as a former math grad student, I can tell you that I retained significantly less than that). So if we need someone to be very comfortable with arithmetic to function in society, stopping at the end of arithmetic won't be enough for them to retain it. They'll need a bit more in order to retain everything.
Since math does build on itself, we can start teaching these students algebra. In using algebra, students will be challenged to use their arithmetic skills in many different ways, forcing them to actually own arithmetic. It will give them the practice of not only performing arithmetic, but also knowing when it's appropriate to use different operations.
Finally, the problem solving and even logic skills one employs in an algebra class are really a dimension higher than that in an arithmetic class. Being introduced to a different way of thinking (using variables to represent unknown quantities, as well as using symbolic manipulation) is immensely helpful in any sort of problem solving arena, whether or not it involves math. Everyone needs problem solving skills: if jobs didn't require them, everything would be run 100% by computers.
After explaining this to the few argumentative students I get, they generally stop complaining. And they're art students. Sure, they might not ever need to solve an optimization problem involving a system of inequalities, but learning how to do it reinforces many of the more basic skills they will use and improves the problem solving skills they will need.
Unless you intend to do something that actually uses maths they are a waste of time. If you would like students to do better at problem solving outside of math, teach them critical thinking. That's were I learned problem solving, not in math. Teach critical thinking in HS. Then maybe students could decide for themselves what math they need.
What Anonymous@3:10PM writes gives an accurate description of the consequences - a downward spiral in math skills held by El Ed majors whose last class was the one before any rigorous learning happens.
Until then, I'll point you to a followup discussion a Uncertain Principles, which contains a comment pointing to a cogent article about the problem.
I'll also look forward to YACP's answer to the question Punditus asked at 7:40PM. My guess is that YACP@11:25AM is talking about something like the following: Everyone I knew in the "college prep" track (but not everyone in my HS) took math through a pre-calculus class based on the Dolciani etc textbook called something like "Analysis". We learned about formal proofs and how (and why) to take a limit. We were very well prepared for calculus.
There are pre-calculus classes today, including the one at my COLLEGE, that lack that rigor. It would not surprise me that there are "AP" calculus classes that do less than this and produce students who know some shortcuts but little math. Those classes might even be defunct now that specific requirements are being imposed on AP classes.
I am a law teacher and I can assure you that lawyers need algebra. Many need it for their practice and many more need it for their coursework.
Punditus was talking about calculus and "serious algebra," (by which I assume he means solving differential equations, etc., not just solving for "x").
What practice areas or law school classes are you thinking about?
Everybody took 4 years math.Some students didn't get to calculus I'm sure.
While my older attended there was a battle royale over "tracking" according to college bound vs. non-college bound.
The school wanted separate tracks . . . the parents (school board) wanted everyone to be treated teh same.
The school's solution was to have requirements that everyone had to take (no tracks!) but to impute tracking by the specific classes.
This in a high school with total enrollment ~500 and graduating classes <100.
And yes, my "pre-calculus" classes included differentiation (chain rule and substitution) and integration (both definite and indefinite; using integration by parts with trig substitution).
In 2009 USA that would probably be the equivalent of the first two years of an engineering degree . . .
[p.s. Brondo has what plants crave.]
According to Wiki, the 2000 census says "The median income for a household in the town was $77,639, and the median income for a family was $82,864." with only 1.7% below the poverty line and over 40% of households having school-age children. No wonder it has such an atypical high school.
Our median income is less than half of that, and the poverty rate is 10 times higher.
There was a "Box Company" and also a tool maker (apex screwdriver sets) called Chapman Manufacturing where I did my apprenticeship as a tool & die maker.
Not sure what the median income was back the but i do remember once when someone in my neighborhood actually bought a new car. All weekend we trooped down the street to get a chance to sit in a new car . . .
The parents wanted their kids to get the same education as those snooty kids going to the private schools in Middletown (a campus town). So even though the administration wanted to water everything down in order to Make Everyone Special In Their Own Way.
Nope, the blue collar parents and farm families wedren't about to put up with that bullshit . . . frankly, I think they were more than willing to "leave some kids behind" back in those days.
What on earth does median household income have to do with the ability to learn math?
Your post implies that poor kids are somehow unable to suss out the mysteries of algebra.
Are you making a backhanded reference to The Bell Curve or some of the work of Murray/Thernstrom? Are we to infer that there is some relationship between intelligence and income?
That perhaps, JUST PERHAPS, the desire of the town to ensure that everyone learned rather than felt good, might have had, in some small way, a contribution to the later and more recent success of that town?
Imagine--a town that puts actual TEACHING ahead of feel-goodism reaps the benefits of said effort through higher income, and near elimination of poverty.
But I suppose THAT would be a bit too much "cause and effect" analysis for us.
How on earth can you compare the obvious successes of our Modern Educational Systems (as practiced in kewl, progressive, wealthy urban centers) against the benighted, hillbilly approach used by rural AmeriKKKa?
Of course, there has to be *some* other explanation beside actual curricular approach to explain the differences in outcomes!!
Why is poverty so closely associated with progressivism?
Must be the man in Moon Marigolds at work!