16
votes
California will discourage students who are gifted at math
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- Authors
- Robby Soave, Glenn Garvin, Eric Boehm, Matt Welch, Elizabeth Nolan Brown, Jesse Walker, Billy Binion, C.J. Ciaramella, Damon Root
- Published
- May 4 2021
- Word count
- 873 words
I tested out of 3 years of math on enrollment into middle school.
I wasn't an easy student in school. I cannot imagine how disruptive I would have been, bored, unchallenged and without work to fill the time in class if I hadn't been allowed to skip ahead. Or if I'd been forced to slow down progression in the courses I was enrolled in during middle and high school rather than moving on.
There was always plenty of time to help others with their homework, to attempt at teaching others things they didn't get and so on.
This sort of system would have been a huge punishment. It would have been extremely disruptive to my learning. I wouldn't have stood a chance at developing good working habits when I'd always have finished homework in class, never would have had to pay attention to the lectures, would have learned that I could just horse around without consequence and so on. Socially, you aren't on the same footing as your peers if you're meant to teach/assist/aid them anyway.
There would have been an economic punishment too. I started college with 7 quarters of maths and statistics completed. I graduated a semester earlier than otherwise just because of math courses. That's a lot of money and half a year of my life saved.
It would have been extra unreasonable to be held back in math because of the knock-on effects. I wouldn't have had the math required to progress at the same rate in physics and chemistry, which in turn let me take 3 years of a tertiary language in high school with my same-age peers as a regular student in a regular class.
Youth are allowed to excel in sports, music, theater, writing, programming, in getting (menial) work experience and a host of other fields. But society is scared of letting young people excel academically.
Progressing faster than your peers academically, or systems that allow that is politically touchy. Saving years in school lets you get ahead in the workplace in ways that's extremely hard to catch up to, just like it's impossible to catch up to someone who's essentially become a musician extracurricularly.
To many, that becomes an issue of creating an "elite" who are at an advantage for rising to various positions of power in society. Isn't that slight injection of meritocracy just a little better than family and connections that dominate more today?
Yeah, this article is a mess. There are a lot of assumptions that I have no idea why I'm being asked to accept (math apparently is not something all kids are equally able to learn? Is the next step finding the math gene?).
I suspect most people who struggle with math simply didn't get the individual attention at the time they were learning the fundamentals to figure out how best they learn the topics. So, when their teachers started moving past what they understood well, they were building on shaky foundations. It's like trying to learn a language and not understanding the concept of grammar... of course it will seem hopelessly arbitrary.
Not to the extent of influencing the likelihood of a grasp of high-school math. The majority of math disparity (and more broadly, what we consider intelligence) is down to exposure and environment in formative years. Why do we not speak of people having difficulty grasping English as their first language, and some people genetically predisposed to not speaking it?
Often people place out of freshman calculus by taking AP classes, but if they don’t, I’m not sure that repeating a subject is necessarily a waste of time, if it’s important to learn. In most subjects there is a fair bit of repetition from year to year. It’s not like you take one English class and then you’re done. There are high school chemistry and college chemistry classes.
But I’m also skeptical of confident claims that certain subjects are important to learn, because it seems like it depends a lot on where you end up, and there’s no knowing in advance.
The only way they have any chance of doing that is by giving each student an incredible math teacher. The best way to do that is by significantly increasing how much teachers are paid. The United States is rare in how inequitable its teacher salaries are compared to other employment options. It’s rare that someone who has fallen in love with math themselves ends up teaching it.
In my experience the teachers that loved math the most are the ones teaching the advanced stuff. My AP statistics and AP calculus teachers both got visibly excited about the topics they taught, sometimes nearly jumping up and down when coming to a conclusion. I don’t know if even that level of displayed interest captured everyone’s attention, but it caught mine.
Anything that ignores classroom sizes and teacher compensation is ignoring the problem. In hindsight, so many of my math teachers didn’t really care about the subject at all. If you’re teaching primarily out of a book then you don’t grok the material deeply enough to teach it.
A mathematically gifted teacher could hold the attention of a gifted student as well as those falling behind, even when the subject is more mundane than calculus. To this day I have small realizations about geometry that blow my mind - like how a circle is derived from the set of all right triangles of a given hypotenuse. And yet no one ever mentioned that one in school.
This isn't true in my experience. Nearly every math teacher I know and have ever worked with genuinely loves math.
Teacher burnout is a very real thing, and advanced courses like the ones you identified are the most sought-after classes among teachers because they're the most enjoyable ones to teach. Classes with high skill-gates screen out problems: students who are unmotivated, have behavioral issues, have lagging skills, etc. Furthermore, they fundamentally select for people who are interested in the topic. For example, not everyone who takes AP Calculus necessarily loves math (some are taking it for the GPA, or to get ahead on college credits), but the class will attract those that do love math -- far more than a standard math class.
These classes are as close to an ideal educational environment as you can get, and it is much easier to bring joy on a subject to a willing and able audience rather than an apathetic or ill-prepared one. It very well could be that teachers who spend their days teaching primarily classes like that have an energy and enthusiasm to bring to the subject because they teach classes like that. The phenomenon that you identified might have been an effect rather than a cause.
Let me provide some non-American perspective: the system described in the article is a watered down version of what I went through in Norway. And it fucking sucks. Norway's education system is egalitarian to a fault. There is no concept of gifted classes. Only a couple of subjects in high school are differentiated by ability. Our education law specifies that each child should get an education tailored to their abilities and needs, but in practice this only applies to the academically challenged.
I remember early on in grade school, I finished my math textbook in record time, because it was too easy. In order to keep me occupied, my teacher gave me another textbook. It was published by another company but covered the exact same material. Teachers had no resources or training in how to deal with even a slightly quicker student. I learned that the reward for excellence was drudgery.
I didn't experience the joy of learning in a school setting until a couple of high school classes, in which an old, extremely overqualified math and physics teacher completely bewildered half his class with overly advanced material. He was a terrible teacher - he joked that the only pedagogy he ever learned was to use different color markers for different terms on the blackboard - and consequently let down at least half the kids in his class. But it was the first time I met a teacher who actually felt like he actually took my abilities seriously.
A system in which gifted kids are only able to thrive when the teacher is both overqualified and fundamentally out of tune with the abilities of most of his students, is not a good system.
Holy spin of a headline.
Counter points to the headline, straight from the article; quotation formatting indicated quotes from the article, quotation marks indicate quotes from the report it draws from:
Can't say I disagree with the report. Calculus is neat and should be taught in many different college courses and, where possible, to high schoolers. But to most it is never useful in life. Therefore, to impact the education of the not-gifted in pursuit of goals useless to them, seems unfair. I also believe that keeping classes heterogeneous will help gifted students really solidify their knowledge. The act of teaching your fellow students what you've acquired is mutually beneficial.
I'm not a huge fan of the report's language around social issues as related to math, but that might be because I read them out of context in an adverse framing by who I can only assume is an elitist asshole.
The framing of math following is good though: "we need to broaden perceptions of mathematics beyond methods and answers so that students come to view mathematics as a connected, multi-dimensional subject that is about sense making and reasoning, to which they can contribute and belong." - I can only agree. Math is in my experience in German schools often regarded as this abstract toolbox with little relation to reality. The task of how to rephrase a real-world problem such that it is accessible with that toolbox is largely ignored and is an important skill that makes math exciting. I had to teach it myself, and I was only able to do that because of out-of-school education (by my parents) and a good amount of curiosity.
I am generally in favor of better tailoring school subjects and emphases to students, but I don't think we're there yet, and acknowledging that some students fall behind on one of the most fundamental subjects this early is admitting defeat.
Not a fan of the piece overall. Too much of an elitist angle. The author seems to be solely concerned with gifted students, to the extent that every mention of concern for other students seems tacked on as defense against my kind of counterpoint.
Paging @kfwyre because this is about education and I want his opinion.
Got more thoughts on the matter that are more detached from the concrete article, but I gotta get going.
Thanks for the ping, vektor.
As identified by @skybrian, this article is pretty useless. It's basically just fearmongering on the term "equity" and a whole lot of hypothetical outrage posturing. I wasn't familiar with Reason, but this article pinged enough negative talking points on education that it made me suspicious. I checked the front page, and, sure enough, school hating is exactly what we're dealing with here.
I don't think this particular article is especially valuable to respond to, but I do think some of the bigger ideas it brings up are valuable to consider. I also think the comments it has generated here are very valuable, as many people have identified some significant, big picture tensions that exist within education. I wish I had time to do justice to all of them, but I could honestly write tens of thousands of words on each and probably still not get to what I want to say. We are in territory where there are NO simple answers.
Unfortunately I'm only in a place right now where I can provide simple answers, which is actually incredibly difficult for me. Here's a quick rundown:
On gifted students:
They deserve better. We don't do enough to meet their needs. I think this oversight isn't out of malice but because there are so many other students who have significantly higher needs that aren't being met that gifted students aren't a priority. By the metrics of education they tend to be a success (i.e. they test well). We don't tend to consider metrics that involve fulfilling potential or personal satisfaction, however, which would help identify students who meet minimums but have unfulfilled maximums.
On equity:
If you are angry about gifted students not having their needs met, I encourage you to get really angry on behalf of gifted students in poverty not having their needs met. Gifted students in underfunded schools experience what others have complained about in this thread ten times over.
On math instruction:
Math standards at present go too fast and do not allow most students to work to mastery. California's own standardized testing data shows that by 3rd grade (the first year of testing), 50% of students are not meeting proficiency. Acknowledging that half of all nine-year-olds in the state are behind is either a indictment of our education system or an indicator that the expectations put on those children are not appropriate for their development.
On standardized test scores:
Standardized testing exists to be an indictment of education. That is its purpose. The inappropriate expectations put on students are by design, so that we can cast the institution as failing and justify the need for further testing and interventions. Everyone thinks I sound like a conspiracy theorist when I say this. I've stopped caring about that. Instead of going on at length to try to convince people I'm not talking out of my ass, I've identified what I consider the most trenchant illustration of the transparent bullshit of testing in the US. The testing industry is machine-grading students' essays in 21 different states, meaning that the scores that assess students' proficiencies in writing in nearly half the states in the country are assigned by algorithm. If that doesn't point to the idea that this data lacks even the pretense of fidelity then I don't know what will.
On standards:
As I was saying earlier: too much, too fast, too railroaded. Students do not get to develop math skills to mastery. Thus they have shaky foundational skills that cannot be adequately built upon. If we do accept the standardized test scores at face value we can see that, according to that data, half of students halfway through elementary school are already ill-equipped to move on to the next grade. This snowballs as they continue on. Students are also all funneled towards higher-level abstract mathematics as a minimum standard rather than one potential pathway. I do not believe that Algebra II needs to be universally taken.
On math teacher quality:
Tildes has a lot of people who are undoubtedly very good at math, and I imagine many people here likely imagine some hypothetical world in which they, themselves, are math teachers. Sometimes this fantasy might even come with a bit of an edge to it, where you imagine yourself as a "good" teacher -- better than those shitty ones you might have had or that you've heard about.
I don't want to take that fantasy away from anyone, but I do want to add a bit to it. Let's say for the sake of the assignment that you envision yourself as a high school teacher. I want you to include the following data point in your fantasy: over half of your students have been behind grade-level in your subject for at least the past five years. Do you teach to your grade-level standards for the portion of the class that is ready and champing at the bit for higher-level material, or do you make your lessons accessible to the students who are several full grade levels behind at this point?
Furthermore, when, after your first month, you walk into a data meeting where your administrators point out that 70% of your students are not meeting your grade-level standards and put this squarely on your shoulders, should you consider yourself a failure?
Stand and Deliver still has people believing that charisma, persistence, and a love of the subject are enough for students, but the real Jaime Escalante shows us that framework is nothing but a fiction:
On teacher quality again:
Escalante provided institutional solutions, not individual ones, and if there's one thing that I want people to genuinely and truly understand about education, it's that teachers do not exist in isolation.
The good teachers you had were good not just because of their skillset, content knowledge, or temperament -- they were also good because of other factors that benefitted them, like the composition of their classes, their workload, and their administrators. Correspondingly, many of the shitty teachers out there aren't necessarily shitty because of who they are individually (though that's definitely true of some) but because of factors beyond themselves.
You might be amazing at math, be able to connect with students, be able to explain concepts really well, and be incredibly dedicated, and you might still be a shitty teacher because of factors outside of your control. What happens when you take a position where assignments and pacing are predetermined and you have to teach the same thing, in the same way, at the same time as the other teachers of your subject in your building? What happens when your students lack prerequisite skills for your class? What happens when you're told to teach four different subjects and you only have 45 minutes to prepare for all of them in a given day? What happens when your administrators don't handle behavioral or discipline issues, leaving misbehaving students to continually disrupt your class? What happens when your school doesn't even have copier paper for you to print stuff on?
Let’s pause for a minute and imagine the absurdity of saying: “Let’s rate limit the excelling athletes to speed X — instead of putting effort into running faster, let them teach their peers.”
Replacing a physical activity by a mental activity doesn’t make it any more sensible. At that young age, most people who “get” math can’t easily explain “how” they get it. It’s very much instinctive, like physical coordination.
It’s definitely healthy to discuss homework exercises with peers and compare ideas, but the typical excelling student at that age doesn’t have enough self-awareness to understand their own learning process enough to teach lagging students. Forcing stilted interaction (among two parties lacking emotional maturity) is likely to engender frustration on both sides! The lagging student is more likely to consider themselves “stupid” and the excelling student will start considering academics/education “stupid”. Both will start acting out, but for different reasons.
The idea that every student has to progress at a uniform rate is an artifact of an industrial approach to education (which was never a great idea in the first place). The best way to build humility and empathy in excelling students is to allow them to progress to challenges they struggle with (in at least some areas, while sharing common classes/platforms in other areas). That will allow them to understand their fellows far better than forced interactions ever can.
much of what is learned in school isn't directly applicable to real-life situations. analyzing books or historical events is indirectly helpful by teaching analysis, the same way that higher math is indirectly helpful by teaching problem-solving, perseverance and abstract thought.
calculus in particular is very important for a lot of engineering fields (especially sequences and series).
it is unfair to hold back the gifted just the same as it is to hold back the less-able. and again, the charge of "useless" could be thrown at almost everything learned past middle school.
dismissing something as useless in order to hold the abled back seems very wrong to me.
you know what happens when you keep a "gifted" kid back? they never get challenged. they never learn how to work for something, how to persevere. everything is academically handed to them on a silver platter as they just chow down and understand almost instantly. they get lazy. unmotivated. sorta like zoo animals in captivity. for many it is very bad and when they are actually challenged a lot of those people collapse in college.
so it's not just limiting their potential, it's potentially harming it too.
I was a "gifted" kid. I was put in gifted classes in elementary school with a wonderful teacher who tried her best to challenge us and keep us engaged. In middle school, 1/3 of the grade was considered "gifted" and I was not challenged. I was bored. I began to resent math, sitting there for an hour as people struggled to understand things I thought were obvious. It wasn't until I was lucky enough to have my parents pay for a private high school which had the flexibility to let me progress ahead by skipping math gradesand taking a class over the summer (spending maybe 1/5th the time on it i would've been forced to in an in-person-class) that math was actually engaging and I was challenged
never challenged. for the misguided sake of "equality"
in short: i believe that people are born with differing ability. while efforts should be taken to elevate others with less ability, it shouldn't be done at the expense of those truly gifted.
also, I am a bit surprised that the short story Harrison Bergeron hasn't been mentioned as it directly addresses this topic.
this article is a bit sensationalized (it seems like in this case the physical proposal is a bit of a non-issue) and reason is kind of a shitty right-wing source but in this case i think the general idea of the article is right as this sort of thinking is very, very prevalent and i think it's for the worse
Unfortunately I can’t think of any math class I had taken here in the US where we were encouraged to help our peers to understand concepts. The only time I taught another student math was when one of my close personal friends was having problems.
That being said, there can be wild differences in how school is taught in the US. Things are better now that most states have adopted Common Core standards, but there are a number of them which have rejected those standards.
Disclaimer: I've had a few too many to drink tonight and math education is a sore point for me. I'm not a math/science major, but I happen to think math is an extremely important subject for many reasons, ranging from self-confidence to problem-solving. I took everything up to a first Calculus class, however, and feel I grew through my math education, and understand where others I am close to have had problems in theirs.
The issue is the backhand of the point: "Kids should choose the level of math they're exposed to." The issue I have is by the time you learn calculus, if you're not an American honors student, you've done 10-12 years of algebra and mostly arithmetic, and maybe one of geometry and/or trigonometry, even if it wasn't entirely by name (in 1st grade I was doing problems like "_+4=5, find the blank" which is basic algebra). I only have the limited academic mental confidence I have because of the relatively low risk of math education providing a relatively safe environment in which I can be wrong and still learn. However, when I was a kid, I didn't want to do anything at all strenuous, and only grew because the adults in my life pushed me out of my comfort zone, both in education, and in my home life.
Advanced mathematics (I'm drawing the line here at calculus and above) provides a unique sort of stress: High psychological stress, but you won't die if you fail. It provides an opportunity to either grow in a specific direction, or change your college major if you get a D (guess what I did?) and ultimately realize that you're better at something else, even if it's just a different system of logic.
Two major reasons I'm at all confident in my mental faculties are a slew of math classes I took (from middle-school pre-algebra to failing my first calculus in college, and passing a survey course after a change of major, and a bunch of statistics/analytics), and philosophy courses which both taught me the ultimate stakes of being wrong (surprisingly low), and the understanding of my strengths (specifically, I think, in analysis). However, I think we need to teach more students more advanced mathematics, far earlier. Considering I did algebra from 1st grade, but suddenly had to re-learn mathematics doing calculus in college, I think this transition should be done at a point of peak neuroplasticity, the younger the better. We spend so much time thinking about how kids aren't capable of math that we don't actually give them a chance to learn the logic of it. Logic, in this case, matters more than being able to label a derivative as such. If you can explain how you get acceleration out of a position function, that's already basic calculus. This also contributes to math anxiety, which by my understanding, is an application of the idea of self-fulfilling prophecy: You think you can't, and ultimately match the expectation.
I think I agree with you about teaching more advanced math at younger ages. Back when I went to school, I think I spent at least four years just learning algebra.
"If we eliminate advanced math from public education that will make everyone equal" works fine if you entirely ignore human nature and a few laws of physics. Now you have created a situation where there are two kids who are very good at math: one rich and one poor. There rich kid hires an expensive private tutor. Congratulations: you made the problem 1000x worse now.
I guess the next step is to make it illegal to learn except in government-mandated ways? Go read "Harrison Bergeron" by Kurt Vonnegut. I used to think that short story was satirical... Now I'm not so sure.
This is probably a good thing. It would be better if it included peer-support style teaching and learning - the gifted children get to help those who struggle at math. That helps both groups. And there probably needs to be something to identify the genuinely advanced learners. The children who may go on to olympiads do need to have advanced programmes available.
"inherited" doesn't mean "innate". Wealth is inherited. Where are the money genes? Heritability for intelligence could well mean some families have the resources to increase intelligence.
What's your thinking on the peer learning being helpful to the gifted kids?
I have a strong bias against this idea, and I'll say that up front, but it seems like they'd be deeply frustrated at covering and re-covering something they understood 2-3 years prior, ill-equipped to support others who struggle to understand something that seems totally intuitive to them, and resentful that they're "doing the teacher's job" rather than being challenged in the subject they're ostensibly learning.
I know I wouldn’t have been a good educator as a child. I was kind of an asshole when I sensed I had an intellectual advantage over my peers.
Even in the frustrating scenario you outlined, there is a big aspect of learning to communicate abstract thought. It helps solidify and repeat topics you already understand, but it also helps a hell of a lot to communicate your intuition. Your intuition is damn near worthless unless you can make other people understand your point. This is particularly important for the people who understand the topic but fail at peer teaching.
I see where you're coming from, and I absolutely agree about the value of communication, but I think you're taking a quite optimistic view about the gap in ability levels you'll see in the average classroom. You've got a kid who could comfortably be doing calculus trying to explain basic algebra to a kid who, try as they might, just doesn't get it. And that's an optimistic scenario where the more mathematically capable student is patient and engaged, and the less capable student is trying their hardest. There's a good chance that neither has the temperament or emotional maturity to handle the interaction like that at all.
I'd also be concerned that, well, it's a mathematics class, not a communication class. I know education is interwoven, especially at younger ages, but there are limits. For someone who developed a deep working of basic algebra literally years before, there's little more to be done without moving up to the next rung of the mathematical ladder; they can teach others all day, but there's effectively no chance of them moving on to more advanced concepts without being taught. You're essentially taking away their mathematical education and giving them teacher training in its place.
As for intuitive understanding vs ability to explain, I strongly disagree. It's good and valuable to explain, no question. It certainly deepens one's understanding. But it's a separate skill; there's a huge amount of value in being able to successfully understand and execute a difficult task, even if you can't remotely explain to others how you did it.
There are some parts of your longer post below I do agree with. The author's tone is pretty one-sided, and the idea of teaching mathematical reasoning in a less abstract and more logic-based way is very appealing. The idea that advanced maths isn't that relevant to most people is a fair one, and the current style of teaching may well be pushing them away. But the gifted students do need someone to speak out for them, just as much as the students who struggle. Both extremes tend to be left to fend for themselves, as poorly aligned incentives force teachers to focus on the students at the margins of the testing boundaries.
Overly complex teaching may well be off-putting to those who struggle, but boredom will be equally off-putting for those who don't. Putting both groups in the same room seems like a recipe to exacerbate anxiety and resentment on both sides.
You get the exact same thing in any math class. I was in the advanced math classes and there was still lots of helping other students out. At any level, there will always be someone who works things out first. I'm not sure how these changes could do anything but hold up those who put in the most effort to learn.
This could also be really damaging to the public school system as parents send their children to private schools to get the math education the public system deprives them of. While those without the money for private school are left worse off in the end.
I think there's plenty of research on this. My take, the last time I looked into it, was that most of intelligence is nurture rather than nature, which of course can happen for a good part at home, thus inherited but not genetically. But there are some genetic factors iirc. This is of course not in contrast to your point: This is in fact describing that we are losing potentially "gifted students" (ewww) by not nurturing them more. Which we could be doing in the classroom.
I am in favor of placing students in courses that challenge and stretch them as much as possible. For some schools the ability to do so is limited, but it should be a goal.
As someone who struggled in math and took a slower math track just to graduate, I can understand why gifted students in mathematics would both need and want to be in an advanced course.
I'm wondering if there is any real news here. Isn't it up to local school districts what they do?
It’s also just a drafted proposal
From reason dot com, no.