The whole algebra debate kicked off by Hacker’s algebra essay has…..well, if not depressed me, then at least enervated me.
A recap:
Hacker:
We shouldn’t make everyone take algebra. No one needs algebra anyway; we never really use it. Statistics would be much more useful. Algebra is the primary obstacle to high school success; millions of kids are failing because they can’t manage this course. If we just allowed students to have an easier time in high school, more of them would graduate successfully and go on to college.
Outraged Opposition:
Algebra is essential to college success and “real life” and one of many obstacles to high school success. No one is happy with the current state of affairs, but it’s clear that kids aren’t learning algebra because their teachers suck, particularly in elementary school. We need to teach math better in the lower grades, rather than lower our standards. Besides, the corollary to “not everyone should take algebra” is “some people should take algebra” and just how are you planning to divide up those teams? (Examples: Dan Willingham, Dropout Nation)
Judicious Analysis:
Sigh. Guys, this is really a debate about tracking, you know? And no one wants to go there. While it’s true that algebra really isn’t necessary for college, colleges use success in advanced math as a convenient sorting mechanism. Besides, once we say algebra isn’t necessary, where do we stop? Literature? Biology? Chemistry? But without doubt, Hacker is right in part. Did I say that no one wants to go there? Or just hint it really, really loudly?
Examples: Dana Goldstein, Justin Baeder Iand II.
Voldemort Support:
Well, of course not everyone should take algebra, trig, or calculus. Or advanced literature. Or science. Not everyone has the cognitive ability or the interest. We should have a richer and more flexible curriculum, allowing anyone with the interest to take whatever classes they like with the understanding that not all choices lead to college and that outcomes probably won’t have the racial distributions we’d all prefer to see. Oh, and while we’re at it, we should be reviewing our immigration policies because it’s pretty clear that our country doesn’t need cheap labor right now.
Hacker, Outraged Opposition and Judicious Analysis to Voldemort Support:
SHUT UP, RACIST!
So really, what else is left to say? The Judicious Analysis essays I linked above were the strongest by far, particularly Justin Baeder II.
Instead, I’m going to revisit a chart I updated from the last time I posted it:
These are California’s math scores by grade and subject, the percentage scoring basic/proficient or higher on the CST. Algebra entry points differ, so the two higher (and slightly longer) of the four short lines are the percentages of “advanced” students with those scores—those who took algebra in 7th or 8th grade. The lower, shortest lines represent the scores of students who began algebra in 9th grade.
Notice that advanced students don’t match the performance of the entire elementary school population through 5th grade. Notice, too, that the percentage of advanced students scoring proficient or higher is just around half of the population. When I just considered algebra students who began in 8th grade (see link above), the percentage never tops 50. Notice that around 40% of the kids who started algebra in 9th grade achieved basic or higher.
NAEP scores show the same thing—4th grade math scores have risen, while 12th grade scores stay flat. In fact, Daniel Willingham, who declares above that we’re doing a bad job at teaching elementary math, was considerably more sanguine about teacher quality back in December, citing the improved elementary school math performance shown in the NAEP. So the strong elementary school performance, coupled with a huge dropoff in advanced math, is not unique to California.
These numbers, on the surface, don’t support the conventional wisdom about math performance: namely, that elementary school teachers need improvement and that the seeds of our students’ failure in higher math starts in the lower grades. Elementary students are doing quite well. It’s only in advanced math, when the teachers are much more knowledgeable, with higher SAT scores and tougher credentialling tests, that student performance starts to decline dramatically.
What these numbers do suggest is that as math gets harder, fewer and fewer students achieve mastery, or anything near it. . What they suggest, really, is that math knowledge doesn’t advance in a linear fashion. Shocking news, I know. We have all forgotten the Great Wisdom of Barbie.
Break it down by race and the percentages vary, but not the pattern. I skipped Asians, because California tracks Asians by subcategory, and life’s too short. I’m going to go right out on a limb and predict that Asians did a bit better than whites.
(Note: I know it’s weird that in all cases, 9th graders in general math have nearly the same percentages as 9th graders in algebra, but it’s easily confirmed: whites, blacks, Hispanics).
Whites in the standard math track perform as well as advanced math blacks and just a bit worse than advanced track Hispanics. Sixty to seventy percent of blacks and Hispanics on the standard track fail to achieve a “basic” score.
Some people are wondering how poverty affects these results, I’m sure. Let’s check.
Hey! Look at that! The achievement gap disappears!
Just kidding. This chart shows the results of blacks and Hispanics who are NOT economically disadvantaged and whites who ARE economically disadvantaged. You can see it on the legend.
So that’s how to make the achievement gap disappear: compare low income whites to middle class or higher blacks and Hispanics and hey, presto.
And that’s all the charts for today. I’m not detail-oriented, and massaged this all in Excel. You can do your own noodling here. Let me know if I made any major errors. The 2012 results should be out in a couple weeks.
Anyway. With numbers like these, it’s hard not to just see this entire debate as insanely pointless. In California, at least, tens of thousands of high school kids are sitting in math classes that they don’t understand, feeling useless, understanding deep in their bones that education has nothing to offer them. Meanwhile, well-meaning people who have never spent an hour of their lives trying to explain advanced math concepts to the lower to middle section of the cognitive scale pontificate about teacher ability, statistics vs. algebra, college for everyone, and other useless fantasies that they are allowed to engage in because until our low performers represent the wide diversity of our country to perfection, no one’s going to ruin a career by pointing out that this a pipe dream. And of course, while they’re engaging in these fantasies, they’ll blame teachers, or poverty, or curriculum, or parents, or the kids, for the fact that their dreams aren’t reality.
If we could just get whites and Asians to do a lot worse, no one would argue about the absurdity of sending everyone to college.
Until then, everyone will divert themselves by engaging in this debate—which, like many kids stuck in the hell of unfair expectations, will go nowhere.
educationrealist 
August 19th, 2012 at 2:17 am
To what, if not economics, do you attribute the difference in achievement between the races? I’m not trying to be a troll; I’m really trying to understand what I’m seeing as a new teacher of non traditional, mostly African American, adults. Is it a cultural values thing– some families value and push kids early on and others don’t? I’d be very interested to hear your speculations (I know nobody has good answers for these questions) because what I’ve read of you so far has been pretty sensible. Thanks for sharing your ideas.
August 19th, 2012 at 5:37 am
I don’t know what causes it. I do not secretly believe that there’s some IQ gene that differs for blacks, whites, Asians, and Hispanics. It really doesn’t appear to be economics, since you have to sort for race first. I also find cultural factors unlikely except at the edges. So I’m less interested in knowing *why*, rather than accepting what *is*—and refusing to let other people engage in fictions about *why*
Rather than restate my views and miss something important, I’d rather just suggest you click on the voldemort category. If that seems like a lot, here’s three important ones.
August 19th, 2012 at 7:50 pm
I think racial differences in intelligence have a substantial genetic component (which does not mean that there is a single “IQ gene” responsible for the differences). The races evolved over millenia in very different environments, and some of those environments selected for intelligence more strongly than others. A summary of the evidence, available online, is in
Rushton, J. P., & Jensen, A. R. (2005). Thirty years of research on race differences in cognitive ability. Psychology, Public Policy, and Law, 11, 235-294 .
August 19th, 2012 at 9:47 pm
I think that’s quite possible. But when people speak of genetic differences, most non-scientists (and I count myself among that group) think of a causal relationshipt. That is, being black *causes* low IQ,or being Asian *causes* high IQ.
Instead, what seems at least likely is that the *distribution* of IQs is different because of the environments and the selection for fluid intelligence. That is, a high IQ person can be of any race, but occurs more frequently in some races.
This distinction is lost, I think, with the words “genetic component to intelligence”.
August 21st, 2012 at 3:51 am
Assume that there are 150 genes involved in determining IQ, with each gene having two alleles, one providing 0 IQ points, the other providing 1 IQ point. Assume also that 50 of them have fixed on the 1 IQ point allele.
This give us a population distribution with a mean of 100 and a range from 50 to 150. (It is a binomial distribution.)
Now, if there is a cost with the 1 IQ point variant of some of those genes, eg, perhaps increased brain size and increased energetic costs, then in an environment where the is no net benefit to a higher IQ, those alleles will be selected against and likely will disappear from the population. It only takes 15 of them to fix on the zero point variant for the average to be pushed down to 85.
Of course, this is a simplistic model, but it seems useful for exploring the concepts.
August 21st, 2012 at 4:22 am
It only takes 15 of them to fix on the zero point variant for the average to be pushed down to 85.
That, is, of course, wrong. Since we have assumed that each allele is equally likely, if 15 of the genes fix on the 0 IQ allele, the mean will be reduced by 7.5 IQ points. It takes 30 of them to fix on the 0 IQ variant to reduce the average IQ to 85.
Of course, some of those that had previously fixed to 1 could experience mutations that drive them down to 0 in offspring.
August 21st, 2012 at 4:54 pm
Being from India and having taken all the math and sciences at mandatory plus college level (many moons ago), the bottom line to math and science excellence is to start early and repeat the subjects ad nauseum.
Find teachers (and text books) that can lay it all out in simple terms so that more people ‘get it’, and don’t confound those who don’t with verbosity and verbiage to show that you (ie the teacher or text book) are one of a chosen few who ‘get it’!
This message is totally from the heart. I am studying again at the advanced age of 55, and find that text books, even those written by leaders in the field, do not show any appreciation of paragraphs, punctuation and prepositions, ramble on a lot, and convey scientific facts in essay format, doling out facts in random order in several paragraphs.
August 19th, 2012 at 6:32 am
what makes you say it’s clear we don’t need cheap labor (I assumed you yourself believed that, as you generally claim allegiance with the Voldemort view)? I can’t think why cheaper labor wouldn’t always be in demand…
August 19th, 2012 at 9:55 am
That was kind of a short hand. Immigration always drives down labor costs. One of the pipedream notions of the “college for all” crowd argues that we can address the problems of the high school graduates-or-less population not by giving them less competition, but by giving them more education. Once this is acknowledged as largely hooey, then it clearly becomes imperative to reduce competition for unskilled or low-skilled labor so that this population has a better chance of making a living.
Obivously, the problems of this segment don’t magically disappear in that event, and limiting immigration has its own challenges. I was just including that suggestion because most HBDers (the official term for the Voldemorts) are concerned about immigration for this reason.
August 20th, 2012 at 7:44 pm
ER,
I’ve got three kids taking math at three different public schools in NYC, which has given me some perspective into the variability of instructional quality within the system.
I wrote an essay for the New York Times blog that puts me in the outraged opposition, but I’m sympathetic to the judicious analysis view too. So I was glad to read your analysis and be challenged.
You posit that poor instruction is not the issue, because in the early elementary grades, most kids are more than proficient. But isn’t this view predicated on the idea that these state tests are effective measures of knowledge?
My thought (based on experiences in Gotham) is that the 3-6th grade state tests in math are aimed very low. Kids can do well on them even if they have not developed a solid understanding of the underlying principles of place value and fractions, or real automaticity with fact recall. Especially with all the test prep they are given in class these days.
In 7th and 8th grade this failure comes home to roost, as the concepts are more abstract. So even on the equally poor tests in those grades, they suddenly look less competent.
I’d love to know what’s wrong in my logic.
Matthew
August 20th, 2012 at 8:41 pm
You cite NAEP scores in your op-ed in *support* of your position and, as I mention in the piece, NAEP scores show the same gap. So if NAEP scores are bad too, why are you using them in support of your position? And if they’re not faulty, then your argument doesn’t hold up. Besides, it’s kind of odd to argue that ALL the tests are bad, but show student performance declining so consistently.
That said, I think the elementary school tests are easier, as I said in the first post on this subject, here: https://educationrealist.wordpress.com/2012/07/30/the-false-god-of-elementary-school-test-scores/ But the tests show a solid, consistent decline, and even after the students are split into advanced (starting algebra in 7th/8th grade) and basic (starting in 9th grade), the pattern stays the same. The stronger half still do worse than the entire population of math students until 6th grade.
In order to believe that the elementary school teachers are doing a terrible job that harms all our students, you have to accept that the top math students, taught by teachers with far more qualifications, are still being held back by the failure of their elementary school teachers who did a poor job at covering fractions. Sorry. Not buying.
But even more damning than that, and this is probably shown in NY tests as well: the achievement gap stays consistent. If the elementary school tests were dramatically easier, then all elementary school students would be acing the test, or close to it. Instead, the gap is consistent—as the tested math gets harder, the gap gets wider. Meanwhile, the scores show the same results as is true of all tests—poor whites do as well as middle income blacks, and so on.
No. The results do not show that math instruction is leading to poor scores, but that math, as it gets harder, leaves more and more people behind.
Incidentally, I’m not a big fan of Dr. Wu, who feeds the fantasies of well-meaning middlebrowers who blame instruction. Dr. Wu has no clue (heh) as to what is involved in teaching kids of low ability. He thinks that instruction will help communicate difficult abstract concepts. That will help with kids of high ability, but not with kids from the mid-low end of the spectrum.
August 20th, 2012 at 10:36 pm
Two addenda: I sound too definite about Dr. Wu. I read his work and am not sold because I think he’s far too optimistic. Teaching proportionality is extremely difficult. But I come off as “yeah, what does he know”, and while * might think that, I also apply that same line to myself all the time. Second, this is a very broad picture and of course, there could be a way to massage the data that would reveal different shades of gray. So I really should say that the results do not suggest a relationship between math instruction and poor scores, but rather a relationship between the cognitive difficulty of math and test performance. They aren’t consistent with an argument that elementary teachers are weak.
In short, none of this is easy or certain and whenever I sound too dismissive, I’m usually going to run back and correct myself.
June 30th, 2019 at 9:27 am
“Gotham” is Boston. So is “Arkham”, the location of Miskatonic University.* Maybe in the universe in which Batman exists they are NYC but in ours they are Boston.
* play around with Greek and Miskatonic becomes a reference to MIT (MIT is in Boston on the bank of the Charles river, Harvard isn’t in Boston, it’s in Cambridge)
August 21st, 2012 at 12:13 am
ER,
My reference to the NAEP was to the point that collectively math scores don’t suggest kids are getting any smarter. I’d posit that the boost we see in the younger grades is because the NAEP too is easier at that level. (how hard can they make the national test if USEd can’t assume the kids have had much more than place value to 1,000 and some multiplication but not much division)
I was not trying to lay the contradiction of rising 4th grade scores and falling 8th grade scores at the feet of teachers. FWIW my wife is a HS teacher and I’m don’t buy the argument that teacher quality is the panacea many reformers would have you believe that it is. (see http://gothamschools.org/2010/03/15/the-role-of-curriculum-in-education-reform/)
As you point out in the ‘about me’ section and in your post on SAT tutors, being ‘smart’ in some objective sense is necessarily the key to success. Still costs you $4 for your coffee.
So the fact that elementary school teachers have SAT scores that are at least near to or slightly above the national average is, in a sense, neither here nor there, right? They should be ‘smart enough,’ on average. But this doesn’t mean they’re all equally effective instructors (separate topic as to how we measure effectiveness other than with the kids’ test scores or the teachers’ SAT scores)
Thus I come back to the quality of the curriculum. You say it’s not the fault of poor texts and curricula that Jose struggles while James gets it?
Any chance James’ parents are more likely to have recognized flaws in his classroom instruction and gotten him support that pays off in the long run, while Jose’s folks don’t? (I know you touched on this in your SAT post; in my district the tutoring starts in 3rd grade)
So James still doesn’t succeed in Algebra as well as he might, but he’s still way better off than the other kids because of these interventions?
August 21st, 2012 at 5:10 am
I don’t think the NAEP is that easy. I go through the sample questions quite often. Fourth graders have to answer questions on fractions, for example.
“being ‘smart’ in some objective sense is necessarily the key to success”
I did? I said that ‘smart’ was essential to learning math the way I did (different post) but I don’t think I mentioned the word “smart” in the SAT tutor post. Maybe I’m forgetting something. I do not, in fact, think that “smart” is a key to success. I think it matters a lot to academic achievement, but that’s a different issue. I think part of our problem with education lies in the fact that we are setting goals for *success* that require everyone to be *smart*, and that’s just not possible. I’m not saying this to start an argument, but because I’m not sure what I said to give you the idea that “smart” is essential to success. )Unless my clarification is what you mean by “success”, of course.)
“So the fact that elementary school teachers have SAT scores that are at least near to or slightly above the national average is, in a sense, neither here nor there, right? They should be ‘smart enough,’ on average.”
Yes.
“But this doesn’t mean they’re all equally effective instructors ”
Just as true for high school teachers, though. You’re beginning from a premise you can’t prove. Demonstrated ability in elementary school students isn’t just higher, but dramatically higher than it is in high school, yet you feel that it’s probably due to simpler tests, that elementary school is where math failure begins, and it’s because not all teachers are equally effective. But your premise is not only unproven, but unlikely as a dominant reason for the high performance of elementary school kids. It’s far, far more likely that they do better because the math is easier.
As for the rest, unless you are arguing that simply by virtue of being white ,James’ parents are more likely to foresee problems–and I know you aren’t—then the data doesn’t support your argument.
And then you switched from elementary school math to algebra. I’m not sure what your point is? I’ve taught Algebra Intervention. It’s brutal. And arbitrary.
August 21st, 2012 at 4:53 am
I’m really out of my element with this post – other than the reference to Voldemort, which I understand completely. Congratulations on being freshly pressed – and good luck. I think with this post, you’re going to need it. 🙂
August 21st, 2012 at 5:02 am
The idea that elementary school teachers need to be improved is crap. I’m a junior in high school and can tell you for sure that I had great math teachers up until seventh grade. I skipped seventh grade pre-algebra (yeah, I’m one of those advanced kids). My algebra teacher was a distractable old woman who wasn’t terrible as a teacher, but she was originally a sixth grade teacher, so seventh grade students found her a little difficult to work with. Eighth grade geometry, we had a teacher with a thick Indian accent who showed us slideshows. Sometimes she worked out problems as examples, but usually, she didn’t. Ninth grade: I took algebra II with the worst math teacher I’ve ever had. I had to learn from the textbook – and California is TERRIBLE at giving us good textbooks. Pre-calc was the one class where my teacher was great, but he was this little old guy who used to work with missiles in the navy, so of course he was good at math and had years of experience teaching it.
That pre-calculus teacher was the one good math teacher on my entire high school campus. My point here is that it’s middle school and high school teachers that are the problem. California can’t hire good teachers to save the lives and educational careers of all its elementary school students.
And as for not needing algebra: It’s how it makes the brain work. Algebraic math is a little like push-ups for the brain. While one may not need algebra, the brain benefits from the solving of equations. It’s like how old people are told to learn new languages and things to fight off Alzheimer’s.
Beyond that, though, there’s the simple fact that interests change. When kids take algebra, they’re usually not sure what they want to do. By the time they have to choose where they want to go to college, they might find that they love astronomy. You need algebra for a lot of astronomy, especially when you get into the area of astrophysics. Not having been forced to take algebra could harm these kids’ chances of pursuing fields they find they love just a little too late.
I don’t think it would be fair to do that to kids who are already at such a stressful, difficult point in their lives. I became furious when I realized that my sub-par high school education had wasted multiple years of my life. Lucky for me, I managed to switch to a school where I take college-level classes that are even beyond AP (mainly because most of them are actual college classes, at a college). Not everyone can do this, though. That’s why we need the opportunity and the truly qualified teachers.
It angers me that the government lets this go on while they bitch and argue about gay marriage and abortion. Give half a damn about us and our future, the future where you’ll be old and dying and unable to get good medical treatment because we’re all brick-stupid, and regulate the idiots you hire to teach us before you try to regulate the country’s genitalia.
(Apologies for the long, angry post. As a student who considers herself an intellectual, I get really, really frustrated by the crapshoot that is modern education.)
August 21st, 2012 at 5:29 am
Great comments, even though I disagree with a lot of them. And as someone who never uses one word when a thousand will do, I’ll never whine about someone else’s longwindedness.
1) High school math teachers are, in every way, better qualified in math than elementary school teachers. This is not open for debate. That doesn’t mean that you can’t get utterly incomprehensible teachers (there were two at my last school), or bad teachers. It happens. Moreover, high school math is much, MUCH harder than elementary school math. Not all knowledgeable math teachers are good at working with high school students, particularly those who aren’t good at math. I’m a tutor and many of my students going to excellent schools have terrible math teachers, teachers who are very knowledgeable about math but have just never given any thought about *how* to teach it.
2) I am not arguing for or against algebra’s “usefulness”, since there’s not one answerfor all kids. Your argument, in my view, only holds for kids with high cognitive ability.
3) You are very unhappy with your high school education. Yet a large part of that unhappiness is caused by the expectation that all students can achieve equally. In that environment, teachers are often prone to simply passing the kids who work hard. Also, don’t make the mistake of confusing your unhappy experience with the sum total of education. There are an infinite number of ways in which school can be bad. Overall, we do a pretty good job given our ridiculous expectations and our challenging populations. In other countries, they boot half the kids to vocational ed.
Also, I hate to break this to you, but your post tells me that your school did a pretty good job of educating you. (g)
You may want to read this post, here, about teacher quality:
Despite your experiences, they really are smart enough.
August 21st, 2012 at 6:13 am
Oh, I know they’re smart. It just doesn’t matter how smart they are if they can’t do their job. I see way too many of my classmates failing. It’s not just from my school; the school I go to now has kids from all over the county who just didn’t get enough at their old schools. They failed classes because they simply weren’t taught well. The issue really shouldn’t be so prevalent, in my opinion.
On those grounds, you are right. Not everyone can achieve equally. Having developed a hobby of researching how the brain works and all that jazz, I know that different people have different levels of intelligence. I suppose I am overly optimistic in that respect.
Haha. Honestly, I don’t know how much of my own intelligence is actually from my school. I participate in a lot of outside learning. I research things that I want to learn about. That’s not to say I learned nothing from them; I’ve had a couple good teachers, particularly my European history teacher, who has really been the only teacher to prepare me for college courses and a truly rigorous curriculum. However, I base many of my statements on what my classmates have reported and what I’ve seen in many of my classes. Most of the students I know complain of not being engaged or taught in a way they can understand. I attribute much of my success as a student to the fact that I pursue the answer if I don’t find it in the classroom. I can’t tell you how many hours I’ve spent on the internet and looking at the textbook simply because a teacher either didn’t explain it well or simply neglected to teach something. Perhaps this is how “good” students become “good” students or just a sign of high cognitive ability (an attribute I don’t lay claim to at all; I just like learning and am in no way considerably intelligent.), but I don’t believe that everyone should have to spend their evenings at the computer just to fully comprehend a subject like English – a subject I only learned in a classroom up to the sixth grade level, having learned everything else critiquing and being critiqued as a writer online. School should be enough to truly educate students, but time and time again, it doesn’t seem like it is, at least in this district. I suppose part of this is the fact that the course offerings are so narrow that certain students simply aren’t offered the classes they’ll flourish in, but that’s an entirely different rant.
And perhaps I misspoke or neglected to clarify myself: I don’t think that all education is the same as the one I received. As a participant in many online writing forums, I’ve spoken to others who’ve received excellent educations. They’ve often been the ones educating me; I certainly didn’t learn grammar beyond the basics in school. This is simply based off of what I and those around me have experienced, and in the past at that. The school I now attend has excellent teachers. While I’ve managed to teach myself much of what’s currently being taught, I know that the English teacher is teaching her subject well because I’ve seen how students have improved, from my classmates to the people I’ve known who graduated after being at this school. If more teachers were of that quality, I wouldn’t be criticizing the education system as I’ve experienced it.
August 21st, 2012 at 5:04 am
I took Algebra when I was in High School (like everyone else) and I have yet to use it in the Real World! Seriously, I’m a designer and we designers don’t have a need for the higher maths. Honestly, the only thing that Algebra proved was that I was lousy at math and it made me hate math from then on. I wish I had been better at it, I really do, because when you’re bad at it, it makes you feel really stupid. 😦
August 21st, 2012 at 6:00 am
Personally, the whole set-up that algebra is less worthwhile than statistics is silly–algebra introduces the ideas of variables and multiple answers that statistics is based in. That said, I do think everyone should be required to take a semester of statistics, because it is so applicable to everyday life and decisions.
August 21st, 2012 at 8:31 am
Algebra, every cartoonist should have an in-depth knowledge of it.
I don’t know much about algebra, and look at how badly this has influenced my cartoons (samples on my blog).
I blame the useless teachers at the school my Mum sent me to.
August 21st, 2012 at 9:05 am
I personally know child-prodigies who say they’re fine with other subjects but stumble over Algebra. It’s their only nemesis.
August 21st, 2012 at 1:33 pm
I wrote this post about learning math later It’s kind of long:
August 21st, 2012 at 11:06 am
Why on Earth do you need to sort test scores by race? Aren’t we all human with the same brain?
I use algebra in real life to change knitting patterns into bigger or smaller sizes. It’s not always about doubling or halving the numbers, sometimes there is a ratio of features to maintain.
August 21st, 2012 at 1:32 pm
We sort scores by race all the time. It’s one of the main ways that we judge educational success.
August 21st, 2012 at 2:49 pm
I know it’s done all the time, what I’m saying is that I don’t see the point. Sure, measure by country or socioeconomic status, variables that indicate differences, but if you keep measuring by race there will always be segregation.
August 21st, 2012 at 3:41 pm
I’m glad to see that someone else uses algebra in real life, sedrate. I’ll bet there are more of us out there as well, who are not geeks (I was a language major). I use simple equations to scale recipes and other mixtures up or down.
August 21st, 2012 at 7:54 pm
When we have no affirmative action, and no disparate impact law suits, and no blaming some people because other people are “under represented” in some field or another, then we can stop sorting things by race. In other words, never. All humans are not the same, any more than different dog breeds are the same, despite all being dogs and having some shared ancestry.
I use algebra all the time. I also use probability, statistics, calculus, logic and many other branches of math.
I haven’t had any use for all of the literature or art that I was taught in high school.
August 21st, 2012 at 11:23 pm
I quite see your point but I think that if we keep drawing attention to race, using it as a reason for things then it will continue to be an issue. And I’d bet that you do use things you learned in literature class, just as the logic you learned in math imbues your daily thinking, so too do the ideas you were exposed to in books.
August 21st, 2012 at 12:07 pm
I expected more out of this blog such as: algebra is not used in the real world. I’ve been out of high school for 22 years and haven’t used algebra once. I believe algebra is useless in this day and age. Why we had to suffer through it and why our kids must do the same is beyond me.
August 21st, 2012 at 9:56 pm
You use a computer since you wrote this, and you likely have a cell phone. Do you have any idea how much cutting edge mathematics is involved in creating these technologies?
You are like a leaf who who does not know you are supported by a tree.
August 21st, 2012 at 12:39 pm
I used to love algebra in school. If not as a separate subject, it could be incorporated in statistics just to introduce the concept of equations and variables, which is the bedrock of statistics. The database you used to tabulate your graphs is really cool. I didn’t know something like this existed.
Congrats on being freshly pressed!
August 21st, 2012 at 12:45 pm
yeah algebra is basically pointless. i’ve never once used it in real life.
August 21st, 2012 at 9:59 pm
Maybe you don’t use it, but the world around you exists because of many people do.
August 21st, 2012 at 1:26 pm
Forget algebra, geometry, literature, physics, and the works. Just teach highschoolers some vocational skills so they actually have a prayer of getting a job in this though economy.
August 21st, 2012 at 7:44 pm
Neat! I agree with you on the first part, but if it were up to me, I’d teach high schoolers how to create their own jobs or run creative businesses instead of working like slaves and earning just above minimum wage for the next thirty years. Traditional education doesn’t even guarantee you a job in the market anymore. It would be a bit more interesting if there was an education system that created jobs for students instead of preparing students for jobs.
August 21st, 2012 at 1:39 pm
Reblogged this on AYUSHMAN PERSHAD and commented:
This is to all the Maths Teachers ruining the brains of children.
August 21st, 2012 at 2:06 pm
I ALMOST didn’t go to college because the algebra intimidated me so much. I pulled through college algebra with a TON of tutoring. Haven’t found a use for it anywhere since… it WAS a waste of time, stress, energy and MONEY . But, it was a necessity in order to graduate. All I really learned anyway was how to use a calculator to figure it all up! (Something I could have learned from the calculators instruction manual) The price of advanced education and the unnecessary classes is deterring a LOT of people from wanting to advance their positions in life. Algebra, geometry, literature, foreign languages, etc should only be required if those are the fields in which a person wishes to advance to. I stressed MONEY above b/c that’s really what it’s all about. Universities are all about profit and so they force students to know this stuff. We need to crack down on this and employers that higher illegal immigrates to bring the workforce back up to par. This won’t happen as long as republicans control Washington. They are all about feeding the rich.
August 21st, 2012 at 2:34 pm
Well let me tell you something i know Algebra and could tech you it took me a minute to learn it but i passed my class with an 82 I needed an 80 to pass. Well I took all the tests and mastered the concepts. Math and learning it doesnt have to be painful if you have the right teacher. Algebra helps you calculate things faster but is more applicable for electricians and plumbers Algebra helps you build without it you are a worker that will be expendable. Calculus to me is worthless but to an engineer is valuable.
August 21st, 2012 at 3:36 pm
Some people love math. Some people don’t, but can do it. Others hate it and can’t do it. I think it will be very hard to ever generalize among class and race on this topic, if we are all innately different on the inside regardless. Not everyone needs to go to college. There are other paths out there–it seems like no one wants to give them a look.
August 21st, 2012 at 3:52 pm
[…] Is algebra necessary? debate is “insanely pointless,” writes Education […]
August 21st, 2012 at 4:52 pm
I challenge the notion that middle and high school math teachers are better simply because they are “more qualified.” They are more qualified to do mathematical computations perhaps (and arguably, given anecdotal evidence to the contrary I’ve read here and elsewhere). But that doesn’t necessarily make them more qualified to teach math. In fact, I would argue that expertise can completely un-qualify someone to teach.
Assume you are an algebra teacher to whom the subject came very easily. The real challenge in teaching it is to recognize, empathize, and adjust to kids who either aren’t as adept as you are, or who have a different learning style from your own.
A good algebra teacher has figured this out, and his or her students learn. Some better than others, granted, because yes, there do exist differences in cognitive ability, motivation, and personal circumstances.
Even the C- students will have gotten something out of the course. Will they ever use algebra again? Maybe not. Will they ever use — and build on — the analytical thinking and problem-solving skills they used to get that C-? Absolutely. Even (or, I would suggest, especially) if they opt for a future that bypasses the too-often waste of time and money that passes for a college education these days.
But too many teachers — not just in math, but in science, foreign languages, English, art, music, athletics, and so on — haven’t figured out how to recognize, empathize, and adjust to others’ abilities and learning styles. Either they don’t know what they don’t know about teaching, or they know, but can’t be bothered to learn.
These teachers have grounded their teaching in false assumptions. If something is self-evident to them, they can’t imagine why it’s not self-evident to everyone else. When someone doesn’t “get” what they’re trying to teach, they either (a) repeat it the exact same way, often more loudly; (b) humiliate the student; or (c) ignore the student and move on, convincing themselves in the process that they own no responsibility for the problem.
And this is just with students who are native speakers of English. Forget the English Language Learners (ELLs) mainstreamed into these classes before they have achieved a level of English appropriate for academic study. Look there, if you would — and not, for crying out loud, to genetics — for an explanation of why certain student populations are at risk.
I’ve addressed the ELL issue in more detail in my blog post, “They Just Won’t Learn” [http://bit.ly/Pb8xsL].
Also look to students’ socio-economic background. As I mentioned in a footnote to the above-mentioned post, ELLs not brought up with middle-class or higher values are considerably more at risk than those who are, or who, through teaching and mentoring, have acquired “middle-classness.”
August 21st, 2012 at 5:05 pm
You have a highly idealized notion of education, and don’t give teachers enough credit. I refer you to this post: The myth of “they weren’t ever taught”…. I spend a HUGE amount of time thinking of different ways to explain math to students (over half of my students for the past two years were ELLs). I’m pretty successful, too. Nor am I unique. And there are thousands of ways in which we can make math challenging without pretending that everyone is capable of advanced math.
As for “learning styles”, research suggests that’s nonsense. Nonetheless, most teachers recognize that students have a preference for concrete over abstract, seeing vs. hearing, and so on, and do their best to apply to all preferences. They have to for evaluations, since they are required to.
But fundamentally, you’re just naive. It’s easy to pretend that it’s teachers. It’s also wrong.
“I challenge the notion that middle and high school math teachers are better simply because they are “more qualified.” ”
I don’t believe I ever said as much.
August 21st, 2012 at 6:29 pm
“I spend a HUGE amount of time thinking of different ways to explain math to students (over half of my students for the past two years were ELLs). I’m pretty successful, too.”
Congratulations. I’m happy for you.
“Nor am I unique.” Unique, no. But I would argue that you are in an unfortunate minority. I would also argue that no matter how “successful” teachers believe themselves to be, they are in denial if they think they have nothing else to learn about teaching ELLs.
“[F]undamentally, you’re just naive.” Excuse me? I would have expected you to be above such an ad hominem attack.
Besides, I’m not “pretending” it’s teachers, and I’m not wrong, although I didn’t mean to imply it was just teachers. I’m basing my opinions on experiences I’ve encountered through experiences with professional development workshops.
“I don’t believe I ever said as much.” I agree: you didn’t. But
there are those who do believe that, in my humble opinion.
August 25th, 2012 at 11:03 pm
A really good student will learn regardless of the quality of the teacher. (That is, a high IQ student.)
A poor student will not learn, regardless of the quality of the teacher. (That is, a low IQ student.)
Those in between benefit from having teachers who can use differing analogies and techniques to reach them.
August 21st, 2012 at 5:18 pm
I’m not about to get involved in an entire debate – I think you put it quite well and I’m not an education expert. However, the striking thing for me has always been the kind of mindset that more abstract math teaches kids. Algebra and calculus do wonders for developing the brain’s WAY of thinking – which is the reason chess has such an influence on math aptitude. I disliked math, but needed a high grade in it to get admission to medical school. So I worked hard at it until I could understand the concepts. Sure, I barely use it now, but I don’t regret being “forced” to do maths.
August 21st, 2012 at 5:25 pm
Kids with high cognitive ability should, ideally, be challenged with abstract math, whether they use it or not. The issue is whether or not it’s fair or realistic to force kids with lower cognitive ability when they have no desire to learn it.
August 21st, 2012 at 5:48 pm
Ah. Yes… true. I don’t think I have the right to speak for those kids, really. One would have to do some good research – although the research you cite indicates particularly that just because math is more challenging does not mean it improves one’s cognitive ability… right?
Here in South Africa, everybody has to do math (including Algebra), but kids who really struggle with pure math get to do Math Literacy, a kind of watered down version focusing solely on those concepts of use to one in real life.
August 21st, 2012 at 5:56 pm
Malcome X + Generation Y = algebra of today
August 21st, 2012 at 6:05 pm
Poor teacher quality is keeping so many of this nation’s fish from riding bicycles. It’s criminal! It’s abuse! //sarcasm
😉
And what I would note here, as well, is that IQ is one measure of intelligence. There are many ways to be intelligent and/or talented. Every individual has some gift, but not all have a gift for math (or overly abstract thought for that matter). This should not be taken as a mark against them.
August 21st, 2012 at 9:59 pm
[…] Education Realist reviews the numbers and responds: […]
August 22nd, 2012 at 3:29 am
It is easy to judge with numbers, but much harder in real life. You know, the sad thing is, teachers are forced to teach the same way, and this is where the true problem exist.
August 22nd, 2012 at 4:30 am
Fifty comments about teaching algebra? Sheesh.
August 22nd, 2012 at 3:49 pm
Not about teaching it, but whether kids should take it. This article got put on the front page of Word Press, and got huge coverage. Hence the huge number of comments.
August 22nd, 2012 at 5:34 am
“So that’s how to make the achievement gap disappear: compare low income whites to middle class or higher blacks and Hispanics and hey, presto. …
If we could just get whites and Asians to do a lot worse, no one would argue about the absurdity of sending everyone to college.”
[Sighs] You know, as another commenter stated, I, too, don’t understand the obsession with categorizing the probability of “success” or “failure” by race. There is no real point to it because an underachiever is the same regardless of ethnic group, as is an overachiever; ranking people by race only serves to demean the individuals of a particular population and uplift all members of another. Apparently, it has stuck because supremacy seems to have sentimental value in this country.
I believe education, IQ tests, etc. benefits those who are of the dominant culture and have a higher status, and in that order.* It would be interesting to study educational performance within the white race. If there is evidence that socio-economic status increases scores, there is a benefit to being wealthier, such as greater access to learning materials, better schools, tutoring, test prep, etc. But that the same benefit disappears between racial groups (e.g. comparing poorer whites with wealthier blacks) could be evidence of cultural bias in instruction and tests.**
No one is saying that we should blame whites (or Asians) for being at least proficient at the average level compared to blacks or Latinos. However, it would be an exercise in denial not to at least question whether there is a problem of culturally esoteric instruction/testing and social preference of those belonging to the dominant culture (and, tangentially, those most similar to the dominant culture.)
I think the problem is with the education system, not the students. I attended schools in one of the bottom five states in this country and can attest to bad teachers who can’t teach worth a damn and have an expectation of misbehavior with colored students, and administrations who measure themselves based only on the top 20%. The problem may be systemic but, yeah, teachers have to get some of the blame, too; otherwise, we aren’t operating in reality…
* It’s a pretty pointless to mention Asians being at the top as a way to invalidate the institutionalization of white supremacy: whites are always at the comfortable average–the standard to which everything is measured–and Asians, in general, as the Indian commenter here mentioned, just work harder at subjects than whites do. Rote learning can make anyone do well; it also bears mentioning that lowest income Asians do worse than lowest income whites. This validates the dominant-culture preference idea.
** I am aware than so-called culture fair tests have been devised and have been unsuccessful at remedying the “gap”. However, how fair are tests that are still written from the mindset of the dominant culture?!
August 22nd, 2012 at 12:42 pm
Repeal laws such as NCLB that mandate the closing of the achievement gap, get rid of affirmative action in college admissions, and stop mass immigration from low-IQ countries, and then HBD’ers will have less reason to discuss racial differences in intelligence.
August 22nd, 2012 at 3:08 pm
Bostonian:
The HBD crowd has zero influence, much to their own chagrin, and are not taken seriously by anyone living in the real world. Theirs is a movement (if one could call it that) doomed to stay in the shadows. As far as I am concerned, they are free to discuss whatever they’d like just as much as a Holocaust denier can rant about our alleged “ZOG-run” media. I don’t know what use it is but, hey, some people have to busy themselves while on the Internet. I wonder about people who write long-windedly of “differences” and the alleged complications of those “differences” and, yet, offer up no practical reason for pointing them out.
Again, as I stated in my previous comment, the point of ranking is to denigrate the individuals of a “lower-rung” group while uplifting an entire group that is higher up, typically the dominant culture.
Labeling black and Latino people as “too stupid” is the red herring used in order to avoid addressing the fact the gap is evidence of bias and that efforts to dismantle institutionalized white supremacy (racism) have not been entirely achieved (not a surprise, really, when you consider that it’s only been +/- 60 years since the beginning of major civil rights changes). The latter is confirmed when you read so-called “politically incorrect” comments by white teachers regarding minority students; it’s just like when you see someone mention that they are former/current police officers amid a racist rant: it gives validity to the claim of racism infecting America’s law enforcement…
Re: affirmative action, it’s strange that people hoot and holler about it when it allegedly benefits black and Latino applicants but are mum when it’s used to benefit whites over Asians at prestigious universities! AA only opens a door–the beneficiary still has to do the work to keep the spot. Bitching about it is a ruse to avoid addressing the reality of the de facto [white]race/[male]gender preferences still marring our society.
I saw you mention Rushton and Jensen’s paper and the ridiculous “Snow Makes You Smarter” theory in an earlier comment, and it got the obligatory eye-roll. Rational people will follow the bread crumbs from these researchers to the Pioneer Fund, see the org’s mission statement of “Upholding white superiority” by using scientific-sounding language and “facts”, note its history with eugenics, and give it’s head honcho Mr. Rushton and all of its grant recipients the scorn they deserve for confirming their biases, a priori conclusions, and generally wasting everyone’s time.
I will say this, though, at least Jensen is honest about being a racial eugenicist and, thus, earns my respect. Everyone who tacks on a “I should be avoided by certain people and my arguments are the fruition of my biases” sign is a good guy.
August 22nd, 2012 at 3:54 pm
I believe education, IQ tests, etc. benefits those who are of the dominant culture and have a higher status, and in that order.
Hey. Some people believe in Santa Claus. Some people believe that global warming can be averted by driving hybrids. I myself believe that a muscle car and a pickup truck would solve a lot of my problems. So believe away.
I’m not sure why you think regurgitating a bunch of tedious pabulum that’s been said a billion times before is worth your time. But responding to it certainly isn’t worth mine. Go find an echo chamber. Enjoy!
August 22nd, 2012 at 4:36 pm
You don’t have to respond to it but you should expect it in any discourse about test scores and the “gap” attendant, especially when people are finding this post because it was Freshly Pressed! It’s just the way it is; it’s relevant. You stated you weren’t a scientist; I happen to be one. Since there is no biological explanation for why the gap exists–no gene–it would be shameful to suggest a priori that the gap is biological, and then run with it. Real science does not validate evidence that is, at best, circumstantial, so it is strange to me that HBD-types, with their belief in science, ignore that truism.
Anyway, you’re a Republican and you blog-rolled Steve Sailer. I don’t expect my pabulum to be digestible to you. Just like yours about teachers being beyond reproach because you’re a teacher is hard for me to swallow as a victim of poor educational quality and bad teachers. But, yes, I guess we can all believe in erroneous things, right? Let’s all just believe whatever we want to believe and let the disparateness keep us from achieving any measure of progress! That’s the great American individualism that has failed us again and again.
Nevertheless, thank you for your men of straw with the Santa Claus, et al. analogies. Totally original. Anyhoo, good day.
August 22nd, 2012 at 4:52 pm
No, I expect discourse to acknowledge reality. I really don’t have much patience with your condescending posts precisely because they are so out of date. One doesn’t need to be an HBDer (I’m not entirely sure I am) or even a Republican (which I’m not, really, although if the Dems don’t ever come back from the leftist idiocy of the last 4 years, I’m kind of stuck) or think that there’s a “genetic cause” to the gap (as I mentioned above, I am unconvinced) to acknowledge that the data is has largely rejected culture, poverty, and institutionalized racism. Your comments were relevant back in the 80s, but outside your little bubble, people snigger.
Let’s all just believe whatever we want to believe and let the disparateness keep us from achieving any measure of progress!
That’s you in a nutshell, toots.
August 22nd, 2012 at 10:50 pm
The discussion at Sailer’s veered into the issue of whether low-IQ folks can still learn useful routines. I don’t think Bryan Caplan was reading that, but he chimes in anyway here.
August 23rd, 2012 at 9:36 am
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August 29th, 2012 at 11:42 am
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September 21st, 2012 at 12:06 pm
*prints this out then runs to her old highschool* SEE I TOLD YOU I WASN’T INSANE! AND YOU ALL LAUGHED AT ME! *ahem* coming back to earth now I’m so flipping happy to have found this since you’ve basically proven what I knew all along. I was one of the many kids that failed math in highschool since past basic arithmetic I saw no point in knowing any more so I shut down. All I want to do is work in animation and game design so I can’t possibly fathom how knowing how to calculate the mass of the sun from the length of a hotdog will be of any use to me.
October 14th, 2012 at 8:27 pm
[…] Algebra and the pointlessness of the whole damn thing: In California, at least, tens of thousands of high school kids are sitting in math classes that they don’t understand, feeling useless, understanding deep in their bones that education has nothing to offer them. Meanwhile, well-meaning people who have never spent an hour of their lives trying to explain advanced math concepts to the lower to middle section of the cognitive scale pontificate about teacher ability, statistics vs. algebra, college for everyone, and other useless fantasies that they are allowed to engage in because until our low performers represent the wide diversity of our country to perfection, no one’s going to ruin a career by pointing out that this a pipe dream. And of course, while they’re engaging in these fantasies, they’ll blame teachers, or poverty, or curriculum, or parents, or the kids, for the fact that their dreams aren’t reality. […]
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January 15th, 2013 at 2:53 pm
Love this discussion! I was the overachiever in HS with AP classes. Ended up with an MBA and minors in French and Japanese. Now a mom, and I don’t see the point of advanced algebra and beyond for every student. My sophomore son loves history – soaks it up. But advanced algebra and chem he sees as pointless, but it’s a requirement for college. I dread physics and trig next year. He did very well in geometry and algebra, but this next level is kicking his bottom. And have I ever used my advanced math? Never.
May 17th, 2016 at 12:22 pm
I see more and more in the work world where people (even verbally inclined) need to be able to at least open an Excel spreadsheet and play with it a bit. Just because of how cost and revenue models penetrate the work world. And I am not talking about high end jobs: medical admins, assistants, etc. Excel formulas and matrices and such are essentially elaborate sets of arithmetic. And that is sort of algebraic. So, some basic grasping of algebra is useful.
X-Y scatter plots and line charts are everywhere too. And I think having in the back of your head worked with linear equations is helpful in at least “math maturity” for looking at a stock chart or product sales chart.
Same for statistics too. I’m not even saying that you need to know algebra to work the SD equation. And definitely not expecting people to know Gaussian formulas or (gasp) measure theory. I’m just saying to even have a comfort factor with X Y data tables, it helps to have done some algebra. Not so much for theoretical reasons but for the mental training to give you confidence.
March 12th, 2013 at 8:29 pm
I don’t think that it’s the quantity of the education that’s important. I think there are four specific areas we need to be concerned about:
Communication, Research, Access and Maths. In other words, it’s not about particular subjects, it’s about teaching children how to learn and letting them leave school with their curiosity intact.
The future is coming. You can either push against it and fight a losing battle. The problem with fighting Death or Time is that even when you win, you still lose.
Or, alternatively, you can embrace it and teach the children for the world they’ll live in now and as adults, not the one you grew up in or into. We’re going to lose if we fight time. Why not co-operate instead.
Functional Communication, Functional Research and Functional Maths give the child access to anything in the world they want to learn. Surely, this way is better, since I highly doubt you’re (general you) physic and (general you, again) can tell me what a child needs to learn.
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