Gutierrez says evaluations of math skills can perpetuate discrimination against minorities, especially if they do worse than their white counterparts, Campus Reform reported.Here's one truth about math skills: if you don't start developing the best ones you can early, many fields of study will be closed to you in college if you follow the traditional path of starting college shortly after High School. These include well-remunerated fields such as engineering, and cutting edge fields like physics.
“If one is not viewed as mathematical, there will always be a sense of inferiority that can be summoned” because the average person won't necessarily question the role of mathematics in society, she writes.
According to the website, Gutierrez adds that there are so many people who “have experienced microaggressions from participating in math classrooms… [where people are] judged by whether they can reason abstractly.”
You could always go do something else for a while, and develop the skills you need during your time away. But if you want the privileges that come from being a successful engineer, say, you're going to have to do the work. Teachers telling you something else to make you feel better about yourself isn't helping you. Since wealth is inheritable, it isn't helping your children either. A teacher who helps you feel good about not overcoming shortcomings in mathematics may be putting generations of your descendants at a disadvantage.
35 comments:
People are judged by whether they can reason abstractly? Say it ain't so. Next you'll be claiming they're judged by their beauty, their athletic prowess, or by their ability to create great art or music.
If only we could get rid of abstract reasoning, some of these tragedies could be averted.
evaluations of math skills can perpetuate discrimination against minorities
How very Wilsonian of her. Next she'll be touting the protections....
This is the [] bigotry of low expectations. Since her low expectations are deliberate rather than borne of ignorance, she's demonstrating her own racism.
And this question from her: As researchers, are we more deserving of large grants because we focus on mathematics education and not social studies or English?
Umm, well, yes. STEM graduates are more immediately productive than social studies or English majors, especially when pupils abuse those majors to focus on semi-pro college sports or to sit in classes of feminist glaciers or the study of Old English as it applies to bonobos.
Regarding the lead image of the article: I gaze into the abyss of her eyes, but there's nothing gazing back. [/snark]
Eric Hines
Equality = the lowest common denominator.
The sole reason to lower standards is to enable people who can't make the grade to feel better about themselves. It's not their fault, you see. It is Racism Inc.
Victim-hood is the last refuge of the incompetent.
Eric knocks it out of the park on this one. Imagine a university study concludes that "minorities are worst at abstract reasoning". Does anyone have a shadow of a doubt that the study would be shouted down as "racist"? But yet, here we have someone boldly make the exact same claim, but in the interest of addressing "microaggressions" and we're all expected to nod sagely and somehow develop a system where people who aren't good at math are patted on the head and told, "there there, we won't evaluate your skills, because to do so might make you feel bad".
I swear sometimes I must be taking crazy pills.
Worse yet, college degrees clearly perpetuate similar discrimination in many ways, as does pretty much any form of education. Let's throw it all out.
If you want to increase the 'privilege' enjoyed by any segment of the population, increasing their capacity with math is a pretty solid way of accomplishing that.
Yeah, but since math is the white man's province, wouldn't minorities getting good at math be guilty of cultural appropriation?
Eric Hines
I'll forgive it.
Gutierrez says evaluations of math skills can perpetuate discrimination against minorities.
The Journal of Blacks in Higher Education: The Widening Racial Scoring Gap on the SAT College Admissions Test (2006)
If we raise the top-scoring threshold to students scoring 750 or above on both the math and verbal SAT — a level equal to the mean score of students entering the nation's most selective colleges such as Harvard, Princeton, and CalTech — we find that in the entire country 244 blacks scored 750 or above on the math SAT and 363 black students scored 750 or above on the verbal portion of the test. Nationwide, 33,841 students scored at least 750 on the math test and 30,479 scored at least 750 on the verbal SAT. Therefore, black students made up 0.7 percent of the test takers who scored 750 or above on the math test and 1.2 percent of all test takers who scored 750 or above on the verbal section.
It isn't "evaluation" of math skills that is the problem. It is achievement of math skills that is the problem.
Evaluation of any kind of skills can perpetuate discrimination against anyone who lacks those skills, if by discrimination we mean taking notice of who has them and who doesn't, in situations where the skills are important. I think we can assume math skills are important, or we'd quit teaching them and obsessing over whether people have them--though I suppose they seem mysterious and irrelevant to people who lack them, or who suspect that they're a fetish, or an outright pretext for treading on the face of outgroups.
Those are really surprising and discouraging numbers. I knew the tail effect was huge, but not that huge.
And this question from her: As researchers, are we more deserving of large grants because we focus on mathematics education and not social studies or English?
Umm, well, yes. STEM graduates are more immediately productive than social studies or English majors
NB: "Math education" is not at all the same thing as mathematics. It's commonly lumped in with mathematics, often to make certain statistics look "better"... but it's education, not math. Which means it's social science, not STEM.
That's true. Like all the education degrees, it is about credentialing for the guild system that runs public schools. It's about how to teach algebra to kids, with emphasis on the supposed psychology of the kids. It's not really about approaching the deep end of mathematics.
A different reality is being avoided here, by conservatives. There are many African-Americans, Hispanics, and Natives who go to very good schools and are well-taught in mathematics. They are still one full Standard Deviation behind Caucasians, and a little more than that behind Northeast Asians.
This is genetic, but it seems unamerican to even think that. We want to believe that anyone who tries really hard and has a good teacher will succeed. With some things, effort is the main component of success. Math is not one of those things. Once we admit that, we come to the real question of "Well, what is the worth of a human being founded on?" Abstract reasoning abilities are very good for individuals, and the societies they live in. They are useful. Societies reward their useful people handsomely.
As long as this is our standard, minorities will fare worse in America. If we persist in pretending that having higher standards, or having more dads around, or teaching kids about gumption will raise math scores, we will be wasting energy on crap solutions just as much as the liberals.
Genetic modification may hold out some hope, though the risks of that are frightening.
I might have rather said that it was only conservatives who ever entertain that idea. But we do so with trepidation, for it is one of those ideas your favorite Slate Star Codex essay talks about: a community that admits the possibility is likely to find itself overrun by people who are mad with it, intoxicated by it, racists of the worst sort.
Nevertheless it might be true, and it's hard to say one way or the other because the rest of the community is so steadfast against testing it. Thus every collection of evidence for the proposition is tainted by the association with people who desperately want to believe it; and the people who really should be testing it won't, and even if they did, they desperately want to believe the opposite just as much. Confirmation bias abounds.
I set such matters aside. There is nothing I can do with them. Maybe it's true; maybe it isn't true. The epistemology is so difficult that I wouldn't hang a weight to it one way or the other.
What I do know is that you won't hurt a man by teaching him math, and as much as he can handle, whoever he is. If it turns out that's not what he's best at, it won't have hurt him to learn what he could -- and it might open a road for him. If it doesn't, well, there are other roads.
I agree. Anyone who wants to give math or any other endeavor should have his shot. If he's not going to spring to the top in that area, he can try something else. Whatever else he tries and turns out to be good at may not be something his neighbors are going to reward with material riches, and so be it. No guarantees.
I don't think I ever subscribed to the notion that gumption would teach someone math who has no aptitude. As Heinlein used to say, if inborn IQ didn't matter, you could teach calculus to a horse. I'd just like to let anyone try who wants to, to try; no need to decide in advance whether he'll succeed. We may think we have a pretty good idea of his chances of success, but nothing counts in the end but whether he actually does it.
This article is just a cover for people who do not know how to teach. I had a conversation with the middle school principal, about my mathematically-oriented kid, who was doing poorly in geometry. He was a transfer from another system, and from a really good teacher. In that meeting, the principal also said "all of the children are having trouble with this class."
I told her, as politely as I could manage, that geometry is a well-known subject, and that if "all" of the children were having problems with it, perhaps they should look elsewhere to identify the problem.
My kid is lily-white, and this is in one of the top school systems in the country. The sad truth is, our school systems do a poor job of training teachers in math.
Valerie
There are standards that need to be changed but they aren't math standards. We have allowed a credentialed elite to define (and renumerate) a successful life as the acquisition of credentials leading to the enjoyment of a certain UMC lifestyle of primarily intellectual effort and enjoyment.
I'm pretty sure I've related this story before, but I'll do it again anyway. In 8th or ninth grade, I had a fine teacher in an accelerated math class. She started off the year with quadratic equations, but somehow none of us caught on. The teacher didn't doubt us or herself. She knew something had gone wrong, so she simply started over after a few frustrating weeks. The second time we got it and caught right back up. Her perfect confidence that we were capable of learning it and that she was capable of teaching it overcame any need to stick to a rigid schedule or curriculum or magic system.
The educational field seems increasingly dominated by people who do not themselves place much value on *knowledge*, and don't see any reason why anyone else should, either.
I wrote up some thoughts about this topic in my post Skipping Science Class:
http://chicagoboyz.net/archives/002938.html
and also a follow-up post here:
https://chicagoboyz.net/archives/5820.html
A different reality is being avoided here, by conservatives.
I don't think anyone is trying to avoid the fact that there are group differences. (Progressives tend to attribute such differences to "systemic racism" and things like "stereotype threat"; conservatives tend to attribute it to either cultural factors or [if edgy] genetic ones; but they all recognize that there are group differences.)
However, group differences aren't individual. They matter only to the extent we insist on treating people as exemplars of their race and sex.
Also, I do think that cultural factors can help raise math scores (across the board, not just for black and Hispanic kids). g sets an upper bound on math achievement, but doesn't determine it. A kid who doesn't know how to study something he doesn't immediately understand, or how to apply himself to something difficult, or who comes from a home where learning is denigrated, won't do as well as he would if these things weren't so, intelligence level notwithstanding. I don't think we're anywhere remotely near getting all students to the level their intelligence makes them capable of.
Certainly true. You can have parents who stare at you like a beached fish if you mention math and ask whether you've tried out for the football team yet, or you can have parents who obviously revel in math and can't wait to share all the jokes and pleasure with you as you learn it. I was lucky in my public-school math and science teachers, but I had a sprinkling of awful teachers in other subjects who did their best to extinguish any spark of interest I might have had by the soggy boredom of their approach--with the result that there are subjects I developed an interest in only decades later.
Or on another level, parents who don't necessarily revel in math or even know much math themselves, but who do value learning, praise you for doing well, teach you to pay attention in class and respect your teachers, insist you do homework, and provide space and time for you to study (and if that means they turn off their favorite TV show to give you peace and quiet in the kitchen, that's what they do).
Do you happen to remember the scene in Stand and Deliver, where the young girl is trying to find time to do her math homework? She's babysitting her younger siblings, they're running her ragged, and finally she gets them down to bed and sits down with her books... and the next minute, her mom comes home from work. Obviously exhausted from being on her feet all day, she sinks down in a chair across from her daughter, but the light the girl is using to study by is in her eyes and she asks her daughter to please turn it off. And the daughter sighs and closes her school books for the night.
You can't blame the hardworking mother... but that's a household where a child wanting to learn will face an uphill battle, because it's not a priority to the parents. And that is cultural.
T99 - there are also developmental issues in learning math. While there are prodigies like Terence Tao who can learn things long before even bright students, the Algebra I, Geometry, Algebra II/Trig, Calculus sequence beginning no earlier than Grade 8 has held up pretty well. In smaller schools, where you can only get a critical mass of A students rather than A+ to have a class, you begin the sequence at Grade 9. It doesn't seem to harm the few A+ students later if they want to go on, because math above a certain level relies enormously on self-teaching. It would seem that your class was on the edge, and a restart after new concepts had settled in was crucial.
Grim - I agree that everyone should have a shot. When I am king I will make all children go as far as they can be pushed in math, electronics, science and/or abstract reasoning, even if it hurts their feelings. I think it is important to introduce the deeper questions of human worth, however, as my experience tells me that people are altogether too willing to stay at the superficial level of valuing intelligence, which is an ability not a virtue, because it is useful.
A fair point. I would be a poor student of philosophy if I disdained the deeper questions of human worth.
I do think there are some things that can make math more comprehensible to people whose minds aren't necessarily of a type that would facilitate their becoming professional mathematicians. For example, a group at Marshall University is doing some interesting work on 'A Visual Interpretation of Mathematics,' using the mechanical differential analyzer they have constructed. These machines, which were used in industry and research prior to the coming of the electronic digital computer, allow differential equations to be understood in an intuitive manner. Here's a paper on the subject:
http://ecommons.udayton.edu/cgi/viewcontent.cgi?article=1024&context=mth_epumd
Playing around with a system like this, and seeing how calculus is applied to problems like a weight on a spring or the predator-prey equation, could help students grasp what 'mathematical modeling' is all about, without necessarily going through the formal derivations and analytic-solutions methods of a traditional calculus class.
I greatly appreciate insights and efforts like those. Thank you.
AVU:
T99 - there are also developmental issues in learning math. ..... In smaller schools, where you can only get a critical mass of A students rather than A+ to have a class, you begin the sequence at Grade 9. It doesn't seem to harm the few A+ students later if they want to go on, because math above a certain level relies enormously on self-teaching.
Regarding developmental issues, I am reminded of a less than outstanding math teacher in 9th grade. She was a Phi Beta Kappa math grad of a flagship state university, so her grasp of the subject wasn't an issue. My recollection of her was that she was a poor teacher, basically because she wasn't a good classroom manager. Perhaps she couldn't explain math well- I don't remember.
While I didn't think much of her teaching, I ignored her and taught myself from the textbook- which was an outstanding example of the so-called New Math. I recently had a conversation with a classmate who had little recollection of our teacher but had fond memories of the class- also due to the textbook.
Family friends had the same teacher in 7th grade math. The same teacher was for them a disaster they could not surmount. As their father was an engineer, it is a safe assumption that it probably was not lack of math aptitude that was the problem.
My take is that 7th graders are more dependent on teachers than 9th graders. I was able to surmount a poor teacher- they were not. Coincidentally, the poor math teacher came to my mother's memorial service.
I later concluded that, at least at the high school level, a bad teacher or a bad experience with a teacher will give a student a good test of his/her innate abilities. With a bad teacher, you are on your own, as working to please the teacher is no longer relevant.Or, if you have an innate ability and thus a liking for a subject, the bad teacher is not a barrier. If you let a bad teacher upset you, that may mean that you aren't all that interested in the subject anyway. Before I had the bad math teacher, I was good in math but was indifferent to it. After a year of the bad math teacher, I had developed a liking for math- I liked all the proofs in New Math.
By contrast, by 8th or 9th grade, I would have predicted a college major of history or political science. I had a bad experience in 10th and 12th grades with a history teacher which extinguished my wanting history or political science for a major or a career. The history teacher taught for 40 years, so he was doing something right- his teaching practices just rubbed me the wrong way.
My conclusion is that from my bad experiences with teachers in high school, I discovered where my greater aptitude lay- more than math than words.
Val, I think your story is a good example of the fact that teachers, especially at lower levels (perhaps mainly in upper elementary levels to middle School levels) aren't themselves very good at math, which is why they didn't become engineers, accountants, programmers or insurance company actuaries. My niece double majored at a good local private college in theater arts and mathematics. Her father (my brother), who has already been a math wiz, says she's better than he is. She is thinking about going to grad school, and if she does, wants to teach college level. Not many people are really going to be drawn to marching kids through the struggle of learning math in middle School- it's just plain hard, and without much of what probably drew you to math in the first place. It's a conundrum- how do you get better teachers, for math especially?
And yet my middle and high-school math teachers were uniformly excellent. They weren't charismatic or pumped up, but they had a quiet confidence that all this stuff was both learnable and fascinating. All of them taught exclusively to accelerated classes, where they could be sure of an appreciative audience, so I'm sure that helped.
I have clear and pleasurable memories of a classmate's father's guest lecture to one of my classes, explaining why a suspended simple cable makes a catenary curve while a typical suspension bridge makes a parabola, and showing us how to derive the formula for the catenary. A high point in my schooling.
But the excellent principal who kept that excellent staff of teachers together retired, to be succeeded by a more ordinary man and a progressively sillier curriculum taught by duller teachers. I had been very lucky. I've always believed I benefitted from the lack of career choices for talented and intelligent women, many of whom taught high school for a pittance instead of going into medicine, business, or law. In those days, too, a strong principal could reject teachers who didn't suit him, and could expel students who couldn't control their behavior. Violence was unheard of. Our sports facilities--the whole physical plant--were minimal. Nothing but good teachers, safe classrooms, and frank set of academic tracks.
Tex..."I've always believed I benefitted from the lack of career choices for talented and intelligent women, many of whom taught high school for a pittance instead of going into medicine, business, or law."
True, I think. Also, one reason why there were more women (%-wise) in computer programming in the early days of the field than they are now is that they were discouraged from fields like law and medicine. So an intelligent woman who might have gone into programming in 1965 might now go into one of those other fields.
" In those days, too, a strong principal could reject teachers who didn't suit him, and could expel students who couldn't control their behavior. Violence was unheard of."
Indeed. There is much talk about the need to increase salaries to attract more/better teachers, but the reality is that most self-respecting professionals will avoid working in an environment where they are consistently treated with disrespect.
Yes, that's just what I meant: we got great teachers cheap because they were basically a captive workforce. Only a few years later, nearly all of these women--and as I recall, they were nearly all women--would have opted for a different career, especially if they didn't have a charismatic and effective principal to work for. It was much the same for secretaries and nurses back then, as well, not to mention stay-at-home moms. Even after several decades, I'm not sure we've yet adapted to the new reality of what it takes to attract willing workers to fields that used to be staffed by over-qualified people with few options. Gone are the days when you could just conquer a town and bring home some Greek slaves to run your accounts and tutor the young prince.
The late Neptunus Lex wrote of his own early struggles with math, and how it finally came together for him:
"For my own part, I was never a scholar in maths. Somewhere around fourth or fifth grade, we were introduced to negative integers. I rebelled. If you had four pencils, and took away five, you’d find that after you’d taken away four, there were no more pencils to take, I reasoned – you’d have to stop. The theoretical, potential fifth pencil my teacher tried to sell me on seemed so much more adult blather, comforting to say aloud perhaps, like the rosary, but ultimately senseless. I was querulous, she was harassed, I was told to get on board. I stayed in the station, awaiting better logic.
My agnosticism persisted all through algebra, a pointless exercise in mental master debation. What on earth were these letters doing in what was ostensibly a mathematical question, and what was a variable, anyway? And what exactly would one do with the area under the curve, in the real world? No one could be bothered to tell me.
It was not until my junior year at the Naval Academy, when we started to do differential equations, that the light came on. Eureka! Drop a wrench from orbit, and over time it would accelerate at a determinable pace, up until the moment when it entered the atmosphere, where friction would impede the rate of acceleration at an increasingly greater rate (based on air density, interpolated over a changing altitude) and that wrench struck someone’s head at a certain velocity, that any of this applied in the real word. By then it was too late, I was too far gone, and an opportunity was lost."
https://thelexicans.wordpress.com/2016/10/07/on-maths/
"Gone are the days when you could just conquer a town and bring home some Greek slaves to run your accounts and tutor the young prince."
Many corporate acquisitions are motivated in large part by this....'hey, we don't have anyone who knows anything about (insert name of discipline or industry here), let's go acquire Company X. They've got a lot of 'em there."
Usually the acquisition turns out to be a LOT more expensive than developing the skills internally would have been, and the new slaves may well escape...or, alternatively, be made ineffective by non-meshing corporate cultures.
According to the website, Gutierrez adds that there are so many people who “have experienced microaggressions from participating in math classrooms… [where people are] judged by whether they can reason abstractly.”
I am reminded of one of my engineering profs, who once told the class when we were befuddled about something, "I hope you're not stupid."
None of us considered that a microaggression- perhaps because the word hadn't been invented yet. We thought it was funny.
The prof was brilliant but had lost touch with what it took to explain to undergrads. Fortunately, he was the only one in the department who had. One week he went to a conference, so a colleague took over his class for the week. The weekly quiz averaged 10-15 points higher that week.
Yes, there are different skills needed to teach brilliant, motivated students vs. skeptical, demoralized ones. There are hugely different skills needed to advance the field when you're one of a kind, vs. being able to communicate your brilliant advances effectively to anyone, even your colleagues.
One reason I like tracked classes is that it lets teachers do what they do best, without sacrificing the 75% of the classroom that doesn't fit.
It's a rotten thing to put people down just because they're having a hard time keeping up in a classroom. But if "microaggressions" include things like honestly acknowledging that the student hasn't mastered the topic, I lose interest. If you fail a test, maybe it makes sense to blame your parents, your flu that morning, the bad teacher, or whatever, but you still failed the test. That means you haven't learned the material. If it's not important to know whether you've learned the material, why are we paying property taxes to fund the schools? It seems an expensive way to build self-esteem.
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