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From the article: Over the next year, a biosciences working group revised the program’s funding guidelines, stipulating in the final draft that it would not su

• brailsafe 5y ago
  Likewise, it's my my less experienced impression that some people just can't get (or at least it's overwhelmingly more difficult) basic programming concepts with even a visual building block system
  • ogma 5y ago
    And why would we ever draw conclusions about genetics, even if what the two of you are saying is true?
• linksnapzz 5y ago
  Some years ago, California tried to make it so that you had to pass Algebra II to graduate high school. I think the state backed down from that, because it meant only 25% of students could pass. Or maybe they just bowdlerized the definition of algebra II. It’s too bad, because I don’t think anyone should be able to leave high school without understanding compound interest-sorta vital for participating in a modern economy. Also, it’s not like we can stop loaning money to the innumerate, even if that might be the ethical thing to do.
  • onlyrealcuzzo 5y ago
    Do you really need to know Algebra II to understand exponential growth? Couldn't you just get by with multiplication and seeing a pattern and learning the FV function in excel?
    • thaumasiotes 5y ago
      > Do you really need to know Algebra II to understand exponential growth? Couldn't you just get by with multiplication and seeing a pattern If you could do that, you could probably pass Algebra II.
    • michael1999 5y ago
      The last 18 months of embarrassing COVID interventions show just how un-intuitive exponential growth is.
  • basementcat 5y ago
    I wonder how much of the difficulty is due to large class size. If the student to teacher ratio were smaller, would teachers be better able to tailor instruction to struggling students?
    • robbedpeter 5y ago
      Most teachers would struggle with algebra II.
      • jessaustin 5y ago
        My high school had one teacher capable of teaching calculus. His seniority allowed him to fob it off on someone who could not. She left the profession entirely a few years after I graduated. Of course, one may learn calculus from a book, which was what many of us did in that class.
      • dorchadas 5y ago
        This is a big problem imo. In my experience teaching high school, a lot of elementary school teachers struggle with basic math... And that's where the problems arise that we have to try to fix later on.
• shashwatak 5y ago
  perhaps some people cannot learn algebra / calculus the way it is traditionally taught in the classroom. perhaps the students who are failing just need a different environment, more time, more patience, different resources?
  • Falandafa2021 5y ago
    Or more likely that people are different and not everything is environment.
    • seba_dos1 5y ago
      Or even more likely the environment fails to accommodate for people being different.
      • sjwalter 5y ago
        Yes, different environments exclude and include some people, those who may be on the border of capability seem likeliest to be impacted here. That still doesn't mean that ALL people can learn calculus, given enough attempts to find the right environment for each of them. Shows, also, the silliness of this argument. Some people can pick up calc at age 10 no sweat whatsoever. Others struggle mightily with the basics in their 30s. Should we as a society invest 1000x the resources in the strugglers to ensure they can achieve the same understanding?
        • mrob 5y ago
          >Should we as a society invest 1000x the resources in the strugglers to ensure they can achieve the same understanding? There's no need for everybody to reach the same level of understanding, but I think the pandemic has shown the importance of teaching as many as possible the basic concepts of calculus. "Flatten the curve" doesn't mean much when you've never heard of integration. The same applies to climate change. People will have more faith in mathematical models if they think it's something they could have done themselves if they really wanted to (overly optimistic judgement or not) instead of some bullshit the so-called experts made up to bamboozle them.
• ctrlp 5y ago
  If you want everyone to pass, lower the standards. The end result will be that certificates from schools without high standards will be worth less in the eyes of employers (while still costing the same to the student). As they progress through such a system, some students will be placed in advance of their abilities and fail out at a higher rate than they might otherwise when they reach an institution with non-negotiable standards, like the hard sciences, demoralizing those who might otherwise have found their place of achievement, self-respect, and independence. Or, even those institutions will cave to such pressures and simply "mark 'em up, ship 'em on", as you have described. Caveat emptor.
  • beej71 5y ago
    Why not improve at teaching the material instead of lowering the standards?
    • ctrlp 5y ago
      Why, indeed. Maybe our standards for teachers are too lenient. In any case, it is possible that there is no quality of teaching that will change a student's natural aptitude. It's a disservice to huge swaths of the population to funnel them, ill-prepared, into colleges. Maybe a network of high-quality trade schools would be a better fit for some.
    • jayd16 5y ago
      The obvious answer is you lower the standards that year because somewhere the system broke down. (It being much more likely that there is an issue with the system than some kind of statistical anomaly with the students) Then you evaluate and attempt to improve techniques as is done every year.
    • concordDance 5y ago
      How? Hundreds of billions of dollars and a million man years have been spent on that problem to get to the current state.
    • rocqua 5y ago
      Two factors. First, there are clearly a large number of people out there who have no business trying to pass algebra 101. Even if they theoretically could with sufficient effort and tutoring, it is not worth their time, nor is it going to lead to that much that is beneficial. Second, teaching is already hard. Teaching math also requires an understanding of math that is rare. Hence finding people who are good math teachers is hard. Finding people who are good math teachers and willing to do it for a math teachers salary is even harder. If it were trivial to improve our teachers we would off course do it. But it is not at all trivial. I think this matters less in a liberal arts college, but especially if you are going to ask students to build on their algebra 101 with other courses. If passing algebra 101 took a lot of effort, chances are that the other courses are going to take the same amount of effort, if not more.
• lifeisstillgood 5y ago
  I like to feel the same way as your colleagues about "everyone can learn to code". I can definitely say that there are many people for whom it is a struggle - even those on college courses. But a hundred years ago we could easily have the same conversation about simply reading and writing - they (the poor, women, or "lower class" ) luke not be taught to read. But it turns out that if you start young enough, and put enough effort in, 99% of everyone can learn So, perhaps society is not putting enough effort in, or asking enough effort from, our kids for them all to learn calculus. As the Agile Manifesto says, the work delivered represents the effort input so far. If society wants all children to learn calculus, we need to pay that price. Edit: I think that we do need a new conversation about education. We have My father left full time education at 14, at 18 most of my peers left school and only 25% of us went to college. Today it's 50% it the total spend has not gone up in line. I honestly don't know what kind of world the "universal education" advocates of the 1870s were imagining - but I am damn sure it was not people doing college courses on their iPhones, but it is the world they ushered in. We need to double down on what worked for the 20th Century (and avoid the, y'know wars and genocide and stuff). Education will lay at the heart of that.
  • Ekaros 5y ago
    I think we can still have discussion about functional illiteracy. That is group who can technically read, but not at level needed for every day life. Very likely there is certain part of normal distribution who can't reach that level. But how large we can expect it to be is good question to consider.
  • tsywke44 5y ago
    Kids are savant at learning ”muscle memory skills”. But there is a reason 2nd graders dont do book reviews of classic literature. Even though they can absolutely read the complex words out loud on autopilot any day of the week.
    • lifeisstillgood 5y ago
      Yeah. it isn't that just saying there is a difference between a 10 year old and a 19 year old Edit: Actually, I think your premise is wrong. Children don't read words they don't understand "like muscle memory". The differences in meaning between, idk, betrothed, engaged, wedded and living in sin are superficial but they carry with them implications of social value, history and more. Children are supposed to read books and pick up context and understand meaning as they go along. We don't expect a 10 year old to grok calculus any more than we expect them to grok social/sexual arrangements. But we have different standards for 19 year olds - in the case of sexual arrangements it's obvious why. Perhaps less so for calculus. Reading and comprehension levels are hard to guage for this reason - at a certain point the words are placeholders for political positions. And it's hard to tell if someone does not understand the word or disagrees with the politics. Please see every election for past ten years for reference
• spaniard89277 5y ago
  > Years of administration telling the math department that our passing rate is too low have led me to pretty much pass everyone who takes the final exam. Last semester 80% passed but only around 50% deserved to Doesn't this contribute to lower the reputation of the universities? I mean, I did sociology in a small university in northern Spain and there was debate between the stats and methodology professors and pretty much everyone else about this. In the end I'm grateful to my stats and methodology professors, because having to work very hard is the only thing that actually gave me something useful to go and fight with the world. Many of my peers had to go to other unis because they couldn't pass there, so in the end they get a pass like me, the same in the eyes of employers, but they know it's bullshiting, and I know too. IDK, It seems to me that there's a lot of lazyness in social sciences, and this kind of hard attitude to it is not only good for the students, but needed in the field. IDK in the US, but this professors got a lot of heat for their stances on what a university is about, but they stood their ground, even when they've got hit by political bullshit, denied money for research, etc. There's another thing (again, IDK if it's the same in the US), but why don't you see it in CS or Engineering faculties? I mean, I remember in my uni the students of this faculties had maybe a couple of professors that where ok to lower the bar a bit, but most of them just assumed that you gotta learn what you gotta learn. And many of them where pretty hostile to students, 180º stance from what I see in Stanford Moocs for example.
  • stathibus 5y ago
    Maybe this is a stupid question, but is there any indication that most US universities cared about their academic reputation in the first place? I don't see any.
    • spaniard89277 5y ago
      Well in Spain everybody says to care, yet I see what I see. Not to mention that everyone complains about the low rankings of spanish unis, but I'd say that's mostly a consquence of money and some biases at play.
  • syops 5y ago
    Yes, this has long term negative effects but I need a job and don’t need the stress of being hounded by administration. In the old days the state funded a much higher percent of a student’s higher education. In those days, society was the client. Today the student is the client and the student does not want to fail.
• fallingknife 5y ago
  There are some questions science is not allowed to ask now. This is, of course, because they fear the possible findings. And I laugh every time some progressive I know shits on the Republicans for being "anti-science." (not that they are any better)
  • ogma 5y ago
    You sound like an idiot.
• DrLindemann 5y ago
  I think in the paedagogy community genetics is often an excuse for the unwillingness to develop right teaching concepts. It's then the "fault" of the pupils. Polya did good works, especial regarding Mathematics. Of course there are genetic influences and not everybody can be an Einstein or rocket scientist. But below that level there is a lot possible that has nothing to do with genetics. Most things are more influenced by motivation than the ability. And on that the real cause does not matter. If the people would spend only a fraction of the energy, they waste with questioning if something is genetic or not, in the development of skills by learning - they would improve beyond the proclaimed "genetic" level. Reduce media consume. Reduce politics. Almost the whole discussion is toxic. The right proclaims everything is genetic but on the other side punish people not having the "good genetics".
  • temp8964 5y ago
    "The right proclaims everything is genetic". I don't know what kind of "right" are you talking about. I don't believe it is mainstream conservative thought to claim family/school training/displine/education does not matter but only genetics matters.
• thatfrenchguy 5y ago
  This doesn’t necessarily have to do with genetics but with the environment you live in when going to school. My parents and grand parents were both born in the countryside and couldn’t get algebra or calculus (whereas myself and my siblings didn’t have issues learning) because they were lacking the basis that you now more easily get in primary and secondary school if you have supportive parents and teachers. By the time you’re in college, it’s already over. It’s why good daycare / preschool / school for everyone matters, otherwise you’re just missing out on a lot of potential talent.
• croes 5y ago
  Is a mental disability not caused by genetic disorder, injury or illness. This would invalidate your claim. You wouldn't use a contergan victim as a example for the thesis that not all can learn shot put. Isn't the whole point that you can't simply look at the gene of a person and know what his mind is capable of except for genetic defects and even then it's hard to estimate.
• TameAntelope 5y ago
  I hope you don't think this article in any way supports your belief that some people can't learn algebra/calculus due to any kind of genetic traits, because I don't think the complexity of either rises to the level of "difficulty" that only gifted minds can comprehend. Very, very little in this world does. Your belief should probably be considered heretical, even among your conservative colleagues, because your colleagues should recognize how deficiencies in one area can be made up for in other areas, sometimes (but not always) at a higher efficiency cost. Where genetic gifts are lacking, determination and perseverance can almost always make up the difference, especially at a basic algebra/calculus level.
  • DangitBobby 5y ago
    While I'm sure almost everyone can learn the basics of algebra or calculus, no amount of wishful thinking will give everyone the brain needed to master them or even be proficient. I'm not sure where your belief that perseverance can overcome all even comes from. I have been trying to get better at chess lately. I grew up playing it so I'm already fairly proficient, and I've been putting a decent amount of free time into studying openings and playing puzzles. Yesterday, I played my friend who hasn't played in literally years and never really played seriously anyway, and he beat me handily 3/3 games. I know that I do not have the brain to be a chess master, no matter how much time I put in, because I don't have enough working memory to keep the board in my head.
    • TameAntelope 5y ago
      I disagree, as it's not a sufficiently difficult topic to warrant some kind of genetic stratification. Life circumstance stratification, certainly, and you will get no disagreement from me that some people don't have the time or energy necessary to devote to something as not-immediately-useful as calculus, but from an intellect perspective, no. Everyone who is not experiencing some kind of mental illness has the intellectual capacity to learn calculus, though I will capitulate it is fortunate for me and this statement that we do classify a low enough IQ as a mental illness!
      • 5y ago
• myWindoonn 5y ago
  Hello, fellow mathematician. The first step in your proof which doesn't convince me is the claim that, in general, "levels of intelligence" exist, admit a partial order, and can reliably predict whether certain people can learn certain topics. In general, you'll find that "leftists" believe that psychometrics is bogus in terms of science. Instead, it masquerades as science in order to fool the public into believing that biased public policy is neutral. There's no denial that some folks have brain damage, developmental disabilities, etc. but a denial that standardized tests are an appropriate proxy for genuine medical diagnoses. Community colleges should present themselves as a public benefit. We shouldn't ask that everybody pass any class, simply that everybody has the opportunity to attend/audit any class. It is unfortunately true that the typical university administration is clueless and money-grubbing, preferring graduation rates to other metrics.
  • syops 5y ago
    I don’t claim that there is a partial order to intelligence. Indeed, I think it’s clear that no such can exist. Let me put it this way. The set of people who can’t learn algebra (using any reasonable standard for this) is nonempty as it includes the set of mentally retarded people. I further suspect that this set is considerably larger than the set of mentally retarded people. I further suspect but didn’t state this that if one doesn’t have exposure to algebra growing up then it is extremely difficult to learn as an adult. Children are easier to brain wash and in low level Mathematics we do a great deal of brain washing.
  • concordDance 5y ago
    "Leftists" don't think the correlations between results in IQ tests and many other things (such as memory, income and reflexes) exist?
    • myWindoonn 5y ago
      Correlation doesn't always imply causation, right? For example, there's a correlation between IQ and income. There are several causative possibilities: * IQ causes income * Income causes IQ * Some unknown thing causes both income and IQ * The correlation is spurious; IQ and income are unrelated Evidence strongly suggests that the third bullet point is true; socioeconomic class causes both income and IQ. Richer people living in nicer neighborhoods both have better opportunities for income, and also better opportunities for education; education causes IQ. This is why redlining is brought up so often as a root cause of so many of the disparities in quality of life; redlining deepened socioeconomic divides.
• threatofrain 5y ago
  IMO, biological differences and barriers certainly exist and are non-trivial, but the differences between private and public schools demonstrates the degree to which institutional finesse can accommodate student strengths and shortcomings, including differences in intelligence or disability. In other words, we have a long way to go. In some schools around the Bay Area, we have half the students on the fastest track, and about half the math faculty as calculus teachers. An immodest minority of students complete Calculus BC early and go on to the local college to continue their math education for their remaining years in HS. And these aren't even the top 50 schools in the nation.
  • rejectedandsad 5y ago
    I do wonder what’s gained by this. There are plenty of physics professors (perhaps even most) that didn’t do calculus until college or at least senior year of high school, what’s the advantage?
    • threatofrain 5y ago
      I'm not sure it's easy to discuss the high school transcripts of people with university posts. How did you get in touch with this information? The gains become clear depending on the degree to which you know what you want, and especially if you're thinking about graduate programs. 1. Calculus in some sense is somewhat disorganized, and it sucks that it's a gateway to more math in the US. By finishing Calculus early you can move on to the math you wanted to learn, such as Linear Algebra. 2. University students may have to spend about a year learning Calculus. That's a long time, and to some people they'd rather spend their money better by learning something else or graduating early. 3. If you're thinking about graduate studies in something technical such as Econ or Stats, then you'll probably want at least Analysis. The problem is that in the grand scheme of things, even Analysis does not leave you very prepared to do things, it just makes you prepared to learn more, so you may want to get ahead of this problem.
      • rejectedandsad 5y ago
        > I'm not sure it's easy to discuss the high school transcripts of people with university posts. How did you get in touch with this information? Because 95% of the time high school work doesn't transfer to the college level even if you do semesters at De Anza. You're back to scratch unless you go to flagship in-state, and even then you can only transfer up to a certain amount (at my undergrad it was up to Calc 2 - several people I know took Calc 3 in the same institution in high school but had to take it again).
• orwin 5y ago
  I do have an anecdotal conter-example to your theory. In my country, highschool last three years. The first year, i was living in the dorms with some of my classmates. One, let's call him M, was fairly dissipated and, while everyone would rather play and discuss than study, and had shitty grades in everything but biology. Math was his weakest, with grade ranging from E- to D+ (i try to convert grades here, my grades wer in the A range and the average was B-), and English/spanish were not a lot better. At the time, at the end of the first year, we had to choose specialities and which kind of diploma we could do. the "general" kind, with to specialities, economics/humanities or science, or the "technological" one, with three (electric, mechanic, civil). He realized at the end of the year that the only thing he wanted to do was biology, but as this subject was only available in the science speciality, he was fucked. Impossible to get to the "general"branch with his grade. He struck a deal with the school administration: 4 hour a week added to his curriculum, one hour every night after eating and before going in our dorms to make sure he worked. The year, in math, did not start well. He had a F/F- as his first grade (the average was D+, top of the class was B), but our professor was exceptionnal. we had 3 math illiterate in our class, and while the notation was pretty harsh on them, he took time to help everyone understand with interesting examples, stories and exercises. He even took hours of his own time for supplementary lessons. Our class relation was special too, we were only 20, and spent a lot of time together, even after college. Last time i talked to M he was doing a Master in marine biology, and aimed for a doctorate End of the 3rd year, we have to get the national test. Our class ended up with an average grade of A-, M had a B+ and wasn't the lowest scorer in math (of our class). Miles ahead of the nationnal average (C+/B- that year). It was a public technological highscool in a rural area. The other close HS was one dedicated to farming. Culturally, we did not start at an advantage compared to the average kid of our country, i'd say we were at a disadvantage. But great teachers and small, but close class can help you emancipate from some of your determinations.
• beej71 5y ago
  Here's some food for thought on "further study": * What percentage of your students hate math? * How do you differentiate between someone who doesn't get it because it's beyond their mental skill level versus someone who doesn't get it because they'd rather be doing literally anything else? * When you say "mentally disabled", what exactly does that mean in the context of a spectrum of ability levels across the species? * There are a lot of reasons people might fail your class. What are they? What's the percentage breakdown? * What are the dangers of thinking that not all people can learn math? What are the dangers of not thinking that?
  • syops 5y ago
    Oh, I’ve thought a great about these things. None of your questions are new to me or are ones I’ve not considered. I did not come to my conclusion quickly. Here are some more thoughts to ponder: Children are easier to brain wash than adults and teaching basic math involves a great deal of brain washing. To what extent is it the case that a person with no exposure to algebraic concepts growing up is at a disadvantage to learning algebra as an adult? There is a theory that if one doesn’t learn a language in childhood then it is impossible for them to learn one as an adult. Is something similar applicable to Mathematics?
    • beej71 5y ago
      Would you mind sharing your conclusions? Though I don't know of any studies about algebra in particular, kids show greater neuroplasticity in general than adults. So learning anything as an adult tends to be more difficult. But I live with an American who reasonably fluent in Norwegian after 2 years of study in their 30s. It's certainly not impossible. I have no doubt that math, like virtually everything, is more difficult for adults to pick up from scratch.
      • syops 5y ago
        What is theorized to be impossible is learning a language as an adult if you did not learn a language as a child. That is, if at age 20 you know 0 languages then you’ll never be able really learn a language. For obvious reasons experiments in this regard are few. My conclusion is that some people simply can’t learn algebra. Be it genetic, environmental, lack of intellectual fortitude, lack of “intelligence”, or any combination thereof it is simply the case that some people can’t learn algebra.
• DanHulton 5y ago
  You're making a lot of leaps of logic here, which might be why your colleagues are disagreeing with you. You go from "not everyone can learn algebra or calculus" and "mental disabilities exist" to "therefore intelligence is a scale and controlled by genetics and unalterable," which doesn't really track. Your previous education, your upbringing, your cultural values, these things all also have huge effects on your aptitudes, and you've just dismissed them out of hand, apparently in favour of pre-determined genetic intelligence. I mean, all I know of you is this comment, so I could easily be missing a lot more context about this argument you've had, but it sounds like you have an axe to grind, not a carefully-considered conclusion.
  • clusterfish 5y ago
    How do you know what effect upbringing and cultural values has on math performance? You know because there's research for that. But you can't base any argument on that when research into alternative (or complementary), genetics-based explanations is being stiffled. Or well you can, but that's just society-scale version of googling for statements that you agree with instead of questions that they're supposed to answer. When you stiffle research directions for political reasons, you're doing politics, not science, and the arguments based on lack of stiffled research don't hold any more water than arguments based on no research.
    • strogonoff 5y ago
      > society-scale version of googling for statements that you agree with instead of questions that they're supposed to answer Unfortunately, in practice science often turns out to be almost as much of a vehicle for confirming answers one already has in mind, rather than open-ended investigation.
      • clusterfish 5y ago
        Nothing is ever perfect. That's not a reason to deliberately make it worse than it normally is.
  • tnzm 5y ago
• bawolff 5y ago
  > I’ve taught mathematics at community colleges for over 20 years and I’m absolutely convinced that not all people can learn algebra or calculus. To me it is obvious this is so since the mentally disabled can’t. There’s a level of “intelligence” that’s necessary to learn a given topic. Not everyone can learn all topics. I think most people agree that there are extremes. There probably exists a small number of people who literally cannot (just like how 1 in a million could probably teach themselves calculus at age 10, also exists). However it's a big jump to conclude that even a small percentage of the people at your college cannot in the literal sense - i.e. if their life depended on it, they had all the resources they could want, they had no other distractions.
  • virgilp 5y ago
    > i.e. if their life depended on it, they had all the resources they could want, they had no other distractions. You just gave the definition of "cannot". Those circumstances will never happen, they're pure hypotheticals. Sure, hypothetically I might be able to play competitive tennis against Nadal. Practically, though, that'll never happen, I cannot and will never be able to do that - pretending otherwise is just naive and purely theoretical discussion.
    • bawolff 5y ago
      If the original claim was merely that a certain percentage of the population are not going to learn algebra - it would be uncontroversial and i would agree with it. After all, we all know that some people fail classes. If the claim was merely that math comes easier to some than others - again it would be an uncontroversial claim and i would agree with it. However, my reading of the original comment was that a good portion of the population literally are physically incapable under any circumstance, including the silly hypothetical circumstances i laid out, to learn algebra. I think that is false. It sounds like you do too. So i guess we're in agreement.
      • virgilp 5y ago
        > So i guess we're in agreement. Not exactly. I read the original claim that they are "incapable to learn algebra even in very good/way above average (but still realistic) circumstances".
• NoImmatureAdHom 5y ago
  As a scientist who thinks professionally about things like culture, behavioral genetics, and psychology, I can say: the idea that there /would not be/ humans who cannot learn calculus is the one that is hard to believe.
  • syops 5y ago
    Thanks for your comment. My statement has unleashed passions in some. It’s been interesting reading the comments.
• kitsune_ 5y ago
  The elephant in the room is that math has a giant UX problem. The notation is inconsistent and not nearly as logical as it could be.
  • xyzzyz 5y ago
    Math notation is very consistent and it’s optimized for convenience. It’s been constantly refined over last centuries. People who complain about notation usually actually have problem with the substance, and the complaints about notation is just a coping mechanism, to deny hurtful reality that one can’t understand something hard, blaming external factors instead. Ask yourself: if notation was genuinely confusing, why would mathematicians make themselves suffer needlessly? Now, to be sure, some people and some books are better at teaching than others, but it typically has nothing to do with notation used, and everything to do with the order of introduction of concepts, level of detail of explanation (which can be both too high and too low), amount and quality of examples, etc. However, the core issue here is that some things are actually genuinely hard, and people of average intelligence simply cannot grasp them without expending ludicrous amounts of effort. If you have some concrete suggestions about mathematical notation, ways it could be improved in more than superficial manner, I (and the rest of mathematical community) is very much open to hear them. Improvements in notation do happen regularly, and when they are valuable, they reach wide acceptance. For example, in the second half of 20th century, the notation of commutative diagrams have been invented, and it spread like a wildfire, because it genuinely facilitates understanding.
    • drath 5y ago
      > if notation was genuinely confusing, why would mathematicians make themselves suffer needlessly? Because they are unable to change it. Just like with any thing evolved over a long time, like music notation, languages, even, to some extent, programming languages. Every change brings a lot of pushback, it's a monumental task to create a new one and even more so is getting any traction with it.
      • xyzzyz 5y ago
        > Because they are unable to change it. That doesn’t square well with the fact that notation keeps getting refined and improved. There is no pushback for genuine improvements. Biggest problem here is that there rarely are changes that clearly and meaningfully improve situation over status quo. I gave one example above, but overall, I am not going to take complaints about notation being obstacle to understanding seriously without concrete ways how to meaningfully improve it. You can of course keep complaining that it’s confusing, but without proposals for improvements, you’re actually complaining about the difficulty of substance, not the notation, and it says more about you than about notation.
• kragen 5y ago
  > I’ve taught mathematics at community colleges for over 20 years and I’m absolutely convinced that not all people can learn algebra or calculus. To me it is obvious this is so since the mentally disabled can’t. There’s a level of “intelligence” that’s necessary to learn a given topic. Not everyone can learn all topics. You know, if you were trying to teach Chinese to 18-year-old English-speakers at community colleges with three hours a week of lecture, you might come to the conclusion that only a few rare geniuses had the ability to learn Chinese at all, and none would ever learn more than a few hundred words. But of course over 98% of people born and raised in China learn to speak Chinese fluently by the age of 5, and that's not because of genetics; it includes almost 98% of white people born and raised there too. There are several factors that I think of as key to this difference: 1. Plausibly there is a critical period for language acquisition, and if so, it very likely ends before age 18. Looking at an 18-year-old you can't tell whether their deficits in Chinese-speaking ability are due to genetics or environmental effects in the previous 18 years. There probably isn't an early-childhood critical period for calculus (I think you need formal operational reasoning for that) but maybe there are other things you need to develop early on for calculus to be easy for you when the time comes. Like, fluency in reading, for example. 2. Three hours a week, 36 weeks a year, for two years, is a total of 216 hours. Native language acquisition more typically involves over 20,000 hours of language exposure by age 5. Sometimes it's surprising how much more you can achieve when you apply literally over a hundred times more effort. Or, to look at it a different way, how little you will achieve when you're applying less than 1% of the effort necessary to get good results. 3. Schooling is a really terrible way to learn things. Extrinsic motivation displaces intrinsic motivation, massed practice displaces spaced practice because it gets better exam scores (especially if you know when midterms are coming up), the feedback necessary for improving is delayed by hours or days by the nature of homework grading, and the pacing is inevitably far too fast for some students and far too slow for others. It's well established that individual tutoring produces results two standard deviations better than ordinary classes (Bloom's two sigma problem). That's 30 IQ points. And Bloom wasn't even spacing out practice over decades the way you ought to; he was working within the semester structure of traditional schooling, extrinsic motivation and all. Is there a possible human culture where 98% of everybody routinely learns to do symbolic integration? Or does human nature render that impossible? Maybe. (Hell, when I have an integral to do in my head, I myself invariably settle for just approximating it unless it's a fucking monomial. Maybe I should spend a few semesters doing them on the blackboard in front of a class, I bet that would help.) But the meat grinder of community college doesn't give us much evidence about that one way or the other, except to know that we don't live in that culture today. It doesn't help us at all with the question of what to attribute to environmental effects and what to attribute to genetics. (One indication that such radical changes may be possible is the gradual transformation of literacy; hieroglyphics were the province of the priesthood and the quasi-priestly scribes, and even after the invention of alphabets, Charlemagne and Genghis Khan were illiterate. Can you imagine trying to teach a classroom full of 18-year-olds hieroglyphics in three hours a week, if they had no previous experience with reading and writing? Yet today literacy rates are over 95% in most countries, though countries with non-phonetic orthographies like Chinese and English lag a bit behind.)
• raducu 5y ago
  The problem is who gets to decide. My english teacher/class master till 8th grade insisted I follow a profession that doesn't involve math -- she even recommend me to be a radio host for a children program -- she thought highly of me, but she thought math was not my thing. She was half right -- I have ADHD and even though my blood relatives are highly successful (doctors, lawyers, judges) NOBODY was good at math. Anyway, my parents thought otherwise and promised to buy me a PC if I get admitted to a math/programming class in highschool and paid for math tutoring. My math skills completely turned around in a year and I ultimately loved math, especially calculus.
  • syops 5y ago
    How’s this for irony. My high school guidance counselor told me that’d never pass college and now I’m teaching at one! I don’t get to decide who has the ability to learn algebra. All I get to do in this regard is determine who knows enough to pass.
• deleted 5y ago
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• cdrini 5y ago
  It seems like you're essentially implying the mean value theorem here. Because there exist some people who cannot do algebra (folks with mental disabilities), and there exist some people who can, there likely must be some sort of transition point where someone doesn't have mental disabilities but can't do algebra. In that graph, you're implying that "mental intelligence" is the independent variable(s) and algebraic ability is the dependent variable. Another assumption is that the function is continuous. That's one I'm not sure about. I don't think there's a continuum between folks with mental disabilities and folks without. I think there's a discontinuity -- or perhaps overlapping spectrums on different dimensions -- but not a continuum. That's why many mental disabilities are the result of very concrete genetic variations. You can't have 80% of a generic variation. You either have it or you don't, which implies some sort of inherent discontinuity. My guess would be algebraic ability is a normal distribution. But that's not a death sentence. People who might, because of genetics or more likely nurture/circumstance be unlikely to learn a lot in algebra, are not doomed to that fate. It just means it might require a lot more time and hard work for them and their teachers -- to the point where they might not find it feasible, and instead choose to do something else.
  • syops 5y ago
    I believe the universe is discrete and that everything in it is discrete. I believe that “intellignece” is not really measurable. A person might have an intelligence as it pertains to art or critiquing art and be utterly clueless in another area. Indeed, I believe all people have a lack of ability in some area. For all of us there are things we just aren’t ever going to be able to learn and can’t learn. There are lots of reasons for this. I don’t know but can believe that genetics plays a role. There is variation on how our brains work so it seems reasonable that genetics plays some role.
• littlestymaar 5y ago
  > I’m absolutely convinced that not all people can learn algebra or calculus. To me it is obvious this is so since the mentally disabled can’t. Not all people can read, it's obvious since the mentally disabled can't. Yet with proper education, all non-disabled people can be taught reading. But that doesn't mean everyone can read, if you're illiterate by your 20s, you're gonna have a hard time catching up. Same for mathematics: most people reaching even high school are too mathematically illiterate to catch up[1]. Is genetics a factor: definitely, but it's among many others. The reason why it's a partisan issue is the following: if I say genetics is a decisive factor, then I can say «it's natural, there's nothing we can do so we don't need to spend all that government money trying to help those people». The left-sided point of view goes as «There's nothing we can do about genetics, but we can change everything else. Then we need to find what are all the other factors, because those are the actionable ones». The conservative focus on genetics is mainly a justification for doing nothing. > There’s a level of “intelligence” that’s necessary to learn a given topic. Not everyone can learn all topics. “intelligence” is conveniently pretty ill-defined, but I don't think I'm more intelligent than my doctor friends, yet they struggled a lot to grasp even the most basic concepts of algebra when I tried to help them during our studies. “Not everyone can learn all topic” but I have yet to find evidences that your ability to learn a random topic you're not interested into is correlated with the common acceptance of the word “intelligence”. [1]: that doesn't mean it's impossible, just likely well beyond the amount of effort they can (or want to) afford.
• bjourne 5y ago
  > I’ve taught mathematics at community colleges for over 20 years and I’m absolutely convinced that not all people can learn algebra or calculus. This is the "As a mom"-argument applied to iq. When it comes to child-rearing mothers will not infrequently claim to know what works best in general because they have had children of their own. I mean an equally valid interpretation of your anecdata is that not all people can learn how to teach mathematics at community colleges.
  • syops 5y ago
    Certainly not all people can learn how to teach mathematics. That is not at all disputable in my mind. I may be in the set of people who can’t learn to teach math. I’ve tried for over 20 years and appear to be just average at it. Maybe I’m below average. My collection of anecdotes that not everyone can learn math works as an anecdote that not everyone can teach math.
• hnbad 5y ago
  Some people can certainly reach an intuitive understanding of mathematics that will never come naturally to "normals". It's worth noting however that we often consider these people "disabled" (or euphemistically "differently abled"). The point is that there's no genetic dial you can turn from "worse" to "better", it's more like a massive board of switches that feed into each other.
• SavantIdiot 5y ago
  Here's a thought I've been tossing around: It's a community college, everyone is supposed to pass. At some point at the bottom of intelligence but with motivation to go to school and try and work and do the assignments, meritocracy literally doesn't matter. Because a diploma is needed even for minimum wage jobs. Why penalize people who are trying by failing them out of the simplest classes? Rich idiots fail up, poor idiots end up homeless. No reason to penalize the poor who try when the entire game is arbitrary. This position tends to make certain groups bristle, especially those with a classist sense of "fairness".
  • syops 5y ago
    It does matter in this sense. Students who are poor end up taking on debt for college and this debt is currently (mostly) unforgivable. If we had universal higher education this objection of mine goes by the wayside. But then a new objection rises up.
• sokoloff 5y ago
  > I’ve taught mathematics at community colleges for over 20 years and I’m absolutely convinced that not all people can learn algebra or calculus. That a well-informed position believes that not (almost) everyone who is attending a college can learn single-variable algebra is fairly depressing.
  • syops 5y ago
    Do you believe everyone can learn algebra? What evidence do you have for this belief? Have you taught in the classroom much to students with a wide range of educational backgrounds? I don’t believe everyone has equal intellectual talent in all areas. My talent for math far exceeds my talent for physics. I’ve tried to learn physics but I just can’t. I have no intuition for it. There is variation amongst our brains and how the connections in our brains formed in childhood. In some people the wiring is such that learning a given topic is not feasible. Such is my belief.
    • sokoloff 5y ago
      Do I believe that everyone should attend college? I do not. Of the people who should attend college, is it frequent that people can't grok single-variable algebra? I'm not disputing your superior experience on this topic (hence "well-informed position"); I'm just saying that it's fairly depressing.
      • syops 5y ago
        In case you don’t know this, community colleges are generally required to accept everyone who applies that has a high school diploma or a GED. We are open enrollment institutions. I understand now what you meant by fairly depressing. Thank you for the clarification.
• Noos 5y ago
  The problem with learning advanced math is that math is isolated. Like if I learn accounting, I know why I'm learning it; to learn how to create, audit, or read the financial statements of a business. If I learn math, it comes across more as "here are these arcane puzzles you need to solve." Like no one does double entry bookkeeping in the abstract; you learn the history, the methods, etc in the confines of an express purpose. But trying to learn precalc as an adult (which i do get), what's striking is how little purpose or context there is to it. Why do I need to know how to factor imaginary numbers, or know the slope of something? I think math when isolated is a big reason why its so hard to learn. They teach the toolset but people don't have the need to use the tools unless they go into a separate subject.
• titovodka 5y ago
  I come from a third world country where to graduate high school, you HAVE to take Calculus I, II and little III. Planar Geometry, linear algebra etc. And thats only if you through the Life Sciences track (Biology and Organic Chemistry) I truly don’t believe my people are genetically smarter because we have a truly awful abysmal track history in governing. My guess as an immigrant who went to community college here and then to University here is that students just have too much choices/freedom. They are told they should strive to whatever they want. I and my friends grew up told you need to choose a major that will bring bread on the table, that should be the only priority.