Another reportfrom the EPI with more recent data and extending the analysis to consideration of the variety of state school systems. More detail there than I have time tonight to even skim well but a superficial look seems like it might be of interest to a few of those participating in this thread.
Perhaps a bit left field, but does the International Baccalaureate get much traction or attention? It seems to offer some attempt at a more controlled and targeted curriculum, although some might argue about the details of what that curriculum is. My old school has offered it for quite some time, and quite a few schools my friends and colleagues sent their kids to schools that also offer it.
It does seem to be a bit of political football, with charges of elitism, or favouring the rich kids.
Great points. When my mother completed her bachelor’s degree, calculus was not a requirement and she never learned it (it turns out that there are careers where the answer to “Are we ever going to have to use this?” really is “No”), so by the time I was halfway through high school she could no longer tutor me in math (since I was doing calculus). She, however, had to read more literature and also had to contend with the lack of word processing systems in her time - she either had to write essays out by hand (and re-write pages if there were minor corrections!) or use a typewriter (which still required re-typing to correct).
Are there differences with respect to the Swedish-speaking minority (5%-10%) in Finland? The Swedish language is also quite phonetic, but I could see that there could be sociocultural issues that could cause a disparity. In addition, Swedish as a native language actually might give an advantage to students in Finland studying foreign languages as Swedish is an Indo-European language (along with English, German, French, etc.) while Finnish is not.
I tried to make it clear that I’m open to arguments about whether or not Alg 2 is relevant.
I absolutely agree. I’m in a school in which the variety of ways in which we teach math varies from freshmen who spend 90 minutes every day for a year on Alg 2 to Freshmen who get through calculus by the end of the year. And if someone wants to say 'We don’t think it’s worth the time and money to make sure every kid learns Alg 2", that’s a discussion worth having. It’s not the same as “some of these kids just can’t handle it”.
This I struggle to believe, and I certainly don’t know how you can state it’s dogmatically true. Maybe elementary instruction needs to be different, maybe they needed two hours of math a day from 6th grade on, maybe they needed different instructional techniques. And maybe that means the light wasn’t worth the candle–that all the time and effort isn’t worth it. I could be persuaded of that. But I am deeply uncomfortable with stating there’s no point in even trying, that some kids are just too dumb.
The thing is, once you introduce the idea that “some kids” just can’t handle something and resources spent on them are wasted, it’s the poor and minority kids who end up in that pile.
That’s a pretty broad brush. Canada may be different, but our kids who make 4/5s the AP Calc exams generally go on to do fine in the next level of math, and the ones who retake calculus (the ones who made 3s) generally report that it’s easy.
The trend is very much towards open-enrollment in AP, and scores are generally holding. For example, in 1999, when most programs had some sort of gate-keeping, 149,061 students took AP US History and the mean score was 3.02.
By 2016, most schools had adopted an open enrollment philosophy and started pushing more kids to take the test. This year, 489,291 students took the test, and the mean score was 2.7. While that does represent a drop, over 256,00 of those kids passed the test–150% of the kids who were even given access to take the course in 1999.
Open enrollment does involve changing how you teach–it involves working in more fundamental skills, spending more time teaching things you think you “shouldn’t have to teach”, adjusting instructional methods, and, yes, sometimes it means you have to change what a “C” looks like in your course, so that kids who took a risk don’t fail. But it’s preferable to kids not having access to the education they want because someone decided they weren’t capable: the data is pretty clear that a lot of those kids are perfectly capable.
We don’t have CC in our state–it’s actually ILLEGAL for schools in our state to adopt CC. But there has certainly been a broad trend toward making graduation requirements more rigorous: we flirted with 4x4–four years of English, History, Math, and Science–but have backed off on that somewhat. But the state still requires more academic courses now than they used to. It’s currently 4 English, 3 history, 3 science, 3 math. Furthermore, college and career readiness is a very big deal these days, which means schools are evaluated based on SAT/ACT scores, among other factors. So there’s a fair bit of pressure on schools to increase the number of students who are ready to do college-level work.
I don’t know if that’s really a meaningful consideration for most students in high school. Few students are really very interested in taking algebra, or for that matter any other academic subject. They’re actually interested in sports, video games, students of the opposite sex, weed, texting, social media, etc…
Stuff like algebra or English is stuff they’re more or less coerced into taking, either through the stick of failing and having to repeat the grade, or through the carrot of being able to get into a college of their choice.
I definitely agree that some students pick subjects up faster than others; and I think that when people say that there are students incapable of learning a subject, there are some unspoken caveats- they’re assuming we’re talking non special ed students, and they’re assuming that it’s within the time frame allotted (i.e. a semester, school year or whatever), and they’re also assuming that it’s using the standard teaching method.
I mean, if you look at it that way, there are definitely students who will NEVER get algebra if taught in the normal classroom method and only get a school year to learn it. They might take a couple of years, or they might benefit from more intensive tutoring, for example.
I kind of doubt that there are people not in special education who can’t understand at least algebra 1.
You are wrong, actually, in my experience, unless by “most” you mean “more than 50%”. Yes, a majority of students find academic subjects uninteresting. But a significant percentage, say 33%, find academic subjects interesting, either intrinsically, or extrinsically. For many, it’s a recognition that they want to go to college, and these courses will help them accomplish that. For others, it’s a love of learning in general, often augmented by an interest in the subject matter itself.
At the school I taught in, I taught the equivalent of “Honors” Geometry, along with regular, ordinary Geometry (what we called "Pre-AP Geometry and College-prep Geometry, respectively). Roughly 35%-40% of students in the Sophomore class took the Honors version. Of those, about a quarter demonstrated insufficient motivation to be in the class, and ended up struggling to get much more than a passing grade. The rest would make good, solid attempts at learning the material, not just on a surface level, but on a deeper level involving actual understanding of the concepts. Of that group, about a quarter of them would go even deeper, seeking out fundamental principles and working out the implications on a wider scale; these were the students who understood what I was talking about when I introduced non-Euclidean Geometry concepts.
Of the students taking so-called “college-prep” Geometry, the ratios were skewed substantially towards more of them being uninterested in anything other than completing the course with a passing grade. For most of them, had Euclid’s existence been wiped off the map of past history, and proofs eliminated as a consideration of the course, they’d have been ecstatic, or, at least, they would have been happier, since they probably couldn’t generate enough excitement about anything academic to be ecstatic. :rolleyes:
That depends upon what you’re taught in Algebra I. And even then, I’ll assert you’re wrong. I famously had one student, a girl of 15 or so, who was taking what we called “repeater Algebra I”, given to Sophomores (or higher) who had failed Freshman Algebra I. Since they had been in Algebra I, they had not been adjudged to be impaired enough in understanding of math in middle school to require the two-year Algebra I sequence. On the day in question, she was attempting to solve a two-step single variable equation, something rather simple involving addition and division only. As I tried to prompt her through the thought process for the steps needed, she memorably replied to me, “I don’t know what comes next. I don’t get it! They’re just letters and numbers to me; they don’t make any sense!” For her, the simple abstraction of a single variable, combined with numerical values in an arithmetic sentence, was more than she could comprehend. And she was not alone in this.
Don’t even get me started on the section of Algebra I involving what we call “literal equations.” Getting students who struggle with abstract symbology to work out solutions for such things as PV = nRT, where a single variable is supposed to be isolated can be impossible. They don’t get that the same arithmetic that allows us to solve for V in 5V = 3(2*4) allows them to isolate V on one side of the equation and P, n, R, and T on the other. Yet, that’s actual algebra; most of what gets taught in an Algebra I course isn’t really algebra, it’s just application of the basic indentities of equality or inequality to arithmetic sentences.
If you do two hours of math a day, what does the kid give up in order to have this extra time? We can devote more financial and staff resources to a kid, but we can’t give the kid more hours in the day, and usually we can’t even give them more hours in the school day.
This is something that is a constant struggle in elementary school. Yes, that kid who can’t add 14+1 using her fingers and a hundreds chart might benefit from 45 minutes one-on-one instruction with an exceptional children teacher. To get that time, she has to miss regular math instruction, or reading instruction, or science instruction–and usually kids who are struggling in one academic area aren’t excelling in any academic area.
While the ideal is great, I’m not sure how to manage it without a time machine.
Of course, and I meant the total opportunity cost when I said that some skills may not be worth it. But that’s not at all the same as saying it’s impossible for a kid to learn something. For one thing, if something’s possible, it becomes feasible to find a better, more efficient way to do that. But once you’ve decided it just can’t happen, it ends the quest.
Roughly when you are at school 
It’s been 38 years since I took algebra 1, but it took me a while to figure it out. I’m sure it took a while for it to be pounded into my head then, too. Anything more advanced than that and I would have been completely lost. Teachers also couldn’t figure out how I could make failing grades in algebra, yet my PSAT, SAT, and ACT math scores fell in the top 10-15 percent. Their solution? I must not be trying. It didn’t help my case that I made B’s and science and A’s in pretty much everything else.
My point, and I do have one, is that I would have had trouble graduating at a high school with the math requirements my kids’ school has (unless they dumbed it down). I don’t know where students like me (problems with math beyond 6th grade or so, fairly good writer, out of this world ability to skim material and analyze it on the fly) end up nowadays. I won’t find out with our kids; one is a math major at a major university and his brother is doing just fine in precalulus.
On a theoretical level, I’m not sure I agree. We’ve got a range of aptitude for certain academic fields. Let’s say that in a school with 100 twelfth graders, there’s exactly one kid who’s ready for differential calculus, if the kid gets a lot of support.
It’s possible for that kid to master differential calculus. Does that mean, therefore, that it’s possible for every kid to master differential calculus?
I don’t think this follows. I think that there’s somewhere that we must draw a line, with some kids capable of performing above the line and others not. This’ll be true in any field: math, music, art, badminton, World of Warcraft raiding, pie-baking.
We may, in practical terms, draw the line in the wrong spot. But the only way such a line would be nonexistent would be if there are no differences between kids.
ISTM that Manda JO is arguing on a practical level, not a theoretical level.
Given an environment where people are making decisions based on politics and budgets, rather than on behavioral science, it becomes too convenient to set the “can’t” level real low and thereby write off lots of students that could be taught more complex subjects successfully if only the effort were made.
In the zero-sum world of funding the more you can take from the weak the more you can transfer to the strong. You just need a fig leaf thick enough for the willing believers in the righteousness of privilege to hide behind to their own satisfaction. The opinions of the weak can simply be ignored.
IMO that’s what she’s arguing against.
What LSLGuy said.
Of course there’s a theoretical line, but I’m not comfortable at drawing that line at “being able to get a C in Algebra 2”. Thirty years ago, it was just a fact that a kid with Down Syndrome could not be taught to read–now something like half the individuals with Down Syndrome are literate. I’ve already mentioned the tremendous increase in passing AP scores, when open enrollment was encouraged–many of those were kids people labeled as incapable.
There is a persistent trend in education of discovering that kids are more capable than we ever believed, and that what were seen as inherent limitations were not immutable facts. We are still fighting the legacy of Social Darwinism in American Education.
The problem is, there’s a wide spectrum between doing and understanding. You can teach kids calculus or fractions or PV=nRT and get them to apply the process, work the numbers; but not all of them will completely grasp the concepts that drive those processes, Even fewer will be able to derive further principles beyond the mechanics of what they’ve been taught - just as some kids 9at first) may be borrows or carries without really understanding the “ten’s column - hundred’s column” thing.
It also depends on how motivated they are, and how much effort they and society want to put into learning. If calculus were the means to easy street, kids might be far more motivated than when they say “when will I ever use this in real life?” OTOH, there’s a serious motivation for everyone to learn to read, even if it’s elementary things like street signs, the TV guide, or the panel that says “game over”.
Reading and math instruction has always had one major divergence that puts math at a huge disadvantage.
We teach the basics of reading and then continue to advance the skill *by actually using it to learn *across all other subjects. It is seen as, and in fact is, pretty much a prerequisite tool in the process of learning other things and applying the skill in service of that process further advances the skill.
We don’t do that so much with math. Ideally the grade level, or at least the previous grade’s level, math skills should be integrated as part of the skills to learn the current level other subjects better, and not just in hard science. And even in science it is usually barely used … the math needed in High school chemistry is far far far below grade level and even physics barely applies most of the math they have learned with very rare exceptions.
Consequently it is perceived as something that you learn as a stand alone, never to use very much outside of the specific subject classroom, and maybe later IF you go into something like engineering or accounting, but not something that most people will use to keep learning with all that much. Learn geometry for the class, take the last test, then don’t use in service of learning anything else except maybe another math class in the future … the way it works with reading works better.
A practical application of math is (or used to be) to handle money. This aspect of math people seem to absorb better than other parts - and probably for the same reason as you mention about literacy - it’s constant use.
Yes and that is used to the point of making change and figuring out what things cost per unit. But I am more talking about integrated throughout the curriculum, applying the math skills that should be mastered to other subject matter in order to learn and understand as much as reading skills are. Although having more test questions that required applying the principles taught to questions that come up in future classes, might be in future career paths, as well as other real world applications, would also be nice I’d think.
Same with me. I remember that I read a book, “Kit Carson, Indian Fighter”. And what was Davy Crockett doing down in Mexico when he was killed at the Alamo? How about trying to carve out a piece of Mexico to set up a slave state.