[HN Gopher] An update on the campaign to defend serious math edu... ___________________________________________________________________ An update on the campaign to defend serious math education in California Author : Tomte Score : 325 points Date : 2022-04-26 17:30 UTC (5 hours ago) (HTM) web link (scottaaronson.blog) (TXT) w3m dump (scottaaronson.blog) | spicymaki wrote: | The tension here is that educational achievement is a proxy | measurement for IQ and in capitalist societies IQ is directly | correlated with income. The cultural ideal here in the US is that | hard work, effort, and grit is what is necessary for success. It | is supposed to be purely egalitarian; you get what you give. | However whether you are born with a high IQ is purely random, and | even worse IQ is heritable. This is creating a technocracy which | is at odds with the egalitarian ideal. This along with the | expanding wealth gap is causing the schism you see today. | n4r9 wrote: | > whether you are born with a high IQ is purely random, and | even worse IQ is heritable | | This sounds contradictory to me. | | Moreover, how does IQ differ in this respect from "capacity and | willingness to do hard work"? | eggsmediumrare wrote: | Who you are born as is random, but who will have children | with higher IQ is not. Work ethic is less nature and more | nurture than IQ, or at least feels that way intuitively. | akomtu wrote: | > Who you are born as is random. | | The essense of materialistic nihilism. | anthonypasq wrote: | I mean they are completely different measures. They both | contribute to success but can be tested independantly. | | Also assuming that "capacity and willingness to do hard work" | is a personality trait, that is also largely random. So no | matter which way you slice it, you gotta get lucky on either | the intelligence or industriousness axes (or both) to be | successful. | throwawayboise wrote: | High IQ by itself doesn't get rewarded very much without hard | work, effort, and grit. If you have all of that, yes you'll be | rewarded more than others who lack one or more of those | qualities. And you should be. | kube-system wrote: | Intellect is not 100% inherited. The percentage is debated, but | it is almost certainly not 100. | TimPC wrote: | Something is rotten in the state of academia when looking at the | evidence there are mathematicians, scientists and social | scientists standing bravely in favour of a high bar and a quality | education program in mathematics. | | On the other side of the argument you have people from the | Department of Education who specialize in Mathematics Education | who seem happy to lower the bar as far as possible in the name of | equality. | | When I was in University the Department of Education was the most | woke department on campus, except for perhaps the Department of | Gender Studies. We are now seeing policies that favour wokeness | ahead of the best interests of the students affected by the | policies. | klodolph wrote: | I don't live in CA and this isn't my circus, but I have some | things to say about math education. From the statement: | | > We write to emphasize that for students to be prepared for STEM | and other quantitative majors in 4-year colleges, [...], learning | the Algebra II curriculum [...] in high school is essential. | | Problems with math are one of the most common reasons why | students encounter difficulties in STEM education and careers. | The most common problem is difficulty with high-school level | algebra. | | I agree, fundamentally, with the relevant premise of the CA | effort here (and agree with Aaronson's criticism of its | implementation). That premise is that you shouldn't have to be on | an accelerated track in middle school in order to take calculus | in high school. And yet... the fact is, we get a lot of adults in | college or graduate school pursuing STEM degrees, who have shaky | foundations in high-school algebra. | | Just looking at the "typical" math track in US high schools it | does seem a bit arbitrary. Algebra I, Geometry, Algebra II, Pre- | Calculus, Calculus--this is the most common math track I see, | with accelerated students starting Geometry in 9th grade, | Calculus in 12th grade. | | The thing is... individual performance is highly variable in math | classes, and to make sure that everyone gets good foundations in | mathematics, we see high-school mathematics curricula that repeat | the core algebra concepts in different classes. This repetition | and focus on fundamentals is why the division between classes | seems so arbitrary--what is presented as a sequence of classes is | really more of a unified curriculum spread across multiple years. | When you combine these two factors (variable performance, | repetition in the curriculum), you end up with a population of | high-school students who develop good foundations in algebra | early on and are bored by the repetition, and a population of | students who really benefit from the time spent mastering | algebra, and it's hard to serve both. | | I think we can figure out a way to let high-school students take | AP calculus in 12th grade without expecting them to take Algebra | I in 8th grade, and we don't need to push everyone into calculus | faster in order to do it. And yet, my experience with high-school | education in the US has left me very cynical about it. Letting | students progress through the high-school math curriculum at the | right rate requires a kind of "personal touch" that seems to only | happen to individual students when their parents are involved, | but not _pushy_. It 's rare. The school system would rather do | the easy thing (everybody moves in lockstep to the next class in | the sequence), and parents are largely either uninvolved or | overinvolved. | | (This is more or less what the article says, I'm agreeing with | the article.) | wbsss4412 wrote: | Considering the fact that the vast majority of students _aren | 't_ going to go onto 4 year STEM degrees, it doesn't make sense | to track all students towards that goal. | | I feel as though there is too much focus on giving everyone | more or less the same type of mathematical education in high | school. This is probably due to limited resources (ie teacher | availability and class sizes), but ideally there would be room | for a more varied approach wherein students don't need to have | every year build on the next if the _aren't_ STEM tracked. Too | many students fall behind and never are able to recover. Math | class just becomes dead time, and those that do make it to | college end up retaking the same subjects over again. | klodolph wrote: | > Considering the fact that the vast majority of students | aren't going to go onto 4 year STEM degrees, it doesn't make | sense to track all students towards that goal. | | It sounds like we agree 100% on that point. | | I'm mostly thinking about the students who are going into | STEM degrees later in life, who will (hopefully) come from | varied backgrounds in high school and middle school. If you | decide in high-school that you're interested in STEM, then it | makes sense to develop solid foundations in algebra during | high-school. Just like it doesn't make sense for all people | to take math like a STEM major, it doesn't make sense to | fast-track all future STEM majors to take calculus in high- | school, and it doesn't make sense to make decisions in middle | school that lock students out of high-school calculus. | | The thing that confounds this is that people overvalue high- | school calculus as _the_ ticket to a STEM degree, when (like | the article says) many people would be better served by | developing stronger foundations in algebra. And public | schools are generally not good at educating students at their | own rate & level. | deanCommie wrote: | Irrespective of specific educational curriculums, I'm curious | what does HN think about Calculus? | | I absolutely loved learning Calculus in high school in Math and | 1st and 2nd year of University. I consistently got 97+% on my | grades. | | And I've never had to use it in my Computer Science degree or my | 20 year Software Engineer career since. | | Am in a bubble because I don't spend much time in the Machine | Learning domain? | Der_Einzige wrote: | Also you don't need calculus to "do" ML (even deep learning | research!) | | I got to the point of writing my own toy neural network from | scratch, seeing backpropegation, figuring that I'd have to use | the chain rule myself on my forward pass, understanding what | "automatic differentiation" was and why it's important, and | decided "screw that I'm not putting myself through this hell | again" and decided to look into | https://en.wikipedia.org/wiki/Derivative-free_optimization | | You can literally just find your own hetrodox subset of | scholars in your field who are like "calculus? pfft!" | npunt wrote: | I've never understood the cult of calculus. I think it comes | from mistaking the importance of its discovery for the | importance of teaching it. It was a huge unlock for science, | but is in no way a huge unlock for most people's lives. | | On the other hand, I feel psychology and stats are the biggest | missing pieces in K12 education. We need to build greater | awareness of human needs and fallibilities, and awareness of | how to make decisions in uncertain environments by | understanding probabilities. Both are about developing a | nuanced perspective on life and making better, more sober | decisions, and they build a great deal of empathy to boot. | | Finally, psych & stats are inherently relatable - everyone | deals with people and has to make decisions. So much of the K12 | experience isn't relatable, which is why students often hate | school. | eesmith wrote: | As I recall from when this came up a few years ago, the "cult | of calculus" was because in the post-war era 'the end-users | of mathematics studies [were] mostly in the physical sciences | and engineering; and they expected manipulative skill in | calculus.' - https://en.wikipedia.org/wiki/New_Math . | | One way to see how curriculum has changed over the last 70 | years is in Sheldon Glashow's autobiography. He graduated | from the Bronx High School of Science in 1950. Quoting https: | //www.nobelprize.org/prizes/physics/1979/glashow/biogr... , | "High-school mathematics then terminated with solid | geometry." | ecshafer wrote: | Calculus is critically essential for learning many later math | fields, and many important topics. Mechanical Engineering, | Electrical Engineering, Physics, Chemistry, Civil | Engineering, Aerospace, etc. There is a lot of very critical | fields to modern society that requires knowledge of calculus. | You can't build a modern bridge without calculus. | npunt wrote: | I don't dismiss its value in the broader education system, | nor for certain industries and jobs. But specifically in | the context of K12 requirements & expectations in the | process of applying for college, it's hardly foundational | knowledge for most of life's paths. | | Ergo, it's best to a) not to have college expectations be | built around most/everyone having it before college and | punishing those who don't, b) focus on teaching it where | it's needed (eg when in college for those majors), and of | course c) if a kid knows their path involves it earlier, | make it available to learn when they want to. | MatteoFrigo wrote: | It depends upon where you think calculus starts. | | If you take the position that calculus is the concept of limit | and all its consequences, then things like exp() and log() are | calculus and it's hard to get anything done in CS without | those. In this view, saying that quicksort is O(n log n) is a | statement of calculus. | | If you say that calculus is derivatives and integrals, then I'd | say that calculus is not that important in a digital world, and | that discrete math is much more useful. However, discrete math | is harder than calculus, but you can use calculus as an | approximation to the discrete answer (i.e., compute the | integral if you don't know how to compute a sum, or use a | derivative to approximate a difference). Ironically, this is | the opposite of the old attitude that the continuous answer was | the true one and the discrete answer was a poor man's | approximation to the true one. | charlescearl wrote: | In the last couple of months, two readings stay with me on | challenging the notion that math/science are things that only | "certain kinds of men" do (more a gendered stance in the u.s. | than eastern europe / asia). | | The first is The Dawn of Everything, by David Graeber. I'm left | with the notion that what we now call science and mathematics | emerged from tinkering, persistent experimentation done mostly by | women, and that what we have now disciplined into mathematics | emerges from the systematic study and production of pattern | (basket making, the organization of communal structures), and | Graeber seems to argue against the hierarchical gender divides | when viewed across the broad stretch of human history. | | Rachel Thomas https://www.fast.ai/2022/03/15/math-person/ also | makes a case that math is something that all people do. | | I think that the larger point both are making is that disciplines | don't have to be the way they are constructed now. | | My only "political"'statement would be the hope that states | (particularly the u.s.) would invest as deeply in mathematics | education at the primary and secondary level, for all of its | communities, at the level of investment in big science and big | military projects. | voz_ wrote: | Wokeness is destroying California. I left after living there for | 20 years. It was a great choice. | [deleted] | [deleted] | phillipcarter wrote: | This is a real _laptop class_ kind of statement, to borrow | terminology from one of the more prominent anti- "woke" | investors. | | Living in California is expensive as hell, especially for | younger folks with no inheritance, and the state operates at | varying levels of dysfunction because it's got 40 million | people in it. | [deleted] | JaimeThompson wrote: | What is wokeness in this instance? | kevin_thibedeau wrote: | Math perpetuates an -ism so we must change math. | JaimeThompson wrote: | Was some of the false statements said about Common Core | match "woke" according to that definition? | micromacrofoot wrote: | Economic disparity is a more obvious answer with the benefit of | being backed by actual data. No need for personal boogeymen | based on social mores. | kurthr wrote: | From the original letter: While well-intentioned, | we believe that many of the changes proposed by the CMF are | deeply misguided and will disproportionately harm under-resourced | students. Adopting them would result in a student population that | is less prepared to succeed in STEM and other 4-year quantitative | degrees in college. The CMF states that 'many students, parents, | and teachers encourage acceleration beginning in grade eight (or | sooner) because of mistaken beliefs that Calculus is an important | high school goal.' | | The updated CMF looks better, but I just don't see how an | educator who knows math or how to teach math could come to such a | conclusion (that Calculus should not be a goal). If it is well- | intentioned, what was the intention... to dumb down math in high | school? Perhaps we need to educate those who are coming up with | the math frameworks in math and science, or to get people who | care on the California Department of Education? | fnordpiglet wrote: | I'd rather linear algebra and discrete math be the goal. | Calculus is greatly overrated. I mean, sure you should take it, | but IMO linear algebra is considerably more useful in the real | world and most people never take it. Knowing how to integrate | and differentiate in continuous space isn't nearly as useful as | learning how to count in discrete space. Most people operate in | a discrete world. | rayiner wrote: | > If it is well-intentioned, what was the intention... to dumb | down math in high school? | | Bingo. It's well intentioned, but the intentions aren't to | ensure that America can keep up with a rising China. | | It's shocking to me that people in California aren't more | worried about this. About 15 years ago, I was talking to an | engineer at Juniper/Cisco. We were joking about how Huawei had | copied one of their router designs down to the silk screened | assembly instructions (in English!) on the PCBs. Fast forward | to today, Huawei is making fully custom equipment down to state | of the art switch and router chips, and Chinese companies are | white boxing lower end products made by American brands. | | There's a big bet out there that the U.S. can survive on | software and social media alone. I would think the success of | Tik Tok would have blown even that rationalization out of the | water. | | On the general point of U.S. math education: my cousin who | lives in a nice California suburb was complaining that the math | education her early high school student is receiving is several | grade levels behind what she got--in Bangladesh. My mom, who | also went to school in Bangladesh (in the 1960s!) was deeply | unhappy about the math education in our affluent Virginia | suburb, until I got into a top STEM magnet high school. My own | kids go to an expensive private school, but are still getting | math tutoring on the side. Math is just a shockingly low | priority for Americans. | klodolph wrote: | In the 1960s, it was the USSR. In the 1980s it was Japan. Now | it's China. | | I'm not trying to suggest that the US is fine and we | shouldn't fix anything, but if you look at the world by | comparing test scores and grade levels in mathematics, you're | going to come to some very warped perceptions about what is | important. I'm speaking as someone passionate about STEM | education, who got a B.S. in mathematics. | | The whole situation is warped. The USA accounts for 4% of the | world population, and 40% of the top 100 universities in the | world. That's fucking _weird._ I don 't have an explanation | for it. I'm just saying that the different signals we use for | evaluating how good our education system is functioning are | giving us radically different pieces of feedback, and our | understanding needs to be correspondingly sophisticated. | | There are all these narratives about how China is going to | eat our lunch (like Japan in the 1980s, or the USSR in the | 1960s) and while I don't feel comfortable betting on long- | term US hegemony, and while I do think we should put more | work into our mathematics education, I do think that looking | at the world through high-school mathematics test scores is | going to give you anxiety more than it's going to give you an | accurate picture of what are problems really are. | | To take another statistic into account, there are actually | many STEM graduates in the US. What do we do with this | information? How do we change our policies? It's unclear. | cuteboy19 wrote: | > The USA accounts for 4% of the world population, and 40% | of the top 100 universities in the world | | that is just inertia, carried over from the time when the | US was the only superpower. More and more Chinese | universities enter this list every year. | nosefrog wrote: | > affluent Virginia suburb, until I got into a top STEM | magnet high school | | TJ? :P | majormajor wrote: | If we look at countries beyond the US and China... what are | they surviving on? | | Should math be a higher priority in the US? Should working | hours in the US be the same as in China? Should the academic | pressure on kids be as high in the US as in China? | | The US is much smaller population-wise, would we actually | need to try five times _harder_ than China? | | Is it not enough to compare today's high school overachievers | with those of 20 years ago, all still fighting for the same | universities but with all similarly-inflated resumes? Do we | actually need to push them even further? | | Do we instead want to be more like the European countries | that currently put themselves under _less_ pressure than the | US? | cwkoss wrote: | Is calculus an important highschool goal? I feel like I may | have benefited more if that time was spent on statistical | literacy than calculus. I encounter stats very often in my | adult life, calculus style problems are rare and I don't | remember the formulas offhand, so end up just looking up what I | need. | zozbot234 wrote: | Stats _requires_ calculus; you can 't even define a | probability distribution without some pretty advanced notions | of real analysis. Discrete math, linear algebra etc. are | viable alternatives. | spywaregorilla wrote: | I took AP Stats in high school. I took a calculus based | probability course at MIT. The former was extremely | important to me and I learned a ton. The latter was | interesting, but mostly unnecessary. A z-score lookup table | is more than enough to teach the concept of a normal cdf | without actually being able to derive it yourself. | | As a professional data scientist I've never needed to use | calculus unless you consider graphical reasoning on | distribution diagrams to be calculus. | khazhoux wrote: | No. Learning high-school or early-ungrad statistics does | not require knowing calculus. The material will not require | integration or differentiation. | BeetleB wrote: | What you say is true. However: | | Most people who deal with data/statistics in their working | lives do not need to know real analysis, do not utilize | calculus to draw (correct) conclusions, and do not use | linear algebra either. They learned all these things once | and forgot them a long time ago, _because they did not need | them_. They utilize statistics an order of a magnitude more | often than they do calculus. | | They are not statisticians, but people who need to deal | with data as part of their job. | l33t2328 wrote: | But statistical literacy doesn't. | | Sure, they may not be able to tell you what is a measurable | function, but they can explain the way you should feel | about a p-value. | teawrecks wrote: | As someone who took both a stats and newtonian physics | course before taking a calc course, I wish I hadn't. It | was a waste of time. They can't explain why you use the | formulas they do, they have to just say "trust us, and be | able to regurgitate it on the exam". For me, learning | means developing an intuition, which means | resolving/building new facts from other facts I have | already accepted. Being handed seemingly random formulas | to memorize goes directly against this. Yeah, I can use | my car without knowing how every piece inside works, but | the moment something goes wrong, I don't know what to do. | I would never say I am car-literate, and someone who | hasn't taken calc cannot be stats-literate. | l33t2328 wrote: | You can develop an intuition divorced from meaningless | formulas. | | It goes without saying this proposed class wouldn't be | based around memorizing unmotivated formulas. | teawrecks wrote: | But how would you "motivate" the formulas without knowing | where they came from? Why is this the formula we use and | not something else? | | To go back to the car analogy, I know why I need an | engine, you might even say I know how to use the engine, | but if the engine dies or I want to use the engine for | some other purpose, I'm not equipped to do anything. | | I don't have "literacy" with engines, I have rote | memorization of a series of steps. I don't have enough | information to know why the steps are what they are, nor | could I know under what conditions the steps should | change or what they should change to. | l33t2328 wrote: | Just don't include formulas you can't motivate simply. | | Will it result in students not knowing as many formulas? | Of course, but who cares? | cool_dude85 wrote: | Not at a high school level. AP Stats I believe does not | require calculus as a prerequisite. | | Discrete distributions can be defined, even infinite | discrete distributions (as sequences and series are taught | in pre-calc). Continuous distributions can't be formally | defined, but a lot of intuition can be given with hand- | waving e.g. the area under this curve. Probably most of the | class is spent with counting and probability-type problems, | but plenty of actual statistics can be done without | calculus - we can learn about distributions, what a | statistic is, expectation, sampling, counting, | probability... the list goes on. | 6gvONxR4sf7o wrote: | There's a diminishing return here. Single variable | differential and integral calc is a sweet spot. Without | that, there's a ton of memorizing seemingly unrelated | facts, but with it, you can learn a few principles that | lead to a huge amount of practical stuff. | hn_throwaway_99 wrote: | Is this really true, in practice? For example, given its | importance in every day life, I think _everyone_ should | understand test sensitivity and specificity, and how these | relate to but are quite different from predictive value | positive and predictive value negative. All of those topics | can be understood with basic algebra. Similarly, I recall | my introduction to biostatistics class I took at an Ivy | League institution, and I don 't really recall using | calculus much in any of it. | fartcannon wrote: | At some point, someone was saying precisely this about | literacy. And it was as true then as your comment is now. | You only need some range of function around the baseline | education to operate in society. But if you want society | to progress, then everyone needs to learn to read and | write. | magicalist wrote: | At some point someone was saying the same thing about | Greek and cursive, too, though, so being merely more than | the baseline isn't sufficient evidence that it should be | included in everyone's education. | hn_throwaway_99 wrote: | Bad analogy. Being able to understand statistics at an | everyday usage level _is_ the equivalent of being able to | read and write. Understanding calculus needed for | statistics is the equivalent of needing to understand | Latin or comparative linguistics. Noble and useful | pursuits for sure, but you can get far with an educated | society that just knows how to read and write even if | they 're iffy on the Latin roots of it all. | heavyset_go wrote: | Colleges have varying levels of stats classes for different | majors, and not all of them require rigorous understandings | of calculus. The ideas and principles presented in those | classes are still important for people to learn, even if | they are unfamiliar with, or haven't mastered, calculus. | It's possible to teach those principles in high school, as | well. | falcor84 wrote: | You can't even define arithmetic on natural numbers without | some pretty advanced notions of logic and set theory. But | you can definitely get a lot of value from arithmetic | without those definitions. | mindcrime wrote: | _Stats requires calculus; you can 't even define a | probability distribution without some pretty advanced | notions of real analysis._ | | Only in the same sense in which operating a car requires | advanced knowledge of mechanical engineering, electrical | engineering, aerodynamics, fluid dynamics, thermodynamics, | etc. IOW, in no sense related to the everyday, ordinary | practice of operating a car. | | Sure, statistics requires calculus... and real analysis, | and probability, and measure theory, and FSM knows what | else - IF you're doing statistics research or trying to | break new ground, or do really advanced things. But all of | this is light years away from the level of statistics | knowledge needed by Joe Q. Public to better understand (and | not be misled by) the "statistics" frequently thrown out in | news articles, government reports, etc. | | Please, for the love of FSM, can we stop this HN "thing" of | assuming that every mention of any mathematical topic | implies that the goal of the user/learner is to do original | research in the field? | the_only_law wrote: | Then I have no idea what my school was doing then because | as a senior you either took Calc or Stats. | hnrj95 wrote: | i'd argue that you can't properly define probability | without notions in measure theory, which is obviously far | too advanced for a high school student. i'm not an | educator, but some middle ground needs to be struck. i | think it's clear to many that the quality of education in | american colleges far exceeds the quality of education in | the average middle or high school. that's the issue, imo | afiori wrote: | You can do quite a lot of useful stuff with just https:// | en.wikipedia.org/wiki/Cumulative_distribution_functi... | | You only need measure theory when working with something | that is not easily replaceable by R^n, Z^n, or finite | sets to meaningfully define integration, otherwise | (in)finite sums and Riemann integration get you very far. | | I am a bit rusty on my advanced probability theory, but | IIRC the only thing that required* measures was defining | conditional probabilities and expected values on zero- | probability events. | | Of course redoing that class without Lebesgue integration | sounds excruciatingly painful. | | * Not just to make proofs nicer and theorems more | powerful | jhbadger wrote: | But that's like saying everybody who learns to program | needs to know electrical engineering so they understand how | CPUs work. Just as most programmers don't need that to be | good programmers, knowing useful statistics doesn't mean | deriving things from first principles but rather knowing | what statistical test to apply to analyze data and how to | interpret the results. This doesn't need calculus. | [deleted] | jeffbee wrote: | I had calculus before college, got a 5 on the AP calculus | exam, and it did not seem to have prepared me in any way for | college-level calculus. I always thought that had been a | total waste of one of my senior year class periods. | pishpash wrote: | That's a totally different argument. I mean, did arithmetic | "algebra" prepare you for abstract algebra or even linear | algebra in college? | zozbot234 wrote: | Actually, yes. The rules for manipulating 'expressions' | with 'variables' in school algebra describe what are | called "free objects" over some set of "generators". The | whole setting generalizes pretty well. | throwawayboise wrote: | I took calculus in High School, it was a dual credit course | with a state university. I got credit at the university for | the first semester of calculus (which was taught over the | entire year in High School, so at a slower pace, but also | allowed the High School class to spend more time on review | in the first month or so, compared to college courses which | basically dive right in). We took the same exams as the | university course. | | I felt I was prepared for 2nd semester calculus when I took | that as my first math course in college. | LeifCarrotson wrote: | It's true that to someone familiar with collegiate | mathematics, it doesn't feel too important to make that the | goal - sure, why not statistics (except perhaps that a | thorough understanding of statistics requires some calculus), | or why not discrete mathematics, or number theory, or linear | algebra, or set theory...there are lots of topics! | Mathematics really is a tree with many branches, and you're | correct that the high school track towards calculus just | develops one trunk with a couple stunted growths, which is | definitely unfortunate. | | Unfortunately, I think it comes down to resource constraints: | When I attended a relatively wealthy and large suburban | school district that offered more courses than most other | school system in the state, there were only 18 other students | who took AP Calculus BC our senior years (and one anomaly who | took it his junior year). There were a couple classes for | Calc AB, mostly seniors and a few juniors. That special | 18-student course was already pushing the limit on the | minimum class size, a couple years prior they hadn't had | enough students and didn't offer it at all. | | If you'd split the curriculum into discrete math and | statistics as well, there wouldn't be enough resources to | support those branches. To take a chainsaw to the analogy, | you wouldn't have the straight but sturdy tree trunk we have | now, you'd have a stump or maybe a shrub. | dymk wrote: | The abstract concepts of calculus are useful and will shape | the way you think about and go about solving problems, even | if you don't explicitly employ an integral or derivative. | Rates, sums, areas, volumes, etc. | | Learn the nuts and bolts in highschool, use the intuition for | the rest of your life. | mrob wrote: | The abstract concepts are useful, but in practice most | effort is spent on applying rote symbol manipulation rules | to questions specifically designed such that applying the | most obvious rule at each step will reach the solution. The | idea of a tree search in symbol manipulation is never | taught, so if you try solving non-trivial real-world | problems you will likely manipulate yourself into a dead | end. | | Highschool calculus should be taught with computer algebra | software. That's what you'll use in real life as soon as | you find an even slightly difficult calculus problem. | There's not enough time to teach both the symbol | manipulation rules and the intuition. | arcbyte wrote: | Seriously this. The average American doesn't grasp how | basic graphs work. This simple idea of trends and how | different functions imply graph differences is a powerful | basic thought model. "Is this a linear or exponential curve | curve problem?" | scarmig wrote: | The point isn't that every single student should take | calculus. The goal is to make it so different students can | choose the path that's best for them. California's proposed | changes make it much tougher for students to take calculus in | 12th grade, let alone earlier. | TaylorAlexander wrote: | I'm certainly very happy that I learned calculus in high | school. I then got a 5 on the AP calculus test and tested in | to third quarter calculus in college. It was important as an | engineer to understand those concepts. I don't use them too | often and I forgot a lot of it, but I really enjoyed it and I | think it would be unfortunate if other students did not have | that opportunity. I agree stats would be great too! | canadaduane wrote: | As a software engineer, I wish I had learned stats instead | of calculus. Some exposure would have been great, but the | high school & university requirements were way off target | wrt its usefulness in computer science. It was a painful | process of learning, failing, and re-taking calculus, | squeaking by, only to never use it again. I was a | straight-A student otherwise. | TaylorAlexander wrote: | I get that. As a robotics engineer, some cursory | understanding of integrals and derivatives is useful. | | But what I really mean is that, as a person, I just | really enjoyed calculus. I found I was very good at it, | and that experience helped me understand why some people | choose to focus their career on pure mathematics. I am | happy I took calculus not as a means of training for the | workforce, but because I found it enriching on its own. | And I never would have taken all that time if it wasn't | offered to me as a class in public school that counted as | credits towards graduation. | shmde wrote: | Lets say you need to find the probability of something | happening 10% of the time to 40% of the time, you need to | perform definite integration of the curve ( lets say normal | curve ) from 0.1 to 0.4 on the x axis multiplied by the | normal curve function. This is one of the easiest examples I | could remember from my undergrad. We could solve these | problems with ease at undergraduate level because we grinded | hard during our high school. And also these type of problems | were just a subset of the huge variety of problems presented | during our undergraduate. But lets say they started teaching | calculus only during Undergrad it would have become a | tremendous task just to first learn about calculus then start | with applying it on other subjects. I am all in for teaching | calculus during high school. | BeetleB wrote: | > Lets say you need to find the probability of something | happening 10% of the time to 40% of the time, you need to | perform definite integration of the curve ( lets say normal | curve ) from 0.1 to 0.4 on the x axis multiplied by the | normal curve function. | | No one does this in the real world. Not even professional | statisticians who know calculus. In the old days they used | table lookups. Today they use software. | | You need to understand the concept of areas under curves. | Calculus is just a means to compute the area. | jrumbut wrote: | I think if the policy was "calculus isn't an important goal, | we should actually teach stats" the reaction would be | different. | | I give the edge to calculus because it allows students to go | right into physics and be able to graduate college with an | engineering degree in four years (saving them time and | money), but any challenging quantitative material would be | good for their development. | | The big picture goal is to show them there is this big world | of problems that can be approached with specialized knowledge | and get them familiar with what it takes to gain that | knowledge. | troupe wrote: | > any challenging quantitative material would be good for | their development. | | I think this is key. What exactly they study may not be | quite as important as whether or not they are actually | getting an opportunity to do some form of challenging | mathematics. | fn-mote wrote: | The quality of mathematical arguments presented in AP | Calculus are significantly higher than other "standard" high | school courses. So to the extent that it is a nationwide | program that promotes some careful learning, it is a big | plus. | | I think statistical literacy is also important, but more than | anything I think students benefit from learning how to think | about hard(er) problems. If they learn that in statistics, | great. | | Generally I would say easy courses is the real problem, not | content. | | However, many many students enter college engineering | programs with 1-2 semesters of calculus, so not having it | could be a competitive disadvantage - presumably to your | understanding of those first year classes. | majormajor wrote: | I would've done better in college - and probably have a | better understanding of calculus today - if I hadn't tested | out of University-level Calc I due to AP credit. I didn't | _really_ know what I was doing in the high-school course. | | But I was a slacker and that experience doesn't necessarily | transfer. | | And yes, I'd generally favor stats over calculus as an | additional HS class; however, I am hesitant about | _discouraging_ the opportunity to take either. | taeric wrote: | I'll bite. Why is calculus a goal? | kurthr wrote: | Because, without it you will be at a great disadvantage in | entering any STEM undergraduate program in the US. | taeric wrote: | I'll agree that any stem targeted students should get | exposure. Not clear that it helps most students. | bawolff wrote: | Maybe for most of them, however i found calculus totally | useless for my CS degree (the only time i recall it | mentioned was defining big-oh notation). Otoh i liked | calculus so still time well spent. | | Of course, that's not counting "mathamatical maturity" | which is super important or if you're doing some specific | thing that needs calculus (hello machine learning.) | pishpash wrote: | It's pretty simple: | | - calculus if you want to do engineering | | - discrete mathematics if you want to do CS | | You can teach these in university, it's not a problem. | Calculus doesn't need to be taught in high school to | everyone but it should be available and it should be the | goal state in terms of curriculum pace for everyone so | that you should have no problem taking it by the time you | are 17 or 18 (which is what we're talking about). | | Anything else propagates back to a regressive dumbing | down in an earlier year, from an already dumbed down | curriculum by international standards. | ryandrake wrote: | > - calculus if you want to do engineering | | > - discrete mathematics if you want to do CS | | I'd guess the vast majority of software development jobs | are like "gluing one API layer to another" and "writing | simple-to-complex CRUD apps". Neither calculus or | discrete mathematics really helps if your goal is to | simply make a computer read data from database X and | display it in webform Y. | | I found all of the math required by my undergrad degree | to be totally useless in real life programming. Whether | you need _any_ math at all will highly depend on the | application domain you get in to. The most complex math I | needed as a code monkey was vector arithmetic (3D | graphics) and trigonometry (ocean and aero mapping | navigation). | VirusNewbie wrote: | The majority of MDs are reading charts or diagnosing the | flu or allergies or stitching up a wound, why should they | understand biochemistry? | taeric wrote: | This begs the question that they do. Probably safe to | assume that most don't. | | Just like it is safe to assume that most programmers | aren't good at calculus. Or discrete math. Or proofs. | ceeplusplus wrote: | I found it incredibly useful for learning all sorts of | probability theory despite hating calculus. And I really | think to be a well rounded CS graduate you need some | background in stats/ML nowadays. So many of our systems | have some element of ML-based recommendation and it's | important that a new grad can meaningfully engage with | those systems in research and in industry. | TimPC wrote: | The intention was to dumb down mathematics. If you lower the | bar sufficiently you can get everyone over it. Then we'll all | be equal, which is the goal of this curriculum. | Spooky23 wrote: | The vision is equality. One way to achieve equality is to get | better at doing something and improve the outcomes of what you | are doing. | | Another way is to lower the standard to make the outcome easier | to attain. It's gross and racist. | H8crilA wrote: | What does "calculus" here mean? I'm not American, no idea | what's included in that word and what's outside, in this | context. Does it mean limits, derivatives, integration | (Newton), maybe even some high level talk about ODEs for the | "very best" schools? Anything more, anything less? | | Also, in case anyone is also wondering, 8th grade means 13-14 | years old. | pishpash wrote: | Calculus without analysis, so the mechanical rules and | recipes of real analysis of well behaved scalar functions | that an engineering course might use (and that were used by | the developers of Newtonian mechanics in the pre-modern era), | limits on intervals, Riemann integration, etc. | SOTGO wrote: | Limits, derivatives, and integrals mostly, plus many | applications. There is also a heavy emphasis on computation | and very little emphasis on proof. | Jensson wrote: | Yes, they talk about the normal things average high school | students learn about derivatives and integrals all over the | world. | zdragnar wrote: | At my US school around the year 2000, precalc was one option | for seniors, which primarily focused on limits and | derivatives. The more advanced pace AP calc course also went | into integrals. Beyond that I don't really recall, but by | that point you also had gone through courses focusing on | basic geometry, basic algebra (using variables, factoring), | and a course dedicated to trigonometry (mostly memorizing the | rules around figuring out angles). | | There were some other courses that had math involvement, but | were more business oriented (finance / accounting type stuff) | and I don't recall if they counted towards core math credit | requirements. | cowboysauce wrote: | It varies throughout the country. But for me it was: | | * Calculus I: limits, derivatives, integrals | | * Calculus II: More integration techniques (substitution, by | parts, table), infinite series and convergence, basic | numerical methods | | * Calculus III: multi-variable calculus (partial derivatives, | multiple integrals), vector calculus (gradient, divergence, | curl, surface and line integrals) | | ODEs were a class you could take after Calc II. | commandlinefan wrote: | Wait, is this high school or college? That looks like 3 | different courses you're listing there - I've never heard | of a high school offering more than a single year of | calculus. | texaslonghorn5 wrote: | Some schools which allow students to take calculus 1 and | 2 before senior year also offer multivariate calculus | (3), differential equations, and linear algebra courses | to round out the fourth year of math. This is especially | prevalent when students can take geometry in 8th grade | which leads to Algebra II, Pre-Cal, Calculus, Advanced | Math Electives as the four year progression. | majormajor wrote: | My public high school in TX had that track. | | Is this uncommon in California schools? | | (I think the idea that it's in any means required to be | able to do STEM in college is ludicrous, but having the | option is great.) | commandlinefan wrote: | > limits, derivatives, integration (Newton), maybe even some | high level talk about ODEs | | My son is taking high school BC Calculus (one step above "AP" | calculus) this year. It includes limits, derivatives, | integration (including integration by parts and partial | fraction decomposition), ordinary differential equations, | infinite series and taylor/mcluarin series. | namelessoracle wrote: | Goodharts law is in effect. They have a target they are trying | to hit and are aiming a different way towards it. | | They are optimizing towards "High School Graduates" and | "College Graduates". And if they need to destroy the value of | being any kind of graduate to get there. So be it. | cloutchaser wrote: | My guess is the intention is to be able to say that the | framework benefits disadvantaged people. But like almost any | policy like this all it does at best is pull down people at the | top, at worst pulls down everyone making the situation worse | for everyone. | | You can have separation of education by ability, and progress, | or you can have equality, and everyone being pulled down to the | same low level. And suffering for everyone. You can't have | both. Take it from someone who has direct experience with | communism, which is the same mentality that drives this. | pessimizer wrote: | > You can have separation of education by ability, and | progress, or you can have equality, and everyone being pulled | down to the same low level. | | This seems a little off. What we're talking about (and what | it seems like you're defending) is directing _more_ resources | towards the most gifted. It 's fine to believe that, but it's | an argument to give the most to those who have the most. | Nobody is pulling anyone down, and communists are as happy to | grant power and resources to those with aptitude and | connections as capitalists are. | | edit: with the constant attacks on teachers, it might be more | realistic to stop aiming for calculus in high school. Any kid | who manages it within a gutted public system would have | gotten there anyway, no matter what situation they found | themselves in. They can download calculus books and calculus | lectures now; with the internet a feral education is within | everyone's reach. | ralph84 wrote: | How is it directing more resources to allow students to | take courses at their level? It's not like you have to pay | high school math teachers a higher salary to teach | calculus. Your typical public high school in California has | 1,000+ students. With that many students it's not going to | be hard to find 20-30 students to register for a calculus | class. It's not like you're running a special private class | just for a few gifted students. | hellisothers wrote: | As the parent of a child who is gifted at math this is | wrong on so many levels, I'll just state one. My kid only | has so much time he can genuinely focus on "school work" in | a day, why should he be forced to spend "school" time on | things wildly beneath his level and then come home and | spend his own time on additional "school" type work? | spywaregorilla wrote: | I don't think calculus should be a goal to be honest. Or at | least not as taught. Calculus could be greatly condensed to a | shorter theoretical view. The ideas of understanding | differentiation and integration are great. Memorizing the rules | of doing it is pretty painful and likely won't stick. But | that's the bulk of classroom time, homework, and testing. | FFRefresh wrote: | I don't doubt that the people crafting these proposals care. I | think they truly believe they are doing the right thing. I | personally think it's just increasingly popular, mistaken moral | beliefs that inform these types of proposals. Some of the | underlying beliefs: | | 1. Blank slate - All humans are of equal ability | | 2. Any observable differences between humans are merely the | result of social factors | | 3. Any observable differences in outcomes between groups of | humans are the result of oppression from the majority group | | 4. If you observe differences at your org/institution, it's | your moral duty to create policies which disfavor groups of | humans performing better and to favor groups of humans | performing worse, as those performance differences are due to | oppression. | | If these beliefs undergird your worldview, and your social | groups/information environment reinforce and reward these | beliefs, it is of no surprise that we'll see a lot of people | soberly propose the types of policies we see here. I can | empathize that they really do think they are fighting the good | fight, and are doing the right thing for society. | temp8964 wrote: | I don't think it has to be related to any point you put in | here. I think when STEM people comment on math education, | they easily forget K-12 math education is for all students, | not future college STEM students. | | Lots of controversies in math education between STEM | professors (especially mathematicians) and K-12 math | educators/researchers are rooted in this. In the community of | math and science education, we educators/researchers always | focus on average students who will grow into future citizens, | not STEM workers. This is really a different mindset to STEM | professors. | zmgsabst wrote: | That logic isn't used in any other discipline: | | "We only cover bad art -- we don't focus on students who go | on to be professional artists." | | "We only focus on bad English -- we don't focus on students | who go on to be professional writers." | | "We only focus on bad history - we don't focus on students | who go on to study history or social science." | | Each of those has an AP and IB track, competitions to find | elites, etc -- just as mathematics should for high | performers. | | If as an educator, you only teach to the lowest common | denominator, then you're failing the children you're | supposed to educate. | | To me, your post reads as if you're bragging about failing | at your job. | temp8964 wrote: | Students do learn art in K-12, but they could be | considered as "bad art" by professional artists... | zmgsabst wrote: | No -- you should fact check that. | | Middle and high schools start auditioning and training | students into "advanced" art, preparing them to go onto | competitions and onto serious careers in programs | differentiated from the casual art classes. | | Learning calculus won't be enough as a professional in | STEM either -- but AP Calculus is the equivalent of | audition-only advanced art classes. (Which exist all | over.) | texaslonghorn5 wrote: | Do most public schools really have the capacity to train | students for serious art careers? At least in dance and | music, at the highest levels everything is purely student | driven (school dance and music is typically not super | competitive for the serious artist) and presumably visual | art is as well. Unless you go to an arts high school, but | there aren't that many of those | zmgsabst wrote: | I went to two high schools, one very poor and one | moderately wealthy. | | Both had audition programs in art for "advanced" classes | (both music and drawing), where students were matched | with more serious training and where their bands went to | competitions and drawings were entered in regional shows. | | I think you're confusing "good, on track for | professional" with "absolute top tier" -- many students | from regular schools go on to, eg, be animators at a | studio or choir directors. | | The same split exists in math: | | - advanced classes you have to place into exist at most | schools, eg AP calculus | | - but to be the "absolute top tier", you're talking about | STEM schools and private mentoring programs | | You need the first for engineers, scientists, etc -- even | if they're not going to be Terry Tao. | pclmulqdq wrote: | So then let's have a few separate paths instead of only one | curriculum. I believe that there is a lot of value to a | basic algebra + personal finance + probability math track | that helps a future plumber understand everything they need | for their career. | | Depriving college-bound students of calculus, though, is a | bad move. A lot of philosophy also involves calculus- | related arguments (ie if we cut up space in really small | pieces, what do we get?), so it has applications outside | the STEM fields. | ceeplusplus wrote: | That's fine, but it's the reason we have tracks. Future | STEM workers can go into the advanced track and everyone | else can go into their own track. | | Germany separates people into vocational school and | something closer to what we'd consider high school in the | US by 9-10th grade. If you embrace the idea that some | people are simply less suited for intensive math - whether | it be because of work ethic, inherited IQ, lack of | interest, etc. - and give them a path towards jobs that | better fit their skillset, I think you'd see a lot less | people drowning in college debt because they got a degree | in sociology when they got weeded out of Calculus 101. | temp8964 wrote: | Totally agree. That's why there is a CTE (career and | technical education) movement in the US now. Perkins V is | the strong push in this regard. | https://cte.ed.gov/legislation/perkins-v | bjt2n3904 wrote: | It feels so good seeing this utterly ridiculously ideology so | thoroughly debunked, and rightfully attributed for the | destructive attacks on education. | | I've run into it so often by a vocal minority who slander | anyone who objects. Fortunately, the popularity is waning. | majormajor wrote: | It's hard for me to square your claim that there's a dominant | belief that all humans are blank slates of equal ability with | the sheer volume of messaging I see in both government- | sponsored and private media about embracing differences, | follow your own goals, find your talent, etc. | | I see a lot more stuff that would lead a kid to believe "it's | ok that I'm not good in math" rather than "I could be good in | math if I wanted to be." | | Frankly, I think this is actually worse educationally than | what you suggest. | | We need to find more ways to reward effort instead of pre- | existing ability (regardless of how that pre-existing ability | is gained... the kid whose parents got him ahead of the curve | through high school math and then bombs out after taking | university-level Calculus is similarly harmed by the current | system as the one who's shunted away from ever being | challenged). | hintymad wrote: | I don't understand how these people could consistently ignore | facts. Case in point, I could earn way more than Scott | Aaronson or had way more social privilege than him, but you'd | think I'm crazy if I claim that I can be as good at maths or | quantum computing as Aaronson. | aaplok wrote: | That kind of arguments goes in favour of the CMS. If you | assume that only a handful of geniuses can do maths then as | a society it makes little sense to allocate resources | toward something completely inaccessible to the masses. | Designing the education system for Scott Aaronson to the | detriment of everybody else would be a mistake socially and | economically. _That_ is how these people think, not some | nonsense blank slate theory. | | In reality it's not quantum computing that we're talking | about, it's high school calculus and algebra. You don't | have to be a hardcore blank slate proponent to believe that | most people _can_ learn it. And that is what these people | don 't believe. | | It's important to consider the goals of this committee. | They propose this reform _because_ they oppose the blank | slate theory. The current structure really isn 't | appropriate to most people. Because it relies on a wrong | form of the blank slate theory. They offer the wrong | solution in my opinion, because they end up going too far | the other way. | zozbot234 wrote: | They're working with a bizarro Blank Slate theory | according to which every student should simply be | learning their math by themselves, and if they fail it's | their own darn fault, or perhaps society's fault, or | anyone else's fault, but certainly not the _teacher_ 's | fault. Because the teachers all have Education degrees, | and that's what they were told in Ed School. So don't | anyone dare "demean" their job by suggesting that they | have actual _work_ to do in properly educating their | students. | mirceal wrote: | it's not about being better than him. it's about the | theoretical possibility of being better + the virtue | signaling that comes with the theoretical possibility | majormajor wrote: | Do you disagree with the following re-formulations: | | _Some_ observable differences are due to social factors. | | _Some_ observable differences by certain groups are the | result of past actions by other groups. | | You _should_ favor policies to correct for the result of past | harms. | | One cannot reasonably claim that no groups in the US are | still disadvantaged today due to actions taken on a | centuries-long timescale. It seems willfully unfair to stick | your fingers in your ears and just say "I'm not actively | discriminatory, so there's no need to try to mitigate things, | everything is peachy." | paulcole wrote: | > Blank slate - All humans are of equal ability | | This is generally true. | | People can find extreme examples that "disprove" this but | they're generally wrong. Most things people do aren't that | hard and people have the ability to learn to do them -- they | either choose a different path, have fewer choices, or just | don't care. | | And yes, before you ask, this includes computer programming. | mikebenfield wrote: | This is so obviously false that I'm always amazed there are | people who actually believe this. | | In _every_ activity I've ever participated in where I can | observe many people's performance and progression - | including powerlifting, bodybuilding, various ball sports, | mathematics, chess, theoretical CS, software engineering, | etc - it is transparently obvious that people's natural | abilities vary dramatically. | | Although it's not the most common scenario (training and | experience do matter), I have seen many situations where | someone with, say, 6 months' haphazard and lazy experience | will absolutely _crush_ the performance of someone with 3 | years of serious and dedicated training. | | Talent is real. | paulcole wrote: | Thank you. I am quite stupid. | | Talent is real, but generally speaking, ascribing failure | or lack of progress to lack of talent is a mistake. | hintymad wrote: | I'm not sure what "generally" means here. In professional | sports, my failure of not getting into any major league | will be due to your lack of talent. In higher-level math, | my failure of passing any exam will be due to your lack | of talent. In chemistry, my failure of not being able to | consistently reach precision of under 0.1% is due to my | lack of talent (and trust me, I really tried and followed | all kinds of instructions in greatest detail, or so I | thought). In mechanical engineering, my failure of not | bing able to piece out a 3D model from a 2D schematics is | due to my lack of talent. In medicine, my failure of not | be able to memorize thousands of latin terms for all the | bones and organs is due to my lack of talent. In | biochemistry, my failure of not being able to internalize | the energy cycle in human body is due to my lack of | talent. But on the other hand, you didn't even use a | computer until switching your major to CS when you were | 20 yet you became the best student in every single class | in a prestigious university. That's your talent. You | studied world history until you were 30 years old, yet | you switched to physics and somehow got Fields medal, | that's your talent. | | Not all failures are due to lack of talent, for sure. A | blank statement like " ascribing failure or lack of | progress to lack of talent is a mistake " in the context | of our discussion is nonetheless a mistake as well. | ravi-delia wrote: | > Most things people do aren't that hard and people have | the ability to learn to do them | | Have you considered that maybe you're just unusually | talented? I know most things people do are very hard for | me, and the few things I do are very easy. Learning history | is an uphill slog even though I love it, but math doesn't | warrant effort. For a while I just figured people that | failed math were lazy and people that passed history were | geniuses, but it turns out people have different amounts of | natural talent. It's not the start, it's the slope | paulcole wrote: | As narcissistic as I am, I don't think I'm "talented." | I'm just like everybody else -- can get pretty decent at | a lot of things. But also just like everybody else I like | to pretend I'm talented at the things I put work into. | And I like to pretend that people who are good at things | I haven't put work into are talented in a way that I'm | not. | orangecat wrote: | _As narcissistic as I am, I don't think I'm "talented."_ | | Huh. To me it seems more narcissistic for someone to say | that they have no special talent and that their success | is entirely due to their superior work ethic and years of | study and sacrifice. | | _I'm just like everybody else -- can get pretty decent | at a lot of things._ | | That's a very different claim than "innate talent doesn't | exist". | paulcole wrote: | > That's a very different claim than "innate talent | doesn't exist". | | Yes! This is why I never said innate talent doesn't | exist. | ravi-delia wrote: | I mean, by hours at this point I've definitely put more | time in to math than any other subject, but it was easy | from the start! Maybe I'm enough of a fuckup that it | intensifies differences in ability which would otherwise | be too small to notice - like math took close to 0 effort | to do and want to do, so anything else is unbearable. | Doesn't square with just how much effort I put into | history though. | mirceal wrote: | yes and no. the old nature vs nurture + not all people are | genetically gifted and a small generic advantage can mean a | huge difference in capabilities. | Aunche wrote: | >Most things people do aren't that hard and people have the | ability to learn to do them | | That's true, but it's the small minority of tasks that | require real intelligence that often matter the most. A | regular person can probably be trained to 95% the skill of | an anesthesiologist just by following instructions, but | then they would kill the patient during edge cases. | | The same thing applies to programming too. I had an | internship at a regular company, and now work at a FAANG. | The developers at the regular company are likely better at | programming than me, especially when it came to regular | tasks, but some of their technical decisions just didn't | seem to make any sense. | paulcole wrote: | > A regular person can probably be trained to 95% the | skill of an anesthesiologist just by following | instructions, but then they would kill the patient during | edge cases. | | You're making the mistake of assuming anesthesiologists | are something other than regular people with training. | hintymad wrote: | I don't know. Have you observed multiple kids in the same | family? Same parents. Same "privilege". Same pressure. Same | education down to the same teachers, tutors, books, and | parent temperament. And you know what, some of the kids | simply beat their siblings who can be years older, in STEM | or writing or reading or leadership without even trying. | Have you observed your classmates? Some are driven, | ambitious, self-disciplined, had access to all the | education they needed, and got perfect grades before grade | 8 or whatever. Then just one day, he simply couldn't | understand maths or physics or chemistry or computer | science, and they simply got left behind and couldn't even | study STEM in college because they couldn't pass the | placement test. In the meantime, their classmates, less | privileged, didn't really understand everything taught in | elementary school, didn't have nor need tutoring or even | challenging text books, simply became the best students at | anything STEM in high school and in college, and again, | without much trying. | | Or, do you really think every 2-year old kid can teach | their neighbor kids maths and then explained what groups | are when he was 7-year old like Terence Tao did? I tried my | own kids. Needless to say, I failed, miserably. | deathanatos wrote: | Me & my sister grew up, like you say, in the same family, | same parents, same pressure. We largely went to the same | schools, even. She probably acceled further, | academically, than I did. (She probably went to the more | prestigious college, her GPA/SAT/etc. were better, she | earned a doctorate, while I got a BS...) | | Without pointing to a vague notion of "we're different | people", I think there's a few key things that _were_ | different, despite everything that was the same: | | * She's the second child, I'm the first: there were some | things in my education that my mother literally said "we | are fixing that for her". (And I should note that I don't | resent this: my mother was clearly doing the best she | could with the information she had -- and because she | loved us. But she had more information during Round 2.) | | * Education is a finite resource: in my home state, | whether I got into a decent school (i.e., a magnet | school) was dependent on the literal roll of a dice. | (Literally literally. I.e., list of names goes in, gets | shuffled, top _n_ go to good school & gets educated, | bottom _m_ talent gets wasted.) In the worst case I was | 5th? 6th? from the bottom of a several hundred person | long wait list. She got in. She got a year in the magnet | system that I didn 't (I got entry a little over a year | later). That missing year was an _enormous_ detriment to | my education and growth; it was such a clear detriment my | parents were contemplating whether they could afford a | Catholic private school (we 're not Catholic) or simple | home-schooling. Had they had the gift of clairvoyance, I | think they _would have_ the moment I was denied. | | * Almost certainly the gift of a computer got me | interested in CS. She didn't get one, and her interests | are different. (She's still STEM, likely due to our | parents.) | hintymad wrote: | To digress a bit: good education will be a finite | resource as we have finite number of good educators and | good schools. I don't think it's possible for everyone to | access good education, especially given that we have | different definition for "good education". Saying | everyone should go to MIT (or any scarce education | resource) is like saying living in beach property is | human right. Maybe so, but it'll be a different topic. | troupe wrote: | Books are a finite resource, but not really limited for | any practical purposes at least in the US. Used books are | inexpensive, libraries are readily available, most things | out of copyright are available online, etc. | | Education is following as similar course. Things like | MITs open courseware, edX, etc. are making it | increasingly easy to get the educational content from top | teachers regardless of how limited these teachers are. | | (Having access to an education is not the same as | actually getting a degree, and getting a degree isn't | always the same as getting an education.) | | But there has probably never been a time in history where | more people had free or inexpensive access to the top | educational content in the world. | hintymad wrote: | Education content is definitely ample now, including text | books and references. we even have great communities to | get answers to our questions. Unfortunately the | bottleneck of education just switched to access to good | teachers. A good teacher inspires students, identifies | exactly why each student has difficulty understanding | something, explains intuitions behind the most difficult | concepts, designs highly tailored homework, leads | engaging seminars, and keeps students in their discomfort | zone. As in STEM field in general, lab staff, equipments, | chemical agents, lab materials are generally scarce | resources too. | troupe wrote: | I understand what you are saying, but I would argue that | lack of access to teacher is less of a bottleneck than | drive, desire, and motivation. A motivated individual is | going to have no trouble finding what they need to learn | and places to ask questions for things they don't | understand. | | I see where you are coming from on access to labs, | chemicals, and equipment. But someone who has fully | availed themselves of everything they can learn from | free/inexpensive online classes, books, forums, emailing | people, etc. is headed on a path where they have a high | probability of getting access to those types of things | once that is the only thing blocking their continued | education. | hintymad wrote: | I don't disagree with you. I just think "drive, desire, | and motivation" is part of one's talent. The progressive | policies will not hurt the best students because they | students will find their resources anyway. It is the | middle, the vast majority like me, who would get hurt. | They would think that they got good education, and then | realize that their understanding of maths is so shitty | that they can't even pass city college's dead simple | placement test. Oh, I didn't make this up, either. NYT | reported this miserable experience of a straight A | student, and I was shocked to read it. | causi wrote: | Problem being an extremely significant portion of that | blank slate is written before the child even enters school, | let alone makes it to middle and high school, and even | during those times it is impossible for a school to make up | for a horrible home life. We single out and spread stories | about people who raised themselves up because it's not the | norm. The vast majority of people whose parents don't talk | to them as infants, don't read to them as toddlers, don't | listen to them as children, and don't keep from hitting | them as teenagers _will_ radically underperform both as | students and as adults. Mucking about with the education of | students who _haven 't_ been sabotaged by their parents is | governmental thumb-twiddling. | innagadadavida wrote: | You are leaving out who is involved and what commercial | interest will be benefitted from these policies. It is likely | those commercial interests are the ones sponsoring and | pushing these by finding sympathetic folks. | | The important thing to note here is- if you reduce the bar in | high schools, a lot more students will end up in college - | more money will spent, more loans will be written out etc. | [deleted] | wonnage wrote: | 1. This is kind of a founding principle of the country, so... | | 2. This follows from #1, if we rule out nature then it must | be nurture. Also, you must not be a parent if you'll accept | "some kids are just dumb" as an excuse | | 3,4. Replace "oppression" with "competition". I think it | might sound better to you. But the conclusion is the same. | | You want to prevent winners from accumulating an advantage, | eliminating all others (which sounds vaguely genocidal in | this context), then you have to handicap winners and support | the others. And the fact that the wealth distribution in | America is so uneven certainly suggests that the initial | premise is true (i.e, winning allows you to accumulate and | compound advantages with repeated victories). | sacrosancty wrote: | 1. So the country is founded on a lie or you misread that | founding principle. | | Those compound advantages you're talking about are good | things that we want people to have because they help them | do more good for society. You seem to want to handicap them | in the name of fairness. Where does that thinking end when | you realize that the founding assumption (1. above) is | false? Disfiguring beautiful people to prevent them | accumulating the compounding advantages that come with | beauty? Brain damaging intelligent people? | hintymad wrote: | I thought the OP was being sarcastic. | abfan1127 wrote: | a founding principle is not everyone is of equal ability. | The founding principle equality of opportunity. The | government won't hold you back because you are a | (peasant|lower caste|other arbitrary decision). i.e. | Everyone gets to go to school, but not everyone learns the | same (qualitatively or quantitatively). | wonnage wrote: | Don't you think the government deciding you're not fit | for going to college would fall into this problem? | rhexs wrote: | The government wouldn't prevent you from going to | college, it just wouldn't voluntarily pay for you to go | if you didn't test well. You could pay your own way, seek | external scholarships, etc. | | As of now we effectively underwrite anyone who wants to | go, often at the expense of the student racking up debt | for a useless degree and later the taxpayer who will | inevitably have to subsidize them. | pclmulqdq wrote: | When I went to public school in a privileged | neighborhood, the "honors" track was opt-in for the | parents and students. I don't think you have to go | straight from "the government shouldn't decide whether | you are fit for college" (which I agree with) to "there | should only be one curriculum for everyone." | jollybean wrote: | 'Equal opportunity' is not a 'founding principle'. | | Just that they are 'equal' i.e. before God, or before the | Law. | | That one man is not from some superior lineage, that | makes him a superior being. | | I would be the founding fathers would have no problem if | one man decided to 'discriminate' among others for some | arbitrary reason - even if they were landholding men of | high status etc.. | tonguez wrote: | " 1. Blank slate - All humans are of equal ability" | | " 1. This is kind of a founding principle of the country, | so..." | | yes those slave owning people really thought their slaves | were the same as them, totally dude | wonnage wrote: | Yeah I heard we tried to end the slavery part somewhere | along the way and have been somewhat successful, but we | definitely kept the first one. | [deleted] | adamrezich wrote: | > 1. [All humans are of equal ability] is a founding | principle of the country, so... | | curious to learn how you arrived at this conclusion? | mindcrime wrote: | _1. This is kind of a founding principle of the country, | so..._ | | Is it? Saying "all mean are created equal" has a lot of | interpretations, of which many valid ones do not include | "all men are born of equal ability in every regard." Given | that some people are born to grow up to be 5'4 and weigh | 100lbs and others are born to grow up to 6'7 and 320lbs, it | should be clear that not everyone is "equal" at least in | terms of their physical abilities. I'm pretty sure the | Founders were aware of this, making it highly unlikely that | their version of "created equal" meant "exactly equal in | all terms of ability." | wonnage wrote: | Hey, thanks for correcting me, I totally thought that | this line meant that the founders had somehow invented | cloning and made everyone physically identical | | Regardless of interpretation, I'm pretty sure deciding | whether a kid is fit for the elite/intellectual track or | the physical labor track at the tender age of 10 based on | whether they can do some tests is not in the spirit of | "all men are created equal" | mindcrime wrote: | _Regardless of interpretation, I 'm pretty sure deciding | whether a kid is fit for the elite/intellectual track or | the physical labor track at the tender age of 10 based on | whether they can do some tests is not in the spirit of | "all men are created equal"_ | | And I would agree. But your earlier comment seemed to | imply a much more absolute stance. That's what I would | disagree with. | klodolph wrote: | I don't think that those beliefs are a workable explanation | here. | | These proposals come from committees and groups of people, | and it's just not realistic to write off the entire group of | people behind these proposals as having some uniform set of | beliefs like that, especially when they give other rationales | for the proposals! | | The current school system makes decisions in middle school | (8th grade and earlier) which determine whether or not each | particular student will be able to take calculus in high | school. This is, simply put, _insane._ | | Because it's obviously insane, when you introduce questions | of race and class into the mix, then it's easy to apply | pressure to the department of education to come up with a | proposal that changes things. And then you end up with bad | proposals... why? Because these proposals are produced by | poorly-shepherded committees full of government employees | under political pressure, and it's much easier to come up | with a bad proposal that responds to political pressure than | it is to come up with a good proposal. | | There's just no need to try and explain that this proposal is | bad _because the people who made it have bad beliefs._ I 'd | characterize this as fundamental attribution error here... | "the committees made a bad proposal because of wrong beliefs" | versus "the committees made bad proposals because it's easier | to respond to political pressure than to write a good | proposal". | ravi-delia wrote: | I feel like in this case fundamental attribution error | would go the other way, no? The explanation you offer is | that there aren't circumstantial factors dominating the | decision (the beliefs on this particular issue), but a | fundamental flaw in how committees work. To be clear, I | agree that this is an inevitable result of the decision- | making structure, I've just only ever seen fundamental | attribution error referring to mistakes in the other | direction. | klodolph wrote: | That's an interesting way of looking at it. | | I would never describe someone's beliefs as | "circumstantial", and I would also never think of being | on a committee as something "intrinsic". | ravi-delia wrote: | Ah, now I get it! I was thinking of the _committee_ as | the entity, not the people on it. Then the question is | "why did the committee make a bad call?" where "the topic | in question coincidentally misaligned with the views of | the members" is the specific cause and "committees always | make bad calls" is the general cause. But looking at it | from the perspective of the people makes it clear what | you were going for | smugma wrote: | While I agree that the proposals are bad, I don't blame | "committees full of government employees". One of the lead | proponents/authors is distinguished Stanford Professor Jo | Boaler. It's interesting that a lot of the arguments made | in favor of the changes are done in the name of equity, but | Boaler herself has been put on the wrong side of racial | equity, threatening to call the cops on a Black Berkeley CS | professor. This article [0] is gossipy, but it's both | interesting and relevant how "Nice White People" can hurt | the minority groups they are supposedly trying to help. | Hurt by taking away opportunities to take calculus, and | hurt by threatening legal action against one of the few | minority CS professors at a leading research institution. | | [0]: https://www.sfgate.com/bayarea/article/Stanford- | professor-Ka... | fn-mote wrote: | > One of the lead proponents/authors is distinguished | Stanford Professor Jo Boaler.. | | I have an issue with the parent's gossipy put-down of | Professor Boaler. | | I think it's important to emphasize that genuine | intellectuals who have put serious thought into this | proposal support it. I would prefer more serious | engagement with it, even if on HN the majority disagree. | zozbot234 wrote: | > The current school system makes decisions in middle | school (8th grade and earlier) which determine whether or | not each particular student will be able to take calculus | in high school. This is, simply put, insane. | | It's not clear that this is the case. The "current | approach" is to offer Algebra I in middle school, which | ought to leave plenty of time for students who want to | shape up in math and be prepared for HS calculus to do so. | Push advanced math later in the curriculum, and you just | expose the students to even higher-stakes dilemmas. | Lowering standards is no solution, since you'll just end up | with lower education quality for all students, that will | make it even harder for them to catch up to reasonable | levels. This is the broad background of OP's letter. | 7speter wrote: | I don't necessarily agree with the proposal in california, | but do all students need to take calculus in high school? | What about solid coverage of algebra 2 and pre calc before | higher education. Community college is a great place to | take a calc class (or even a pre calc class) affordably. | Source: took pre calc, calc and stat in community college | after being signalled to that I was terrible at math | throughout high school. | andrewprock wrote: | No one is suggesting that all students take calculus in | high school. | | What is being recommend is that no one take calculus in | high school. | | Both of these ideas are bad, but only one of them informs | the California Math Framework. | AlchemistCamp wrote: | > No one is suggesting that all students take calculus in | high school. | | It's very commonly taught in 10th grade in France, | Germany, Singapore and Taiwan (where I used to teach). | It's not universal by any means but as far as I can tell, | the idea that calculus should be delayed until university | is a nearly uniquely American idea. | | https://www.mathvalues.org/masterblog/calculus-around- | the-wo... | zozbot234 wrote: | "Very commonly" in STEM-focused prep schools (i.e. the | "academic" part of the tracked education system that's | common outside the US). Which leaves you with very | roughly the same percentages as the U.S. approach where | Calculus is an elective course. | ryukoposting wrote: | I like your argument. It's basically Hanlon's razor. | CivBase wrote: | > These proposals come from committees and groups of | people, and it's just not realistic to write off the entire | group of people behind these proposals as having some | uniform set of beliefs like that, especially when they give | other rationales for the proposals! | | You don't have to write off entire groups of people - just | the few at the top. They got there by sucking up to those | who were already at the top. Everyone else just has to keep | quiet if they want to keep their job. Worse, they're | expected to express visible support for their "superiors" | and their ideas if they want to keep their jobs. | jollybean wrote: | There are no two people in the world with the same beliefs | - nobody is suggesting that. | | There is however a very broad movement of people who | believe that unequal outcomes are a manifestation of racism | and so they act accordingly in their roles in government | etc.. | | Many of these people are in the civil service and so this | will influence their view. | | It would be 'insane' to ignore this movement, it's one of | the most powerful social forces in the US right now. | klodolph wrote: | You're saying it's one of the "most powerful social | forces in the US right now"... is there any particular | reasoning here? To be honest, it sounds like an extremist | take on the nature vs nurture argument which has been | playing out for millennia and I don't see a reason to | believe that somehow the extreme version nurture side of | the argument has become dominant here. If anything, it's | easy to remember the pendulum swinging back and forth in | the past decades, and the pendulum doesn't seem to swing | that far in either direction. | | > Many of these people are in the civil service and so | this will influence their view. | | It influences the political pressures placed on people in | the civil service more than anything else. People in the | civil service are in the civil service for a long time, | typically. Often they are in the civil service for | decades. On the other hand, elected officials and | political appointees rotate in and out much more quickly. | | I know people in the civil service, they have a much more | long-term and level-headed view of things, and my | impression is that they "weather the storm" of changing | political pressures. At least, the ones who survive in | the job do. Political appointees and elected officials | are much more mercurial. Appointees know that their | position is (somewhat) an extension of their own | political power to begin with. | jollybean wrote: | Yes, it's been going on for a while. | | Christians are fond if it: "You have an innate, direct | relationship with God, in his eyes you are equal to the | The King" etc.. | | But we've only had 'governance' in the broad sense for | 100 years. | | And we've never really tried to apply such principles | into education until the 1960s. | | Now we have actually made incredible progress on social | issues, we have our 'wars' in Social Media with Holy Anti | Racism Fanatics trying to do their best - because 'racism | is bad' - which of course it is - and 'systematic racism | exists' - which of course it does - but the 'kernel of | truth' of these issues drives people into ideological | fervour as though it's some giant overwhelming issue, | when really it's not. Racism is still pernicious, but | it's not fundamental. | | And FYI don't think it's all rubbish. | | For example - 'Math' is heavily based on prerequisites. | If you 'fall back' in Grade 4, you may never be able to | 'catch up'. While that's true in general, it's not as | acute as in math. | | Poor kids might be far more likely to 'fall of the | bandwagon' and a lot of poverty might be due to | systematic racism, and so the 'Hard Requirements' for | certain things may not be ideal. | | You could have 'summer school' or 'after school' or | 'accelerated catch up' programs. | | Those would be 'reasonable' solutions in my view - and | FYI these are mostly issues of poverty, not race, they | are couched as racial issues because that's what fires | people up. | | Edit: and yes, I agree 'most people in the civil service' | are level-headed. Most people actually are. But some | groups have outsized voices, amplified by 'allies' | elsewhere. | | The 'Anti Racism Agenda' is a 'fundamental pillar', like | a religion, of 25% of the US population, and they are | pretty active about it. And the actions of the most | extreme 5% end up really upsetting other people. Much | like a very powerful fool using made up constitutional | manoeuvres to try to take over the government would upset | a lot of people as well. | | Good intentions, surely, but that doesn't make them | right. | tonguez wrote: | "I don't see a reason to believe that somehow the extreme | version nurture side of the argument has become dominant | here" | | watch "the news" or go on twitter | klodolph wrote: | Twitter's algorithm promotes whatever tweet will make | people angry, because angry people spend more time on | Twitter. I'm on Twitter, but I've been on Twitter for a | while now, I've selected who I follow, and my feed just | doesn't get that kind of noise in it at any significant | level. Most of what I see on Twitter is people arguing | about Elden Ring or showing off how they can access | YouTube from a Mac SE or something. | | "The news" is dominated by organizations which are trying | to maximize their social media engagement metrics so they | can get more money from advertisers, so they're subject | to the same forces that drive Twitter. | | Neither of these sources reliably give you a picture of | national affairs. Right now the best I can do is get a | picture of local affairs by talking with people that I | happen to encounter because I live near them. | drewwwwww wrote: | jollybean wrote: | Well Mr/Ms Drewwwww - you have very graciously made point | for me. | | Since I have no such 'scientific racism' views and claims | of 'proto-fascism' are ridiculous at face value ... | | ... that a common person would take some rather mundane | comment somewhere to mean those things, implies that | they've been radicalized in some way in the manner that | I've described. | | "Racists is everywhere, under my bed, in the jingle for | that product, in our schools! Math is racist! We Need | Action Now!" | | 'Anti Racism' is a reasonable concept at face value, but | the issue has obviously created groups of wayward | ideologues in large swaths in the US, who are more likely | than not to be involved in the civil service, | particularly in education. | | Since 'improving education' is a perennial issue of | contention anyhow - if we throw 'math is racist' into the | fire, along with legions (at least a critical mass) of | fervent supporters - and then finally allow the hollow | politicians and media to misrepresent and aggrandize all | of it in bad faith (votes, money, attention, power etc.) | ... then we have yet another toxic cocktail of public | malaise and dysfunction distracting us from dealing with | the core issues. | rayiner wrote: | I know progressives love to portray things as a dichotomy | between "fascism" and "equity" but that leaves out the | position that the majority of people in minority groups | actually support--color blindness: | https://www.pewresearch.org/fact-tank/2019/02/25/most- | americ... | rayiner wrote: | It sounds like you and OP differ only in that he thinks the | people on the committee have these beliefs, while you're | implying that they're afraid of "political pressure" from | people who hold these beliefs. Which I suspect is correct. | klodolph wrote: | I was thinking less that they are "afraid" of political | pressure, and more that responding to political pressure | is one of the things that these committees do, by design. | | Political pressure is a manifestation of the population's | problems / beliefs / perceptions. It's wrong to bow | completely to political pressure, but it's also wrong to | ignore it. | michaelt wrote: | I agree with you somewhat, but I think there's an | important distinction to be made. | | If a political decision-making process concludes "men | account for more road traffic deaths than women, but | we've decided that gender can't be taken into account | when pricing car insurance" that's fine; the facts have | remained the facts, and a political decision has been | made by a political process. | | But if the same process concludes "men and women cause | the same number of road traffic deaths" the process has | gone off the rails _despite the fact the outcome is the | same_ because in one situation the facts have been | acknowledged and the decision to act contrary to them | made knowingly; while in the second situation that isn 't | the case. | namelessoracle wrote: | If you talk to these people though. They DO have bad | beliefs. Let's not even talk about politics. Their goal is | to get a kid a degree,(especially in groups that dont | normally get degrees) and many of them believe just having | the degree to get past the job resume hurdles is good and | helping people. | | They ignore the fact that the degree is supposed to be a | proof of "This person has X skillsets at minimum". It no | longer is. There is basically no job in the United States | that cares if you have a high school diploma or GED other | than government jobs. They are repeating this process with | College right now. The College Diploma is now the new High | School Diploma, and pretty soon jobs are gonna want Masters | or Doctorates for entry level. | | This is a bad belief, they don't (or won't) understand that | they are ruining and devaluing a thing by their actions and | beliefs. | munk-a wrote: | Given the situation on the ground you can comment that | it'd be great to stop de-valuing college degrees but I | think it's pretty clear that ship has sailed. A lot of | jobs do unnecessarily demand college degrees, even going | so far as to accept irrelevant degrees... anytime you see | "Our ideal candidate has a BS from an accredited | university" you can be confident that an arbitrary and | discouraging requirement is being placed on the post. | Now, in reality, a lot of employers don't actually care | about those "requirements" but young people often don't | realize that, and the ones that do can't be certain their | uncertainty won't be invalidated by the time they secure | a diploma. | | I don't have a specific comment on the policy under | discussion, I'm not a californian and I'm not familiar | with the specifics - but telling people "You'll be fine | without a degree" isn't going to go over well and, | honestly, is asking the recipient to accept a large risk | regarding their future while you, an employed person, | have already passed that hurdle. American colleges | definitely have issues with over enrollment but even if | wanting that state is a "bad belief", it's certainly an | accurate belief. | zozbot234 wrote: | You can't get a college degree without passing the | College Algebra weedout course (let alone Calculus, which | is required for the bulk of STEM courses), and you can | only realistically pass College Algebra by getting a lot | of rigorous math in K-12. Lowering the bar is doing | _every_ student a disservice, and the most vulnerable | students will be the hardest hit. | namelessoracle wrote: | You'd think that but there are work arounds. | | Yes pretty much every college requires "college algebra". | But some schools have "college algebra for stem majors" | vs "college algebra for non stem majors". Guess which one | is easier, has lots of bonus credit and extra curricular | stuff to earn extra credit. (You attended the college | showing of "vagely related math movie?! Here's 10 points | on your final!") And also grades on a curve. Also you | only need 69.5 (and sometimes just a D!) to graduate. | | There's also other cheats/hacks. Like lots of state | schools will let you transfer from a community college | with credit for your "core courses", and some of those | have questionable standards. There's also the fact that | college algebra usually has some kind of test out or | online option. There was a whole sub industry of "pay you | to take the online test for me" at colleges for stuff | like college algebra. Some of those courses did have some | kind "you have to take 1 test in person so we know its | you" rule. But they didnt check super heavily that you | were actually that person other than a cursory | examination of your drivers license name matched who was | supposed to take the test. (and oh boy let me tell you | about how covid and masks interacted with all of that) | | Dont get me started on the "Statistics for Sociology" | that was different than actual "Statistics" (but | fulfilled the Stats requirement for the degree) | | This is also ignoring that taking College Algebra to | begin with IN COLLEGE. Was a major sign you were not a | Stem Major. Stem Majors took that in high school and were | taking at minimum precalculus. (and even that was viewed | as the slow lane, you should be talking Calc 1 as a red | blooded STEM freshman) | WalterBright wrote: | > pretty much every college requires "college algebra". | | Caltech didn't. In fact, they expect you to know calculus | before entering. I didn't, and that nearly capsized my | college career before it left the dock. | zozbot234 wrote: | I do expect that such "workarounds" will always exist. I | just don't think they're more _realistic_ than just | getting some good-enough math fundamentals in K-12, | without mucking about with "data science" silliness. | (Data literacy is of course appropriate to Science class, | and the letter even mentions that.) | WalterBright wrote: | > Statistics for Sociology | | An acquaintance asked me if she should take "Calculus for | Artists" after I suggested she take a calculus course. I | laughed, and said that such a course should be named | "Pretend to Learn Calculus". She should take a real | calculus course, which she did, and did well in it. | | If you're in college, stick to the real math classes, not | the "math for losers who are forced to take a math | class". You'll be with other students who want to learn | math, and you'll have a prof that wants to teach math | (the loser math course has a prof who doesn't want to be | there, either). It'll be a much more pleasant experience. | | Hey, if I was running a college, I'd have the two track | math system, too. That way the students who want to learn | won't be bothered by the ones who don't. | [deleted] | devindotcom wrote: | cool_dude85 wrote: | No, even Ayn has never claimed to be a psychic, able to | penetrate the deepest thoughts of school board members to | distill their entire world view down to a bulleted list. | pfisherman wrote: | I never understood why people try to make "blank slate" into | a binary thing. | | Can people not have varying degrees of physical and neural | plasticity? Perhaps some people are more like blank slates | and can adapt more readily than others? Maybe plasticity | changes with age? | dionidium wrote: | There's almost no opponent of the blank slate theory who | thinks societal factors never matter. There's only one side | that takes a hard-line dogmatic view on this issue and it's | the blank slatists. | jollybean wrote: | Of course they do. Even if someone actually believed in | some 'hard' type of ideology, they might not act that way. | | It's just a 'general set of principles', intuitions, pop | culture ideals that lead a large group of people to | assumptive believe that 'unequal outcomes are driven mostly | by systematic racism' and that's that. | | Ergo 'the world is deeply racist' and 'there is racism | around every corner' including in your math textbooks and | teaching. | | Ad nauseum. | | Some of it is actually correct. | | Some of it is reasonable from an intellectual perspective, | but it's hard to take anything from it. | | Much of it just ends up being toxic. | dragonwriter wrote: | > Blank slate - All humans are of equal ability | | Not only does the earlier version of the framework explicitly | reject this view, it cited specific empirical studies that | the broad approach targeted (which I gather had not changed | in the revisions which is why the complaints remain despite | some revision to details) was better for people across the | ability spectrum. | | Similar points apply to each of your bad-faith assumptions | about the underlying beliefs. | FFRefresh wrote: | > Not only does the earlier version of the framework | explicitly reject this view | | Can you share that explicit rejection of the idea that | there are not innate differences in ability, in the CMF? I | have not seen it myself, thank you ahead of time. | | To share what I've read, and colors my views a bit, is the | following, from 'Chapter 1: Mathematics for All' of the | Second Field Review [1]: | | > An aim of this framework is to respond to the structural | barriers put in the place of mathematics success: equity | influences all aspects of this document. Some overarching | principles that guide work towards equity in mathematics | include the following: | | > All students deserve powerful mathematics; high-level | mathematics achievement is not dependent on rare natural | gifts, but rather can be cultivated (Leslie et al., 2015; | Boaler, 2019 a, b; Ellenberg, 2014). ... | | > All students, regardless of background, language of | origin, differences, or foundational knowledge are capable | and deserving of depth of understanding and engagement in | rich mathematics tasks. | | > Hard work and persistence is more important for success | in mathematics than natural ability. Actually, I would give | this advice to anyone working in any field, but it's | especially important in mathematics and physics where the | traditional view was that natural ability was the primary | factor in success. --Maria Klawe, Mathematician, Harvey | Mudd President (in Williams, 2018) | | > Fixed notions about student ability have led to | considerable inequities in mathematics education. | | Note that my pointing to this doesn't mean I inherently | disagree that hard work/education can't help improve | outcomes. I show the above citations to show that the CMF | is not explicitly denying the Blank slate theory, which is | what you are suggesting. If anything, they go out of the | way to view ideas of innate ability negatively. I'm happy | to also look at the references that you alluded to but did | not cite. | | [1] https://www.cde.ca.gov/ci/ma/cf/ (it's in the bottom | section, the format is .docx, so don't want to directly | link to it as that format can sometimes be cause for | concern on random links shared on the internet) | mc32 wrote: | It's almost a case of inmates running the asylum --but in this | case, it's not even the inmates but their caregivers who in | their maternalistic view seem to think they know what's best | for the "inmates" and are guiding them to the path to "hell" | --hell being a reduced education in an increasingly competitive | labor market. | duxup wrote: | >to dumb down math in high school? | | There's a lot of competing / strange interests in school | systems that can have well intended but BIZARRE outcomes. | | My wife works in early childhood education. At one point it was | recognized that the early childhood department should be more | involved in helping students with learning disabilities as soon | as possible. There was lots of outreach to parents to get them | into free classes and education, and most importantly screening | so they could get free services if they qualified / needed | them. | | However, it was noticed at some point by some very vocal | parents that some students with specific backgrounds were | refereed to these services more than others. These services | were provided in and out of school, the kids weren't moved to | another school or anything like that, but despite all their | efforts... The result was deemed to be some sort of bias, or | outright racism. | | Therefore it was made very clear that they could not | disproportionately "single out" students of some backgrounds | for these services, that are free, to help them learn. | hintymad wrote: | I have two theories: | | 1. Math is a differentiating subject for getting into those | competitive colleges, departments, and professions. In the | meantime, the progressives simply refuse to believe that some | people are just better at studying math. The logical choice, | then, is to dumb down math to "level the play ground". It's the | same unspoken reason why so many people pushed the magnet | schools to use lottery to pick students (I actually think | lottery with threshold can be a good solution, but that's | another subject). | | 2. Progressive math educators have been advocating self | discovery and that everyone can learn math in their own pace | for years. What educators need to do, per the progressive | argument, is to protect the fragile passion and creativity of | the kids. Jo Boaler even argued that kids should discover all | maths by their own. Naturally, we have to dumb down math | courses, otherwise we would inevitably hurt the confidence and | passion of some kids. As progressives always said: no kid | should be left behind and some people got better at math only | because they were socially privileged. I disagree with the | progressive view of math education based on my personal | experience, as so many classmates of mine simply were not | interested in STEM, and maths in particular. I'm not sure why | we don't accept that most people will hit a wall sooner or | later when learning maths. To some it is arithmetic, to some it | is calculus, to some it is abstract algebra, etc and etc. To me | I definitely lost my drive when taking courses like model | logic, and I certainly do not have interest or talent to get | good at things like functional analysis or topology or | algebraic geometry, but I make peace with it. I really don't | understand why the progressives are hell bent on insisting that | everyone can learn maths equally. | spoonjim wrote: | I think you're looking at it the wrong way. The job that the | administrator is hired for is "make Black and White test scores | identical." With only the leverage of the school, and no | broader socioeconomic levers, the only way to make this happen | is to reduce all assessment to 1+1=? (Multiple choice) | overview wrote: | The perception of math by the public has led to a cognitive | predisposition that math (especially calculus) is beyond the | ordinary person. I wish pop culture would transform this. | [deleted] | dboreham wrote: | I think I can translate this: | | It's saying that it is impossible to get the bulk of students | (with the teachers we have) to complete the standard mathematics | curriculum by the end of high school. This has always been true, | in all countries, hence "streaming". But now they're saying let's | do away with the advanced stream, therefore students can't | complete the last part of the US mathematics curriculum (which is | called "Calculus"). Rather than justify that move in terms of | cost or fairness, we're going to say "because Calculus isn't | important now". | | This is obviously completely bogus. If their assertion that | Leibnitz-style calculus isn't important now, they could replace | it with Linear Algebra, Number Theory, or some other "important | now" subject. | | Add to that, the fact that in the US the names of high school | mathematics classes are by convention. "Geometry" isn't all | geometry, for example. And "Calculus" isn't all calculus. The | classes are really : Math 1, Math 2, Math 3, Math 4, AP Math. | [deleted] | 0000011111 wrote: | Why can we do both? | | 1. Make it possible for HS students who are interested in | Calculus to take the course under the instruction from a college | profess on the high school campus. That way it would be set up | for students to get college credit for the class and they would | not need to travel to a college campus or deal with the AP exam | system. | | 2. Make it possible for HS students who are not interested (Yet) | or at all to graduate with out taking the class. Lots of student | are ready for Calculus until college anyway. No need to force | them on a single path IMO. | dfdz wrote: | > 249,871 High School Mathematics Teachers in USA [1] | | > 5,972 Math Professors in USA [2] | | 1. There are simply not enough college math professors for this | to work. | | [1] https://www.zippia.com/high-school-mathematics-teacher- | jobs/... | | [2] https://www.zippia.com/math-professor-jobs/demographics/ | dymk wrote: | Probably the optics that will ensue - Our public schools seem | intent on making sure that to ensure everybody is as achieved | as everyone else, but rather than improving education for the | bottom percentile, they'll simply remove the advanced stuff for | the top percentile. | 0000011111 wrote: | Fortuity there are free options for good online instruction | available to everyone in the world with youtube access. | | https://www.khanacademy.org/math/ap-calculus-ab | | When we focus narrowly on what brick and mortar Public HS | should and should not be teaching in regards to math curium | we sideline all the pathways for learning available outside | of this bureaucratic model. | | Folks in most places in the United States a least can check | out a Chromebook from a local library and use their free | internet to access this information. | s1artibartfast wrote: | My high school did exactly that in the 2000s. The local | Community College teacher drove to the high school and taught a | class. You got high school credit and college credit if you | payed the $50 community College enrollment. No ap test | required. | | Students could also take additional ge's at college outside of | school hours, and I entered University with about 80 credits | timcavel wrote: | lr4444lr wrote: | Efforts like this are well meaning, but only treat symptoms. The | major impetus for watered down curricula is the very rational | fear that large swaths of the student population will fail if | expected to perform at the prior standards of rigor. Schools are | not prepared to hold back massive numbers of kids, drop out | proclivity for students held back rises, and teachers will be | poorly evaluated by virtue of their students' inability above and | beyond reasonable expectations of what they can learn in a single | year given prior failure to build a proper foundation. | | How we got to this point is perhaps a lot more complicated and | politically fraught, but it has to be dealt with. Administrators | and state education leadership are often simply responding to the | incentives and avoiding dire outcomes suggested by the data. They | have to craft palatable excuses for it, and it's ultimately a | waste of time to engage those excuses on face. | poisonarena wrote: | What happened in California over the last 50 years to make math | scores plummet ? | micromacrofoot wrote: | Declining math scores can be tied almost entirely tied to | economic disparity (which unfortunately tracks with race | pretty closely). Rich kids are on track, poor kids are far | behind. | | Unfortunately I don't expect these changes to impact that. It | will likely take more rich kids out of public schools and | further widen the gap. | JumpCrisscross wrote: | > _Rich kids are on track, poor kids are far behind_ | | The achievement gap is growing. Part of this is explained | by union dynamics [1]. Part by California's elites caring | less about addressing the gap than talking about it. | | [1] https://journals.sagepub.com/doi/abs/10.3102/0013189X21 | 10063... | micromacrofoot wrote: | yuup | | > Altogether, this study provides some evidence that | contract changes are associated with the educational | opportunities of school districts' diverse and | economically disadvantaged students. | | Essentially, if you want to prioritize your child's | education above all else, get them into the richest | school district you can manage. | logicalmonster wrote: | > How we got to this point is perhaps a lot more complicated | and politically fraught, but it has to be dealt with. | | How many folks are really willing to do that? The problem is | that actually discussing the perceived root causes of this | issue will get you shunned out of polite society. | solenoidalslide wrote: | Are you referring to all of the recent laws banning | discussion of these topics labeled CRT? | | Those are the only topics I am seeing being outright banned | from being discussed or taught. | umanwizard wrote: | This is a natural consequence of the American myth/narrative | that everyone is suited for academic high school and | university. Other countries simply sort people into different | schools much earlier, and spend the high school years teaching | meaningful vocational skills to those not on the academic | track, rather than wasting everyone's time. | brightball wrote: | The approach makes sense. How are claims of bias within the | process handled? That's the only thing I can imagine from a | similar system here. | frostburg wrote: | At least here you can just go to the school that you want. | People that don't like math or the idea of studying dead | languages do not pick the lyceums. | | Obviously indirect social stratification is still at work | in the process. | texaslonghorn5 wrote: | It's possible this is a good thing. Though it's also possible | sorting too early determines someone's life path before they | are mature to understand their talents and abilities. So I | don't think early sorting is superior to the American model | because at least the American model can uplift late bloomers. | bigcat123 wrote: | DoingIsLearning wrote: | A famous example of this that absolutely blew my mind is | Ugur Sahin. | | For those not familiar, he is the founder of BioNTech, the | German researchers who developed Pfizer's SARS-COV2 mRNA | vaccine. | | Ugur moved from Turkey to Germany at age 4. At the end of | primary school his teacher had assigned him to | 'hauptschule'. It was only because of a neighbour's | intervention that he was later put through 'Gymnasium' i.e. | on track to study 'higher' studies. | | The rest is history, after med school he did a doctorate in | Imunotherapy, he founded a 18billion revenue biotech | company and saved countless lives with what we now call the | Pfizer mRNA covid vaccine. | | Had that primary teacher's decision been held it really | would have been a 'butterfly effect' of catastrophic | proportions for Humanity. | umanwizard wrote: | You don't know the counterfactual, though: how many | Americans' talent is wasted because they are forced to | sit through watered-down school until age 18 before they | can begin serious studies? | DoingIsLearning wrote: | Absolutely fair. | | This one example just stuck with me when I read it | because of how serindipitous his mRNA research turned out | to be during an all out worldwide pandemic. | Czarcasm wrote: | This is probably the best counterargument to raise in | response to the "late-bloomer" anecdotes that many people | raise. | | For every unit of societal productivity created by a late | bloomer that is saved by a common-stream system, I would | personally argue that there is an order of magnitude more | societal productivity lost by holding back the more | typical high performers. | | Late blooming intellectuals aren't the norm. Most highly | intelligent people begin performing as such from a young | age. | ghostbrainalpha wrote: | How do they deal with the late bloomers? | | I didn't really find my academic ability, and programming | until I was in my twenties. | tshaddox wrote: | That doesn't explain what has changed within American public | education, if it's true what the parent commenter said: | "large swaths of the student population will fail if expected | to perform at the prior standards of rigor" | zozbot234 wrote: | Unfortunately, tracking is awful for the low-track students | because guess what, no self-respecting teacher wants to be | stuck teaching underperformers. So the students are trapped | in that situation, being taught by terrible teachers who | don't actually care for their educational achievement, and | unable to improve. You see those outcomes across the board, | including in the celebrated German system of academic vs. | vocational school tracks. Yes, there are ways to cross | through to the highest tracks, but very few students can | avail themselves of those practically. | alimov wrote: | > "...no self-respecting teacher wants to be stuck teaching | underperformers." | | If you look at people that are not academically inclined | and call them under performers then maybe that's part of | the issue. I think everyone has strengths and weaknesses, | and if someone is more inclined to do vocational training | rather than the standard track I think their strengths and | interests should be developed / encouraged. An educator | teaching someone that is actually interested in what they | are being taught sounds like a more rewarding experience | than lecturing a class where maybe 5 of 40 (not an actual | stat) students are actually engaged. | pessimizer wrote: | It's not whether people are more suited for vocational or | "standard track." It's our aptitude for judging that in | children. | alimov wrote: | That's a good point. I am not aware of a "good" way to | make that kind of judgement, especially considering the | lack of resources available to those that would be making | such a judgement (k-12 educators at public schools) | zozbot234 wrote: | > If you look at people that are not academically | inclined and call them under performers then maybe that's | part of the issue. | | It's not _me_ doing that, it 's education schools telling | prospective teachers that their students will just be | "learning their math by themselves", and the teachers can | simply be facilitators. It must be a comfy job teaching | math class to little Carl Friedrich Gauss and the like, | but what about the remaining 99% of students - who will | need _actual_ teaching? | alimov wrote: | Sorry, I should have worded that better. | micromacrofoot wrote: | I've talked to some high school students about going to | college despite high costs, and there was a general fear | (statistically backed) that they would make less over their | lifetimes without a degree and that not going to college | would put them in a worse position to do basic things like | buy a house as costs continue to rise. | OnlyMortal wrote: | The Netherlands been an example. | Bostonian wrote: | Yes, but if you do sort students by academic achievement, you | will send a smaller fraction of blacks and Hispanics to | academic high schools than whites, and a smaller fraction of | whites than Asians, since there are differences in academic | achievement by race. I say so be it, but currently many | people assume that disparate outcomes prove racism. | adamomada wrote: | The irony of course is that focusing on who they are not | what they do has to be more racist by a rational definition | throwawayboise wrote: | If it's based on ability, it should not matter what | percentage of advanced students are white, black, asian, | or other. All that matters is that if you're good enough, | you get in. | sefrost wrote: | Which countries do that and which countries don't? | brummm wrote: | Germany splits students into different schools starting 5th | grade and it's absolutely great. | TulliusCicero wrote: | Deciding the future of your life in 4th grade (when | students are evaluated in Bavaria, at least) is maybe not | great. Was living in Munich for five years and I'm glad | we left before our son got sorted. | | There's also a strong racial/class component to who gets | into Hauptschule/Realschule/Gymnasium, surprise surprise. | Lev1a wrote: | Here in M-V I had to go through "Orientierungsstufe"1 | which I _partly_ blame for my learning difficulties and | anger issues later in school, since in those two years we | later had to find out that we missed 1-1,5 years of | material and /or learning methods depending on the | subject. | | I mean... e.g. in Philosophy the teacher was absent for | most of those two years resulting in us having to | entertain ourselves for those "lessons". When we finally | entered Gymnasium at 7th grade we received a culture | shock when we had to learn the "Zauberlehrling" by Goethe | in 1,5-2 weeks for recital in the first weeks. | | Realschule felt more like Kindergarten from the treatment | by teachers like their attitude while teaching and them | not being interested in bullying unless it turned | _really_ physical, then protected the bullies when the | bullied hit back. What I 'm saying is, as the slightly | fat kid who also didn't get all the shiny new things from | his parents I was bullied by a group of other students | surrounding and harassing me almost every single day | during breaks those incompetent "teachers" only had the | "advice" to basically let the bullies tire themselves out | from bullying but heaven forbid once trying to break out | of the encirclement i tried to hit one of those bullying | lowlives, the teachers descended like vultures isolating | me in a room for the rest of the break questioning why I | did that instead of "just ignoring the bullies". Those | bullies never received any kind of discipline/punishment. | | Later in Gymnasium, I _once_ had a very heated verbal | altercation with a classmate within earshot of a teacher, | we were taken aside, our parents called in for an evening | sitdown that same week, there we resolved our differences | with some guidance from a teacher and remain friends even | now. | | Both schools were only staffed by older teachers with the | youngest being late-40s/early-50s and several teachers | retiring during my stay at the Gymnasium, so probably | little to no influence from education during newer eras | of teaching. | | Honestly I wish I could smack that idiot Brodkorb for all | the stupid shit he did as education minister. | | 1: no split after 4th grade, instead have everyone go | through Realschule for 5th and 6th grade, only starting | the split at grade 7. | TulliusCicero wrote: | I've heard pretty terrible things about Germany | tolerating bullying, +1 for that count I guess. | Lev1a wrote: | Clarification (can't edit the above post anymore): | | > our parents called in | | should be | | our parents were called in | watwut wrote: | It is genuinly too soon. | morelisp wrote: | In Germany you can be sorted into a Hauptschule around age | 10. At this point you will definitely not get a university | education via any usual path. Increasingly even "the | trades" are closed off to graduates and people expect a | Realschule (HS/GED equivalent) degree for those. | | I don't think university is appropriate for everyone and I | dearly wish skilled trades had a higher position in | society, and generally don't believe in the idea of | "unskilled labor". But the German system is ultimately as | cruel as the American one. | TulliusCicero wrote: | I don't think either system is great right now. From an | American perspective, I really wish that there were still | trade-type classes in high school, and those were more | accepted as a viable career path at that stage of life | for those who want it. | | One path could be partnerships with local | community/technical colleges. My high school participated | in a program called "Middle College" where high school | students took classes at a local community college (can't | remember if it was all or just some) and that seemed to | work well. | pmyteh wrote: | England mostly doesn't (though there's some local | variation). Most secondary (11-16/18) schools are | 'comprehensive', covering the full range of abilities. It | is standard to set pupils by ability in most subjects, but | uncommon to track/stream pupils by general ability across | the whole curriculum. | | We previously ran a split system, with exams splitting | pupils at 11 into academic ('grammar') and non-academic | ('secondary modern') schools. Many grammar schools were | good; most sec mods were awful. The exams also famously had | pretty poor predictive power for underlying academic | ability as an adult, so pathways had to be developed to | allow bright pupils to go to higher education despite being | mis-sorted in the original exam - which somewhat undermines | the point of the system. Comprehensivisation has never been | nationally mandated, but nearly all areas have now done | away with academic selection at 11. The remaining holdouts | are mostly suburban Conservative areas where political | power is in the hands of the well-heeled upper middle | classes who are strongly in favour of grammars (and expect | their own children to go there). Interestingly, Margaret | Thatcher (as Education Secretary under Heath) was | responsible for more grammar school closures than Labour | was. | | Vocational/academic choices are now being made at age 14 | and 16 either within the secondary schools or by moving to | local further education colleges (similar to US community | colleges and trade schools). Vocational classes are low | status. Britain no longer has a strong industrial sector to | use such skills, and although both parties advocate for | better vocational education essentially everyone who | matters would be most unhappy if their darling children | were diverted from a university track in the direction of | trades. That's something they want _other_ (poorer) people | 's children to do, not their own. We've never developed | good vocational training for offices/services jobs, and | although such courses do exist they're not taken | particularly seriously by employers, despite several rounds | of national reforms. | selimthegrim wrote: | I think Northern Ireland still does the 11+ | umanwizard wrote: | France does. | usrn wrote: | Germany famously does. Children are given a test and | depending on the score they go to Gymnasium (in | perpetration for university) or one of two other options | which trains them for either trades or labor. | frostburg wrote: | I'm not sure it's merely that. Most vocational track high | schools types (except the hotel / restaurant ones that are | well designed) here in Italy are honestly bad, not really | helping students reach their full potential, but the content | of the courses isn't on-its-face farcical like that "data | science" course. | | There are clearly decision makers detached from reality | involved here. | frostburg wrote: | They're avoiding dire outcomes for themselves while damaging | society, however. A merely performative education is truly | something awful. | wonnage wrote: | I think the cause/effect is reversed. Society is damaged | because parents cannot raise kids properly for a variety of | reasons. You have kids who don't come to school, entire | classrooms where 80% of the time is spent managing behavior, | kids who receive zero parental support at home because the | single parent is working two jobs, etc. | | That problem is hard to fix, whereas the curriculum is soft | and malleable. You also have an entire industry of education | PHDs who have never taught class for any appreciable amount | of time who have a neoliberal fetish for minor policy tweaks | as the path to heaven. | | Teachers have the same problems as police, random societal | functions have fallen to them by default because there's no | alternative. They're surrogate parents, social workers, | mental health counselors, etc. and there's barely any time to | do any teaching afterwards. | mrguyorama wrote: | >surrogate parents, social workers, mental health | counselors, etc | | And they're paid dick all on top of it | adamsmith143 wrote: | This makes no sense even as a well meaning. "Some kids are | going to fail so we need to prevent other kids from excelling." | Obvious BS from California | jimbob45 wrote: | Okay but what if American children were subjected to the | standards of Chinese schools? You'd see 70% failure rates | overnight at every school in the nation. Surely, in that | case, we'd see policies like these pushed even by white | people. | | Likewise, the minority parents and schools simply see upper- | class white schools in this country as we do the Chinese | schools. I'm not saying that this is the best solution to the | problem but I can at least understand where these parents are | coming from. | throwaway894345 wrote: | We're not talking about abruptly changing standards, we're | talking about holding kids to existing standards for which | our society is already calibrated. I don't think your | analogy applies (also, are Chinese schools really so much | more rigorous than American schools, or is this assumed | based on performance of Chinese immigrants?). | apetresc wrote: | Yes, they really are. Look up example questions for the | Zhongkao (national high school entrance exam) or Gaokao | (national university entrance exam) and ask yourself how | North American students at those respective stages would | fare. | throwaway894345 wrote: | I'm not necessarily surprised, just curious. Thanks for | clarifying. | [deleted] | civilized wrote: | Rather than standing tall for universal high standards, | education officials pass the buck to look good. The result will | be an increasingly unproductive, stratified, and unequal | society. | | You can pass and pass and pass people, but eventually an | employer is going to need someone to do the job, and they will | make sure they get that someone. So there will be a hard | standard sooner or later. The only choice is whether we give | all students a chance to meet that standard. | legalcorrection wrote: | When the utopian plans to elevate the masses fail, just bring | down the elites instead. Equality achieved. | snowwrestler wrote: | Is the curriculum being watered down? My reading on this the | last time it came up on HN is that the sequencing of math | topics is being changed, which results in classes not having | the familiar names like Algebra 2, Geometry, AB Calculus, etc. | That doesn't mean the concepts will not be covered by the end. | | I remember the huge blowups over "Common Core" years ago, which | included new ways of teaching math concepts. I got to see some | of it in action during COVID as I sat in on elementary Zoom | school with my kid. I have to say I was impressed; they used | techniques I did not recognize, but they seemed to work well. | wbsss4412 wrote: | As someone with a math background I found the blow ups over | common core to be ridiculous. Focusing on parents | unfamiliarity in place of any actual discussion of | effectiveness. | | If we are going to get anywhere with math education, it can't | be based on pandering to parent's expectations. | dc-programmer wrote: | I think America is going to have to take a hard look at its | math education if it's serious about re-industrializing. Where | are all the extra engineers going to come from? | | I think you are touching on theory I have that Americans are | becoming increasingly resentful that technical skills are | becoming more necessary for middle class living. This is a huge | driver of the pervading sense of precariousness. For some | reason there's a huge math phobia in this country | AlanYx wrote: | These things go in cycles. A lot of people don't realize that | Scopes actually lost the Scopes Monkey Trial, and that the | tide didn't turn overwhelmingly to rationalism in public | education until the 1958 National Defense Education Act | (which was motivated by the idea that there was a risk of the | nation falling behind scientifically). The tide will turn | towards rationalism and rigor again, eventually. | dc-programmer wrote: | Homer Hickman came to my mind reading your comment. His | Sputnik moment catalyzing the journey from coal mining town | to NASA is a metaphor for that ideal. However, I'd have a | hard time imagining America in 2022 has anything in common | with 1959's West Virginia. | TedDoesntTalk wrote: | > Where are all the extra engineers going to come from? | | Unfortunately, maybe where they come from now? India, China, | and other immigration. | dc-programmer wrote: | The unstated irony is that there's a large overlap in the | anti-immigration and re-industrialization crowd. | | I think an interesting part of 20th century American | industrial/scientific history is that many of the prominent | figures were European immigrants (many Jewish) or children | of immigrants. | | Maybe there is something exceptional about the environment | itself. But the talented and privileged native citizens | rarely aspire to be an innovator; they dream of being a | leader or strategic thinker or mover of capital. | | That's why I think hard math is so marginalized even in | elite circles ("I've never been good at math"). Technical | work is essentially blue collar to the upper middle class. | Many of my peers are in this group, and the only time they | were ever interested in math or programming, was due to its | possibility as a conduit to a more prestigious position. | | This attitude is directly ingrained in undergrad | institutions. They focus on general knowledge to serve as a | justification to skip over front line work to become a | leader (military officer, factory manager, investment | banker). | | There are excellent American technicians no doubt but most | of them don't fit the typical WASP mold or are predisposed | to obsessing over systemic topics (which describes myself, | being ADHD, although I can only strive to be excellent). | | And the upper class? They have never aspired to much of | anything really other than hedonism and protecting their | position of status. At least in other countries, the upper | class ideal is a renaissance man. | | Edit: some of these assertions are sweeping and maybe a | little mean. But I do think the thesis is directionally | correct. America will need to change the culture around | education to succeed in the 21st century. Immigration has | and will continue to be a boon; but we have to accept the | possibility that America could become a less desirable | immigration target | shadowfox wrote: | > At least in other countries, the upper class ideal is a | renaissance man. | | Sadly, I don't think that is very true in many (most?) | places. | dc-programmer wrote: | Yeah I felt ridiculous saying that. Perhaps that false | contrast betrays a romantic idea more than representing | any material reality | [deleted] | robotresearcher wrote: | Unfortunately? | | Well-trained people showing up by themselves is a huge | advantage. | ejb999 wrote: | Yes unfortunately. | | The unfortunate part is we don't educate enough of our | own citizens for these well paid jobs. | TedDoesntTalk wrote: | Right. "Unfortunately" doesn't mean we should not | continue to rely on immigration for high tech. It means | it's unfortunate we're not providing the a similar | pipeline of people domestically. | nemo44x wrote: | I have to imagine these countries are going to begin | limiting or restricting this type of emigration as a | nation's people is its biggest asset. Brain draining the | world without reciprocity is the greatest foreign policy | we've had. | dc-programmer wrote: | I have strong suspicions that certain countries are | Astro-turfing movements on western social media to lure | talent back. | danans wrote: | > The major impetus for watered down curricula is the very | rational fear that large swaths of the student population will | fail if expected to perform at the prior standards of rigor. | | I don't think the previous standards of rigor were ever so high | for most students. | | When I was growing up in the 80s and 90s in the suburban | _working class_ Midwest, the vast majority of the students in | my high school didn 't advance beyond algebra. This was in a | well resourced school district. | | But that was a time when it was felt that most people didn't | even need to know anything past basic math to be employable. | Times have changed of course, but the vast majority of | educational paths, even STEM paths, don't require calculus. | | However a great many do require basic data analysis abilities, | so it's reasonable to emphasize those. | | This shouldn't be done at the cost of offering calculus as an | option for students who are prepared for and motivated to do | it, though. Of course in the end this is about cost. Assuming | the same resources, to teach a broader set of students data | science will require reducing the availability teaching | resources for something else. | | I also recall that in the 1980s in some places there were | programs that taught calculus at public community colleges for | students who were on an accelerated academic path in high | school. That is another option to consider. | acchow wrote: | > the very rational fear that large swaths of the student | population will fail if expected to perform at the prior | standards of rigor. | | Why is this a rational fear? It seems shocking to me that | students can't perform at the same prior standards given their | parents are more educated than the prior generation's parents. | frostburg wrote: | Are the teachers as good? | amanaplanacanal wrote: | Hard to know. The public perception of public employment as | a whole has gone considerably down since about the Reagan | era. The pay is mostly not very good, and states and the | feds have much more power over things that were | traditionally local. | falcolas wrote: | Potential reason it's rational: The shoulders of those giants | are higher than ever before. Climbing to those heights is | correspondingly harder to do. | | Speaking for myself, I had to worry very little about | computers until late in high school (Senior year, | specifically). There were no spreadsheet or word processing | classes, and the typing classes were only for the girls. | There was Algebra (up through Calculus as an optional | course), but many others that my niece has that I didn't. | cortesoft wrote: | Maybe I am missing something, but how would allowing some kids | to take more advanced math cause other kids to fail? You could | allow kids to graduate without taking the advanced math, but | still let kids who want to/are ready take the more advanced | classes. | jake891 wrote: | Californians would do well to compare themselves to Massachusetts | https://www.doe.mass.edu/frameworks/math/2017-06.pdf | jl6 wrote: | Which states are doing it right? | 2sk21 wrote: | In New Jersey and Massachusetts at least, there is absolutely | no move to water down the math curriculum in any way. On the | contrary, the schools here compete on how many AP courses are | offered. | idoh wrote: | Here's a comparison between MA and CA standards: https://twit | ter.com/BethKellySF/status/1518991575526699008?s... | ecshafer wrote: | New Jersey also has an _excellent_ practices of magnet | schools at the county level. So that even if you are in a | poorer school district you can go study and apply for a | magnet school at the county that is better and more focused | on high academic schools. These schools focus on basically | college level education for their area in health care, | biochem, technology, arts, etc. with many AP courses. The | normal public schools are also good in NJ with a solid | baseline, but the magnet schools open up access to what would | otherwise be private specialized schools to all income | levels. | texaslonghorn5 wrote: | Magnet schools benefit the individual student but they are | a bit problematic for many schools because they pick off | the highest performers and whoever is willing to do the | work to get admitted / physically drive to the magnet. | | And then the home school quality goes down and that hurts | everyone else who isn't among the small group at the | magnet. | nemo44x wrote: | One thing I notice in NJ is that although there are plenty | of private schools and academy's, you still see a lot of | people in multi-million dollar homes paying 60k a year in | property taxes sending their kids to the public high | school. Even the most progressive mother wouldn't do that | if the schools weren't at least up to snuff at offering the | curriculum that can get their kids into "good" universites. | pishpash wrote: | A reflection of the electorate. There are enough dummies in | California who feel the need to cry out through political | power. | whymauri wrote: | When I moved to MA, it blew my mind when I learned that what | Florida considers an 'advanced' or even 'specialized' | education is literally the baseline education in Boston and | the suburbs. The best schools in Miami Dade County would be | median in Middlesex. | [deleted] | ckemere wrote: | Text from the CMF: | | > "Since achieving a solid foundation in mathematics is more | important for long-term success than rushing through courses with | a superficial understanding, it would be desirable to consider | how students who do not accelerate in eighth grade can reach | higher level courses, potentially including Calculus, by twelfth | grade. One possibility could involve reducing the repetition of | content in high school, so that students do not need four courses | before Calculus. Algebra 2 repeats a significant amount of the | content of Algebra 1 and Pre-calculus repeats content from | Algebra 2. While recognizing that some repetition of content has | value, further analysis should be conducted to evaluate how high | school course pathways may be redesigned to create a more | streamlined three-year pathway to pre-calculus / calculus or | statistics or data science, allowing students to take three years | of middle school foundations and still reach advanced mathematics | courses." | | At face value, that suggests that the root problem is that | students reaching middle school Algebra 1 aren't ready and need | more remedial math instruction. As an Electrical Engineering | professor, I can definitely attest to the fact that students | reaching higher level classes with a precarious foundation are | rarely as successful as those whose foundation is more solid. I | suspect Scott would also agree that barely passing calculus in | high school is not an adequate preparation for a career in data | science. As a parent of a kindergartner and a second grader, I | can also see that there is opportunity to push more math further | down, but even at that age there are kids who have a huge | variability in how they view their math. | | With regard to resources, I thought this statement in the CMF was | particularly insightful: | | > "While early tracking of students into low-level courses has | been problematic, there is evidence that thoughtful grouping of | students to ensure they receive high-quality instruction geared | to their needs at a moment in time can be helpful. This includes | students who need to fill in gaps in their prior learning and | high-achieving students who are ready to be more intensely | challenged. It is also true that teaching heterogeneous classes | requires greater skill for differentiating supports than teaching | in classes where the range of performance may be narrower, and | should be accompanied by high-quality professional development to | enable success." | ckemere wrote: | Update - having re-read the first post about this, it seems | that the issue of resources is exactly the problem. I think | that opponents of the CMF would prefer to see More Resources | put into careful, thorough elementary/middle school math so | that middle schoolers would thrive in 8th grade Algebra. And in | their view, the CMF simply lowers the bar, masking the need for | more resources. | | I agree with that! | 300bps wrote: | _masking the need for more resources._ | | Want to know the one resource that schools can _never_ give | students? Parental involvement. It also happens to be the #1 | variable in success for students. | | If parents aren't checking their children's grades on a daily | basis, asking what they're studying, staying in frequent | communication with teachers and the school, there is nothing | that is going to replace that. | | My oldest son was on a robotics team during high school in | which we were a minority. All the other parents, their kids | were studying calculus by the end of high school. I asked | every one of them how their kid was able to do that and each | one of them shrugged and said, "nothing". | | To them, "nothing" was their child spending 2 hours per day | at Kumon after school and a few hours on the weekend in | addition to their constant checking of their work and | insistence on academic excellence. | bcrosby95 wrote: | You also have to be careful about "well performing" school | districts for a similar reason. I live in one such district | and most of the parents I know have a regular, dedicated | tutor for each of their kids. | | The teachers expect a lot because of this. Good luck if you | can't afford such help. | danans wrote: | The lack of resources for public education, coupled with the | every increasing level of competency that students are | required to internalize over time drives many of the fights | in education. | | I can understand how an electrical engineering professor like | yourself is rightly concerned about your incoming students | having less calculus proficiency. On the other hand, there | many (possibly far more numerous than EE) education and | career paths that would benefit from better general numeracy | but not necessary calculus. | | The terrible thing here is that these goals should be set | against one another due to resource limitations. The blame | for that lies with the broader societal inequities and their | reflection on the educational funding system. | rayiner wrote: | What exactly do you think are the facts regarding the "lack | of resources" in education and "the educational funding | system?" Are you aware that the U.S. spends among the most | on primary education (adjusted for purchasing power) of any | developed country: | https://www.statista.com/statistics/238733/expenditure-on- | ed... | | Or that 50% of total K-12 school funding comes from federal | and state sources, which is directed mainly at lower-income | districts? And that, when including those funds, only a few | states (ironically blue ones) have more than a 5% gap | between rich and poor districts: https://edtrust.org/wp- | content/uploads/2018/02/Gaps-in-State.... Meanwhile about | 20 states (including many red ones like Utah and Georgia) | direct over 5% or more funding to poor school districts | than rich ones? | danans wrote: | > Are you aware that the U.S. spends among the most on | primary education | | Yes, and I'm also aware that in the US we expect the | public school system to be a primary treatment center for | the disadvantages and traumas associated with poverty and | unequal opportunity. | | It's more expensive (and harder) to educate hungry, | ignored, and traumatized children than it is to educate | children who are well take care of. They need more | support staff, more psychologists, more free lunch | programs, after-school care that their parents can never | afford. And it's hard to attract good teachers to teach | academics in those circumstances. | | The major problems with primary education in the US are | largely faced disadvantaged communities, not prosperous | ones. If we decide to remove educational funding from | disadvantaged communities, we have to be prepared to | either put it into those communities in other ways, | otherwise we'll face even greater problems in schools. | | None of that is to say that there doesn't need to be more | accountability in school systems - there is a lot that | needs to be done to re-examine how education is | delivered. But just looking at the situation by comparing | $ spent on primary education between countries is | oversimplifying things. | rayiner wrote: | > Yes, and I'm also aware that in the US we expect the | public school system to be a primary treatment center for | the disadvantages and traumas associated with poverty and | unequal opportunity. | | That's true in virtually every country, because the | school system is always the government's primary point of | contact with poor families. | | > It's more expensive (and harder) to educate hungry, | ignored, and traumatized children than it is to educate | children who are well take care of. They need more | support staff, more psychologists, more free lunch | programs, after-school care that their parents can never | afford. | | Agreed on school lunch. Large school districts already | offer after school and summer programs. | | Disagree on more staff and psychologists. That's the kind | of waste that detracts from money for instruction. | Countries like Japan and Singapore went from being | desperately poor (at a level unimaginable even to an | inner city American) to developed in a couple of | generations in the 20th century. I'm pretty sure they | didn't (and still don't) have a bunch of school | psychologists on staff. | danans wrote: | > Countries like Japan and Singapore went from being | desperately poor (at a level unimaginable even to an | inner city American) to developed in a couple of | generations in the 20th century | | Those countries did so by making absolutely massive | infrastructure and human development investments in their | poor populations during their industrializing phase, very | similar to what the US did for its previously poor white | population after the 2nd world war. | | The people who face the greatest educational obstacles in | the US today are disproportionately people who were also | largely excluded from the huge post-WW2 investments and | ensuing economic miracle, and have since faced the | economic brunt of de-industrialization. | | > I'm pretty sure they didn't (and still don't) have a | bunch of school psychologists on staff. | | They have far less crime and trauma to deal with, are not | awash with weapons, and had very strong communal support | systems. They were/are also quite authoritarian. Those | are very different societies with very different | circumstances. You can't directly compare the situation | in post war Japan and Singapore with inner city America. | By dint of our own history, issues of education and | equity actually quite a bit harder here. | rayiner wrote: | > Those countries did so by making absolutely massive | infrastructure and human development investments in their | poor populations during their industrializing phase, very | similar to what the US did for its previously poor white | population after the 2nd world war. | | Japan and Singapore aren't Nordic social welfare states. | They invested heavily in development but not particularly | targeted at the poor. | | > The people who face the greatest educational obstacles | in the US today are disproportionately people who were | also largely excluded from the huge post-WW2 investments | and ensuing economic miracle, and have since faced the | economic brunt of de-industrialization. | | Only if you pretend that white people in Appalachia are | the same group as white people in Massachusetts. | | > They have far less crime and trauma to deal with, are | not awash with weapons, and had very strong communal | support systems. They were/are also quite authoritarian. | Those are very different societies with very different | circumstances. | | That indicates that America's problem is culture, not the | availability of school psychologists. | danans wrote: | > Japan and Singapore aren't Nordic social welfare | states. They invested heavily in development but not | particularly targeted at the poor. | | Nor are they comparable to American inner cities. | | My own anecdote about Singapore is an old friend who grew | up very poor in Singapore (themself a child of | impoverished rural immigrants laborers from India), but | whose family received subsidized housing, transportation, | and most of all, stability and security. If their family | had arrived in Singapore as slaves, their outcome might | have differed. | | > Only if you pretend that white people in Appalachia are | the same group as white people in Massachusetts. | | Who is pretending that? Not me. I agree that they also | have born the brunt of disinvestment and de- | industrialization, and we are seeing the effects of that | in the opioid and methamphetamine epidemics in those | areas. It's interesting that we don't usually call it a | culture problem with them though, like we do with black | inner city communities facing similar challenges. | | > That indicates that America's problem is culture, not | the availability of school psychologists. | | It indicates a problem of economics and disinvestment. | The psychologists are only there to manage the impacts of | that disinvestment on society, not solve the original | problem of lack of economic opportunity. | | I'm also happy to reduce the number of school | psychologists when teachers no longer have to deal with | traumatized children disrupting and endangering their | classes. Until then someone has to manage those issues, | and as you stated, that's what we expect public schools | to do. | keneda7 wrote: | I'm a product of public schools and a state college. Due to | my experiences I will never vote to give teachers one more | dollar in funding until major changes occur. | | I had multiple high school teachers that were checked out. | Would watch movies and do worksheets. We learned nothing in | their class other than how bad they thought students were | now days. Yet they were never fired. Some lasted another 10 | years before retiring. | | I also had multiple professors that would start terms by | saying if you have conservative views and you express them | in class I will fail you. Had another professor joke about | how she found out a student was part of a club she didn't | like so she failed him. Often times these were not GE | classes but CS specific. Politics have nothing to do with a | class on OOP or AI. That is not teaching IMO. I have a ton | of friends that feel the same way. Until this issue is | actually recognized and addressed I do not believe you see | anything change. | Dig1t wrote: | It's kind of funny how both sides of the political aisle have | extremists who find ways to argue that being dummer is better. | They mirror each other in so many ways and sometimes the two | extremes kind of wrap back around to the other side and have the | same goals. | Drblessing wrote: | Horseshoe theory supremacy | reducesuffering wrote: | https://en.wikipedia.org/wiki/Horseshoe_theory | | There were three factions in WW2 and the Cold War. It was about | preventing the assault of extremists on both sides. | threatofrain wrote: | No, the two sides of this debate aren't mirroring their | arguments. | | One side (Equitable Math) is engaged in a discussion of white | supremacy in Californian math pedagogy. The other side (Moses | Charikar, Scott Aaronson, et al) is arguing against a weakening | of math standards. | daveslash wrote: | Sorry for being out of the loop and asking a (possibly) dumb | question: What is the stated reason that the CMF suggested these | changes? | | Is it about budgets? Is it because some people might think these | classes " _aren 't that important?_". The open letter seems to | suggest that it's about closing gaps between privileged and less | privileged - is that it? Honest question - I'm not trying to stir | the pot. | cortesoft wrote: | I believe the gist of the argument is that when you split | students into 'normal' and 'advanced' classes at a young age, | the students who are not put into the advanced classes will | believe they are just naturally not good at math and will give | up on trying to get better because they will think they just | "don't have a math brain". Here is a short blurb about the | idea: | | > The framework would not forbid districts from accelerating | students in middle school. It does, however, recommend that | middle-school students all take the same sequence of | "integrated" math classes that blend concepts from arithmetic, | algebra and other subjects with the goal of cultivating a | foundation and comfort level with numbers. | | > On top of that, the framework recommends that schools | postpone offering students Algebra 1 until 9th grade or later, | when it says more students are likely to be able to master the | material. | | > "When kids struggle, they immediately say 'I don't have a | math brain,'" Boaler said. "That changes how the brain | operates." | | https://calmatters.org/education/k-12-education/2021/11/cali... | | I am sympathetic to the idea that we don't want to send the | message that some kids are just bad at math, but it does seem | to be a bit of throwing the baby out with the bathwater by | holding back the other kids who are doing well. Even if you | keep the advanced kids in the same class, the kids are are | struggling are going to be well aware that some of the kids are | getting it really quickly. | npunt wrote: | Yep, tracking students into systems like high/low early on | makes it very hard to ever escape that track, as they're a | sort of self-perpetuating system. That has downstream effects | for one's entire life. It's a crude method of personalizing | education within the context of factory education. | | Downsides are that kids develop at different times, have | different educational needs, have home life issues that can | temporarily derail progress, etc and if those happen around | the time kids are getting tracked, they may not reach their | full potential. | | A good education system would offer students a way to rise up | whenever they're ready to rise up, let them learn at their | pace, focus on mastery, build upon knowledge gained rather | than schedule followed, etc. There's a lot of edtech out | there that incorporate these concepts but school models | struggle to integrate it into the (literally) old school way | they operate. It's quite difficult to reorient school around | these new concepts at scale, it has to be done school-by- | school, leader-by-leader, school board by school board. | | Agree its complex, as it may be the 'best of the worst' | option for certain contexts. Anything involving balancing | equity/access/etc is like that. | ceeplusplus wrote: | From what I've seen there are three major problems with | edtech that gives a personalized education: | | 1) A lot of K-8 education is babysitting. If you let kids | do their own thing they'll just watch YouTube and play | Roblox instead. Most kids are not _that_ self motivated at | this point in life. It's hard for teachers to manage a | classroom if everyone is working on different things. | | 2) Staring at a computer screen is not a great learning | experience. A classroom is an interactive, social | experience with active feedback. It's hard to socialize | when the kid next to you is not working on the same | activity or problems you are. | | 3) Personalizing education diminishes the importance of | teachers in the classroom, which teachers unions obviously | oppose. Teachers can't teach if every kid is learning | something different, and online education strongly promotes | winner-take-all dynamics where the best teacher and content | can scale up infinitely and dominate. | | Out of all these I think 2) and 3) are the hardest problems | to solve and whoever solves them is going to meaningfully | advance education. But I'm not very convinced by the | startups I'm seeing in this space that anyone has solved it | yet. | npunt wrote: | Yeah we're early on in really nailing the formula. Butts | in seats staring at screens doing single player | activities isn't a particularly compelling education | environment nor one children are accustomed to | biologically. We need more embodied, social, | psychologically safe, and intrinsically motivating | learning environments, and I don't think the enabling | technologies and designs have yet emerged to fully | satisfy these needs. | | That said some of these programs have solid learning | science foundations and good outcomes. Teachers roles | necessarily change to 'guide on the side' and motivator, | there's a lot more there to go into but basically it'll | take time. | ThrustVectoring wrote: | Another non-obvious problem is that you can get mis-tracked | too low _even on the highest track_. It happened to me. | There was an assessment test on entering middle school for | how many classes up you got shifted, I went into the | highest bucket with 4 other kids. Last year of middle | school we had to get bussed into the local high school for | math education and back for everything else. | | I was not seriously challenged and felt like math classes | wasted my time. | commandlinefan wrote: | > we don't want to send the message that some kids are just | bad at math | | But some kids _are_ just bad at math. Some kids are bad at | sports, music, dance, etc. Some kids are good at some things | and kids are good at different things. | cortesoft wrote: | Yes, some kids are bad at math... but they could be better | than they are. | | Let's use your example of sports, for example. Yes, no | matter how much I train and practice running, I will never | be as fast as Usain Bolt... but I sure will be faster than | if I didn't practice at all. | commandlinefan wrote: | Yes, that's correct. So you (and I) should be taking | remedial running and Usain should be taking AP running. | acomjean wrote: | I was in the "middle" tier math program in high school. But | around sophomore year I wanted to get more into | science/engineering but you can't switch tiers or catch up to | those ahead of you, no matter if you're making extra effort | and doing well. It was frustrating. | | In my case I got a letter about summer school at a local | university. So I pre-calced over summer school to get moved | into calculus in high school. It honestly changed my path. I | get having tiers, but once placed into one its hard to move. | If I wasn't self motivated, and had the opportunity to try I | would be in a different place. | digisign wrote: | Nice work. However you say you couldn't switch tiers but in | the next paragraph you did find a way. So, it sounds like | you can. | PebblesRox wrote: | I read it as an unspoken "within the school system." It | seems reasonable to expect schools to include a path for | changing tiers if they put such a system in place, rather | than leaving it up to students to find a workaround. | | My school supported me in taking trig as an independent | study over the summer (with a textbook and slides from | one of the teachers plus a few meetings as needed.) This | let me take AP Calc senior year; otherwise I would have | missed that opportunity due to being placed in the wrong | math class freshman year. | pishpash wrote: | Many public schools take local college credits. There is | always a path. | zdragnar wrote: | My school allowed changing tiers, and I am very grateful | that it did. I had a bad year in my early teens with some | mental health stuff, and spent my first year in high school | with kids who needed much more time and practice to get a | handle on concepts than I did. If I had been forced to stay | in those tracks, my life would have taken a drastically | different course, as I didn't really need to work to learn. | Getting bumped into a higher tier challenged me, and that | challenge is what prepared me for college. | | Had I gone into college without that work ethic, I almost | certainly would have failed out early. | lordnacho wrote: | Why wouldn't you just let everyone take the same class and | the same exams, but let the kids who have interest do extra | work? Want to do calculus a year early? Here's the book, | here's the exercises, why would I stop you? | cool_dude85 wrote: | What you suggest is already the case. The book and | exercises are "here" for you to do, nobody to stop you. | It's called the internet. The calculus police doesn't come | get you if you're reading a calc book in 10th grade. It's | just that you don't have any way of getting instruction or | school credit - so you are very unlikely to be successful, | and not very likely to have your university credit you as | having mastered the material without taking a college | class. | throwawayboise wrote: | Any high schooler can take the AP calculus test and earn | credit, no? | [deleted] | nafix wrote: | Sounds like more woke nonsense. Sounds nice and easy to a | layman from a super high level but not practical or put | through any kind of rigorous rational thought. | vkou wrote: | > Sounds like more woke nonsense | | You are right that this is a lot of nonsense. Specifically, | 'you aren't good at math/math is hard' is the nonsense meme | that gets hammered into student heads so frequently during | school that most of them actually start to believe it. | | It's not some kind of novel woke nonsense, though, it's how | math instruction on this continent has been happening over | the past X decades. | | The wokies are pushing _back_ on this nonsense. | inglor_cz wrote: | 'you aren't good at math/math is hard' may be nonsense, | no doubt. | | 'you can be good at math/math is easy' may be an equal | nonsense. | | This seems to be a symmetrical situation to me. You can | absolutely underrate or overrate a person's abilities to | do X. I don't see how one is preferable to the other. | Both are pretty destructive when taken to their extreme | logical conclusions. For example, from the relative | underrepresentation of blacks in advanced math classes, | you can draw a conclusion that _math as a science is | inherently racist /white supremacist_. Such sentiments | can be sometimes seen in discussions and I consider them | dangerous, toxic nonsense. | khazhoux wrote: | I don't understand if you're saying that every kid is | equally good at math. Or, similarly, that every kid that | the same capacity for it or ability to pickup math | concepts. | | Because it seems to me that if you have experience with | any sampling of children where N>1, you'll see that's | simply not true. | [deleted] | vkou wrote: | > I don't understand if you're saying that _every_ kid is | equally good at math. | | I'm not, there are always extreme outliers and | exceptions, but I do believe that the vast majority of | children can meet the incredibly low bar for mathematics | education that is considered normal in North American | schools. | | I also believe that teaching them to be afraid of math, | (and having their teachers be afraid of math) is a major | contributing factor for why so many of them struggle so | much to meet that bar. | rayiner wrote: | > (and having their teachers be afraid of math) | | This is a big one. I was in sixth grade when my science | teacher told me that the boiling point of water was 132F, | because she thought you added 32 to convert from Celsius | to Fahrenheit. | | This problem runs all the way down, from teachers | colleges to the kinds of people who apply to be K-12 | teachers. That fearing math is okay and normal is | pervasive in the culture and it's not clear to me you can | even do anything about it other than implement gating | math credentials for teachers that would exclude a huge | fraction of teaching school graduates. | dorchadas wrote: | > (and having their teachers be afraid of math) | | This is a huge part of the issue I feel. I know way too | many elementary school teachers who are afraid of math | themselves and struggle to understand it. Is it any | wonder the kids they teach don't? It causes big problems | when they get to me for mathematics in high school. | khazhoux wrote: | I would agree with this. The standards aren't super high | -- from my POV as someone who always excelled in math. | But it's clear (to me, at least) that even the | "incredibly low bar" is actually quite challenging, at | every grade level, for very many students. | | Speaking of teachers... my own grade-school math | development, decades ago, was stunted by the fact that my | teacher didn't know anything about linear algebra. I | asked her for help deciphering my "Amiga 3-D Graphics | Programming" book, and she concluded that the vector and | matrix notation must be a bunch of typos. Arrgh! | nafix wrote: | Like I said, sounds good to a layman in general terms | (just how you explained it). But the actual | implementation is half-baked, short-sighted, and favors a | weak/easy solution rather than something more well | thought out and complex. | cortesoft wrote: | Ok, so what would your approach be to address the issue | of huge groups of kids underperforming what they are | actually capable of? | | I feel too often the people who play the 'woke nonsense' | card think that we should just allow the current failings | to continue, and any work to help struggling groups is | wrong. | woojoo666 wrote: | Wouldn't cutting out high level math courses make _even | more_ kids underperform below what they are capable of? | | The cited issue was that higher level math courses were | making other students feel like they weren't cut out for | math. So it seems more like the issue is a mindset one. | They shouldn't be looking at better performing kids and | think "I can never do that". We should be instilling a | better growth mindset to these kids, so they understand | that they can overcome their inabilities. | | The "woke" solution of removing high level courses | actually achieves the opposite. It reinforces the idea | that such a level is inachievable for some people so it | should be cut out for all people. | twofornone wrote: | >You are right that this is a lot of nonsense. | Specifically, 'you aren't good at math/math is hard' is | the nonsense meme that gets hammered into student heads | so frequently during school that most of them actually | start to believe it. | | No, the nonsense is the idea that we are all cut out for | math. That's the fundamental underpinning behind the | "wokies" push for equity, a silent conflation of equality | of opportunity with equality of outcome based on the | totally untrue premise that we are all equally capable | given identical environments. | | The only possible resolution to this goal, given the | obvious uneven distribution of innate human ability, is | the handicapping of those who are capable, because there | fundamentally is no way to boost those at the bottom to | match the middle and top. | | And I don't think people understand how dangerously | pervasive this mindset has become, as it is also the | foundation for diversity and inclusion in the workplace, | the equally misguided idea that given equal opportunity | all demographics would see equal representation in a true | meritocracy. | HelloMcFly wrote: | > No, the nonsense is the idea that we are all cut out | for math. | | I think the nonsense is making a decision about who is | and isn't cut-out for math at such a young age, and | keeping them hemmed into that path for the duration of | their education. That's not merely _recognizing_ the top, | middle, and bottom - it 's creating it. | | I see that as a worthy thing to try to avoid. I also | think we should strive to avoid falsely concluding that | all persons are equally capable. | | But every decision is one that creates tradeoffs. I don't | know what should be done. I'm an observer on this topic, | and I think there's a lot of hubris in this thread from | others oh so certain they know what's best. | TimPC wrote: | What's the longest we can go without streaming and still | meet reasonable targets? The people designing this | curriculum seem to say they can't get rid of streaming | without dramatically lowering the bar. | | This means an informed discussion needs to be had about | the costs of lowering the bar against the costs of early | streaming. I think people are rather strongly against | lowering the bar to the point of effectively removing | calculus from high school based on the general reaction | in this thread. | vkou wrote: | > The people designing this curriculum seem to say they | can't get rid of streaming without dramatically lowering | the bar. | | If over twelve years of math instruction you can't figure | out how to teach the average child algebra, trigonometry, | logarithms, and the very basics of calculus, I would | advise the educators to look into why their peers in | other countries are managing to accomplish these feats. | | But, of course, it's easier to just throw your hands up | into the air, and just bifurcate people at Grade 7 into | 'good math' and 'bad math' tracks. | zozbot234 wrote: | > If over twelve years of math instruction you can't | figure out how to teach the average child algebra, | trigonometry, logarithms, and the very basics of | calculus, I would advise the educators to look into why | their peers in other countries are managing to accomplish | these feats. | | You think they're doing it with "Common Core" and | "ethnic" rainforest math, let alone this new "data | science" insanity? You couldn't be more mistaken on that. | Take a look at the popular Russian and Singapore Math. | Not even the smallest trace of the failing "progressive | education" thinking, just a lot of solid, high-quality, | direct, rigorous, focused teaching. | jimmygrapes wrote: | Perhaps a simple solution is worth a try: publicly | praise/acknowledge those who excel, while also teaching | that it's okay to not be at that level [yet]. Encourage | peer mentorship, so that the more advanced ones can help | someone who struggles. For the outliers who are | absolutely stuck in the "I don't care" mindset, apply | additional resources to find alternate ways to make the | material matter to that individual (practical examples, | scenarios, hands-on application, etc.). Ask other | students who _are_ interested what real world uses they | can think of for the material /topic/equation/concept. If | something works, consider implementing that method for | the entire class earlier on for the next class. | | This is where the goalposts generally get shifted toward | teacher resources and/or pay. That's fine to discuss as | well, but likely not a significant factor for the above | suggestions. | cortesoft wrote: | Can't we agree that both extremes are wrong? While I | agree that it is wrong to assume there is no such thing | as innate human ability, and it is wrong to assume | everyone can achieve equally, you seem to be arguing the | opposite; that there is nothing that can be done to | improve achievement for those who are struggling. | | This simply isn't true. There are things that can be done | to improve the outcome for students, and we should | continue to work to try to improve the success of all | students. This doesn't mean that you expect everyone to | achieve equally, just that you can help people achieve | more than they would have without the help. | | I also find this argument a bit paradoxical; if you truly | believe that innate ability is the only determining | factor for how well students do, then why do you worry | about handicapping those who are capable? It shouldn't | matter if we force them into classes they are too | advanced for, since how we educate them doesn't matter | and only natural talent matters. | | It seems that you believe schooling does affect | achievement, since you want to make sure we aren't | holding back the high achievers, yet you are saying at | the same time we shouldn't worry about how we educate the | low achievers because they are stuck where they are no | matter what. You can't argue that it matters for high | achievers but not for low achievers, that doesn't make | any sense. | [deleted] | rajin444 wrote: | > That changes how the brain operates. | | I didn't think our understanding of the brain was that | advanced yet. AFAIK we run some experiments and observe | results, but we can't explain why those results were | observed. | | Which is useful and awesome from a learning perspective, but | extremely worrying we use it to craft public policy. | fn-mote wrote: | > "When kids struggle, they immediately say 'I don't have a | math brain,'" Boaler said. "That changes how the brain | operates." | | This really jumped out at me. | | I didn't read any context, but students CAN and SHOULD learn | to struggle. Productively. Without thinking they are failing. | | Imagine you thought everything should come easily? That's not | my experience in the world. | | The fact that students (are reported to) shut down when faced | with difficulty is a failing of the educational system and | something that should be worked against. | zozbot234 wrote: | > I didn't read any context, but students CAN and SHOULD | learn to struggle. Productively. Without thinking they are | failing. | | Unproductive struggling with math is the natural | consequence of substandard math education, such as is | encouraged by the unscientific and arguably insane notion | (which is however common throughout the Education field) | that all students can simply be expected to "learn their | math by themselves", and therefore have no need for actual, | focused and direct teaching of that subject. | Miner49er wrote: | From my understanding, they revisit this framework every 8 | years. California is doing poorly in 8th grade math scores, so | I think they want to make changes to improve that. | adamomada wrote: | Goodhart's law In action? | prepend wrote: | It seems like such a bonehead solution to the problem. Of | course if you're doing poorly in math scores, you can make | math easier in the hope to increase scores. | | It's sad that the state is proposing these changes. I | remember in school there were kids who argued "algebra is | stupid, who needs it, why waste time" and there were one or | two sympathetic teachers who would respond "well, I rarely | have to use algebra to balance my checkbook" or something | silly. It seems like those kids have grown up, gained power, | and are literally pushing the argument that this math isn't | important. | deanCommie wrote: | The person quoted (https://en.wikipedia.org/wiki/Jo_Boaler) | is a "Nomellini-Olivier Professor of Mathematics Education | at the Stanford Graduate School of Education" who "won the | award for best PhD in education from the British | Educational Research Association" | | I'm not saying I agree with the proposed California | Framework. As a formerly gifted maths student, I hate it. | But let's not dismiss the rigorous work of an academic who | is attempting to improve education for a public education | body for a state with 40 million people as "bonehead" (or | "woke nonsense" as another commenter did). | | 90% of the reasons why kids say "<subject> is stupid, who | needs it" it's because they are not enjoying it or | struggling with it and using this as a defense mechanism. | Noone who is doing WELL at a school subject dismisses it as | useless. | | So maybe, just maybe, it's worth evaluating the education | process to make it easier to teach kids to give them the | foundations that then the more gifted ones can invest and | build on top of, and everyone comes out with baseline math | competency. | chmod600 wrote: | The path to hell is paved with good intentions. | rayiner wrote: | I believe this is a paper from her thesis work: http://ma | th.coe.uga.edu/olive/EMAT6990Sp10/JRME1998-Jo_Boale... | | It's mainly a qualitative analysis that wouldn't pass for | rigorous in any real scientific or engineering field. | fn-mote wrote: | I find this kind of shallow dismissal of a tenured | Stanford professor's work based on their thesis | unproductive. | | Engaging with their current, relevant work would be more | appropriate. | | This is exactly what the GP is saying - many of us don't | like the conclusions, but just blowing off a whole body | of work in a sentence is pretty arrogant. | rayiner wrote: | There's tenured Stanford professors in many subjects, | such as theology. I'm sure their work is impressive | within the context of the field. But that doesn't mean | it's rigorous or has real world application. PhD | publications are supposed to be a serious contributions | to the field. This particular work won a major award. | | Stop it with the accusations of "arrogance" and naked | credentialism. Any of the millions of people with an | undergraduate STEM degree (mine is in aerospace | engineering) learns enough about the scientific method to | distinguish "rigorous" work from non-rigorous work. It's | actually kind of an important thing they try to teach. | | Scientists and engineers who don't call out non-rigorous | work that claims the mantle of "expertise" are shirking | their moral obligations and helping to erode the | credibility of science as a larger discipline. | TimPC wrote: | A Professor of Mathematics Education is a role that fits | into a woke section of academia and generally publishes | woke forms of advocate research. Many people can study | mathematics education without studying much mathematics | at all. | | When the Mathematicians and Scientists are screaming that | the policy is nonsense, I'm not convinced by an advocacy | researcher saying it's rigorous work. | deanCommie wrote: | https://twitter.com/sfmnemonic/status/1504687870006620163 | | Can you make specific arguments instead of devolving to | shorthand dogwhistles that are completely up to the | interpretation of the reader. | | The term 'woke' has no meaning, depending on the context | it's anything between "We should shame all white people | for the crimes of their ancestors" to "We should make a | movie with a female lead". | | By using it, you leave it ambiguous as to where on the | spectrum you fall. | TimPC wrote: | The specific argument is that the Mathematicians and | Scientists are screaming that the policy is nonsense. The | other specific argument is that a researcher in | mathematics education doesn't need to take a lot of | mathematics. The inference is that we should trust the | former set of people more even on matters of mathematics | education. | RC_ITR wrote: | I think the argument (though not necessarily one I agree | with) is a spin on what you said: | | The current system pushes 50% of the kids into calculus and | 50% into 'I hate math.' Of the 50% that go into calculus, | 50% go into STEM. | | That leads to (hyperbole) 25% A's / 25% B's / 50% F's. | | The intent of the new rule is to maybe be more like 25% A's | / 10% B's / 50% C's / 15% F's. | | The key questions are 1) Is that actually better (I | certainly think bringing up the floor is a good idea, but | at what cost)? 2) Is this policy even going to get us | there? | leodr21 wrote: | Are other states doing the same thing too? | legalcorrection wrote: | s1artibartfast wrote: | This is actual argument that I saw presented as well, just in | different words eg reduce racial disparity in outcome. | burner556 wrote: | jimmygrapes wrote: | My (anecdotal but common) presumption is that the disparity | often comes from a cultural / behavioral divide, which is | increasingly blurry along racial lines but still distinct | enough to recognize usually. By behavioral I mean things that | are disruptive to standard teaching, like, during a lecture | or presentation, students are spending time on phones or | chatting with each other or listening to music or drawing or | walking around. General "I don't care, I'm going to do my own | thing" behavior. Sometimes the behavior is based in a | cultural or subcultural expectation or standard. What methods | or authorities do teachers have to enact behavioral change in | such cases? | | In most cases, none at all. If any attempt isn't derided as | racist (or other -ist/-phobic accusations) it's viewed as | authoritarian/inhumane. Decades of legal precedent and risk | aversion have caught up to education, perhaps rightly so. I | don't think there's any chance in hell of going back to | paddling and such, so we need to come up with newer ways to | enact behavioral change. In order to do this, I think we have | to stop being afraid of slights against culture. Unity of | purpose, of many one. Diversity is not a strength if there is | no unifying principle among the diversity. | truthwhisperer wrote: | bawolff wrote: | Everyone talking about calculus, but they also seem to want to | cut logrithms?? That seems super fundamental to me. | IshKebab wrote: | > as is suggested on lines 1226-1239 of Chapter 5 of the | California Math Framework | | It's a MS Word document. How am I supposed to find lines | 1226-1239? They might want to actually quote it. | JaimeThompson wrote: | Here you go. Multiple methods listed but in short it's under | Home / Find / Goto then select the line option. | | https://www.groovypost.com/howto/quickly-go-to-a-certain-pag... | umvi wrote: | Just my opinion but... is Calculus an important high school goal? | I took AP Calc in high school, got a 4 on the exam. I did | Electrical Engineering in college and took college level math | through differential equations. And yet... a) I've never used | calculus once in my STEM career, b) looking back I realize I | never really understood calculus back when I was in high school | and college. | | I came to that realization a decade after college when I was | digesting 3Blue1Brown's series on Calculus for fun and had it | finally _click_. Before then I was basically a Chinese Room that | was able to solve calculus problems via pattern matching (i.e. | "oh, this problem fits the shape of these rules, etc.") without | really understanding how calculus works. | texaslonghorn5 wrote: | Ultimately the solution is better STEM foundation at the very | very early ages. Universal pre school would probably be very | useful. Empirically [edit: n = 1 or 2], it seems that drilling | basic arithmetic and then multiplication tables early in pre K | and earlier elementary will give students a better intuitive math | foundation to do algebra very well. That would enable everyone to | go into more advanced classes at the same time (earlier) rather | than these policies which want everyone to go in at the same time | (later). | civilized wrote: | More and more earlier and earlier doesn't comport well with | child development and can backfire by making students feel | incompetent. We need better teachers, probably by paying more | so more talented people join the profession. | zozbot234 wrote: | Other countries do a lot of "pre-algebra" in the later grades | of primary education, when the kids are quite ready for it; | "drill and kill" rote methods are generally focused on in | very early grades, since they help build familiarity with the | sort of rigorous, algorithmic thinking that's required for | good math proficiency. This is what Russian Math, French | Math, Singapore Math, etc. are built on, and the approach has | stood the test of time indeed. The fuzzy "Common Core" | approach pushes abstract content way too early, and ends up | confusing kids as a result. | civilized wrote: | I wholeheartedly endorse Singapore Math, Russian Math, | Canadian Math (this is a thing, check out John Mighton's | fantastic JUMP program). ANYTHING but US math. | FredPret wrote: | I wish we did probability with equal gusto as kids. I very | occasionally multiply 7 and 6 in my head, but have to reason | with probabilities and statistics all day long. | texaslonghorn5 wrote: | Agree. I think getting really good at addition subtraction | and multiplication and then division/fractions is the way to | go though. Have really strong math fundamentals and then | learn algebra and then everything else is far easier to pick | up. | FredPret wrote: | Fair point. My first introduction to stats was at second | year in uni though, far too late. By that time I had | already done a lot of calculus, which while important, | hasn't exactly been critical in my daily life. | Jensson wrote: | Arithmetics is absolutely the most important topic to learn, | since it is the basis for all other quantitative reasoning. | | For example, it is really important to understand that 1 / 3 | chance is the same thing as 3 / 9 chance. It is obvious to | you now since you have done so much arithmetic's, but to | someone who never properly learned it they wouldn't be able | to properly compare those two and could think that one is a | very different number than the other. Without basic | understanding about quantities all other quantitative skills | become worthless. | wardedVibe wrote: | As a math PhD with dyscalcula, I'm very skeptical. I was nearly | held back as a child because of poor arithmetic performance, | and really only started to be above average when we started on | algebra. Poor arithmetic isn't that uncommon among the | mathematicians I know. | NegativeLatency wrote: | Poor arithmetic actually drove me to learn how to program | calculators and caused me to be interested in being a | software engineer | zozbot234 wrote: | Did that dyscalculia prevent you from learning and attaining | familiarity with the standard algorithms? That's the sensible | goal of "drill and kill" in early grades, not doing routine | arithmetic with high amounts of significant digits. | chadash wrote: | I love this. | | On a similar note, I have a friend who majored in math at | Harvard. He once told me that he came into Harvard being | arrogant because in high school he was always at the top of | his class in math. He enrolls in his first college level math | course thinking he's got this, but he soon realizes that | "higher math", which is largely proof-based, is a completely | different subject than what he learned in high school. A | month in he bombs the first exam. He went to the professor, | who is originally from Italy, and explained his situation and | how he was a star in high school. He responds in a thick | Italian accent "that was not math, that was computation. In | this course I teach math". | | The math you typically learn in high school is very | important, but I wish that we did a better job of explaining | to high school students that what they are learning is | completely different from what "real mathematicians" study | (although I do think that computation is quite important in | engineering, for example). | texaslonghorn5 wrote: | Interesting. I do not know much about dyscalcula. At an early | age do word problems make it worse or better? | usaar333 wrote: | There is little evidence universal preschool would reduce | academic variance later on. On cognitive measures (though not | necessarily social/emotional), randomized trials of such | programs tend to show fade-out (no difference between control | and treatment groups) within several years. | chadash wrote: | Pre-K (4 year olds) seems a bit young for teaching | multiplication tables. | fortran77 wrote: | If you can memorize the alphabet, you can memorize the | multiplication table to 12x12. | | And you'll start seeing beauty in patters and sequences of | numbers. The sooner the better. | frostburg wrote: | They do not require abstraction, I don't know if it is | necessary but it is practical to teach them. | chadash wrote: | What's the point of teaching kids to memorize something | that they can't apply? When I was a kid, schools taught | multiplication tables in 2nd grade, when most kids are 7 | years old. The difference in cognition between a 4 year old | and 7 year old is insane. | | I'd be surprised if there were any countries where | multiplication was formally taught to pre-K students as | part of the standard curriculum, but i'd love to be proven | wrong. | texaslonghorn5 wrote: | I don't know if there are countries. I believe that if | there actually was a unified accelerated math framework | that was really emphasized starting age 4/5 then kids | would be absolutely fantastic at math. | | > What's the point ... ? | | Paraphrasing what I said a comment above, you drill | addition and subtraction until everyone is good at it, | then you drill multiplication, then you do basic | division, then you start introducing basic one variable | algebra with "move plus to the other side to get minus" | etc. The application is using algebra for word problems; | formalism can come later. | texaslonghorn5 wrote: | In context I meant get really good at addition/subtraction | starting pre K and then multiplication once +/- is mastered. | | Though empirically, I don't know about age 4 but kindergarten | is definitely not too young for learning up to 12*12. And | once you figure out multiplication and eventually mental | division, it's not too big of a leap to have one variable | algebra with "move a plus to the other side to become minus" | etc. The formalism can come later but it's fantastic to have | some exposure to moving numbers and symbols around from an | early age. | chadash wrote: | Out of curiosity, is that a hunch or are you aware of any | schools teaching multiplication tables even in | Kindergarten? This used to be done in second grade when I | was a kid. | texaslonghorn5 wrote: | You're right, it's a hunch (n=1.5+-0.5). | chadash wrote: | When I was in kindergarten, I used to do math booklets at | home with my mom for fun. I learned basic multiplication | sometime around then. 13 years later I majored in | engineering. | | So I'm not saying it can't be done by _any_ 5 year olds, | but it seems young to teach this to the _majority_ of 5 | year olds. | amanwithnoplan wrote: | I'm not aware of any schools teaching multiplication | tables in kindergarten, but I did memorize the 9x9 table | when I was in kindergarten because my older siblings' Big | Kids Notebooks all had the times table on the back and it | formed a rhyme/ditty in the local language. After it was | explained to me that multiplication was repeated | addition, that made perfect sense. | | But don't ask me about division, my | siblings/parents/whoever tried to explain it as "the | opposite of multiplication", which was complete | nonsensical gibberish and I didn't learn division until | years later. | ryneandal wrote: | My sixth grader and first grader score in the 90+ %ile in | mathematics and didn't come close to learning | multiplication up to 12 in kindergarten. In fact, the topic | isn't even covered until second grade at the earliest. | | I think establishing a foundation of addition and | subtraction takes far longer for children to master than | you're considering, especially since there is evidence that | children of this age appear to intuitively view numbers | logarithmically rather than linearly [0]. | | I suppose you could take advantage of this by somehow | prioritizing multiplication and division over addition and | subtraction, but I think there's too much value in | comprehension of linear numbers and addition/subtraction | since that is the lion's share of interactions they will | experience at that age. | | On the other hand, if you're merely talking about | abstracting multiplication and division into patterns, then | I wholeheartedly agree with you, and there is evidence | supporting this [1]. Although pattern identification is | already part of kindergarten/1st grade curriculum here. | | Ultimately, IMO the most important aspect of education in | general is covered in the open letter linked to the OP: | | > There cannot be a "one size fits all" approach to K-12 | mathematical education. | | My children have thrived with their current math | curriculum, and I know some of their classmates have | struggled in contrast. One size does not fit all in | education, nor in many aspects of life. | | 0: https://news.mit.edu/2012/thinking-logarithmically-1005 | 1: https://www.tandfonline.com/doi/abs/10.1080/15248372.201 | 2.68... | sethammons wrote: | Anecdote: my then 5 year old and I would "practice counting | by different numbers" on the walk to school. By the end of | kindergarten, she could count by everything up to 12s. In 1st | grade, we started reversing it and asking how many 4s in 48 | and the like, and by the start of second grade, we were | firmly in adding and subtracting fractions with different | denominators (though, on paper at this point, no longer | mental math). | | She had (has?) a solid grasp on numeracy. I recall asking her | why, around 7th grade, "0.999..." is equal to 1. I was | prepared to show some fancy algebra and she one upped me when | she said "well, 1/9 is 0.111... so 9/9 is one and 0.999...". | | She never liked math though. She spurned calculus. | BitwiseFool wrote: | >"drilling basic arithmetic and then multiplication tables" | | I get the sense that such rote methods are no longer encouraged | and a lot of the "new math" in Common Core is aimed at | approximation and reckoning so that students won't rely on | memorization. | heymijo wrote: | > _Empirically, it seems that drilling basic arithmetic and | then multiplication tables early in pre K and earlier | elementary will give students a better intuitive math | foundation to do algebra very well._ | | This aspect of the Common Core was about recognizing deficits | in conceptual understanding resulting from rote methods of | drilling arithmetic. | | The empirical evidence is the opposite of OP's assertion, but | the end point of giving students a better intuitive | foundation for higher level math is indeed the goal! | | Signed, | | An elementary school math teacher who has studied the 60 | years of math reform in America, internationally, and worked | very hard to ensure all students have a foundation to succeed | in higher level mathematics | [deleted] | texaslonghorn5 wrote: | Makes sense, the drilling that works for one student | probably doesn't generalize all. Thanks for your | perspective! | frostburg wrote: | If you want to teach people methods to solve equations, | limits, integrals etc. speed with basic algebraic operations | is necessary. | | Facility with those methods is then necessary to be able to | adequately follow important proofs and gain understanding of | more advanced concepts. | | I don't know how you would teach people important results in | their fields (physics, computer science etc., I'm not talking | about actual mathematicians) without those skills. | RangerScience wrote: | TL;DR: algebra != arithmetic AKA real math doesn't use | numbers | | I'm only good at _arithmetic_ because of making Warhammer | 40k armies (true story bro). | | I'm good at _algebra_ because I was taught well, on top of | a knack. | | Speed with basic algebraic operations was very helpful in | many places but speed with arithmetic operations has only | been helpful in board games. | | I don't think anyone here would disagree with your point | about algebra, but I think a lot of people such as myself | would disagree that pre-K memorization of arithmetic helps | with algebra later. | frostburg wrote: | Performing a bunch of calculations for tabletop wargaming | is basically the same as learning multiplication tables | and solving related problem sets. It should help every | time that for example you have to simplify a polynomial | involving fractions and similar operations. | | As I stated in another post, I don't know when it is | neurologically ideal to learn arithmetics, it seems | something that would be important to study carefully | (personally I learnt before grade school, when I was 3-4 | years old, but I didn't learn to read until I was 6, | something that is often taught earlier). | texaslonghorn5 wrote: | Algebra does use numbers. I learned to move the numbers | to one side and the variables to the other. | | 10x+7 = -2x+31 | | Move 7 to the other side (picking up a minus sign) | | 10x = -2x + 31 - 7 = -2x + 24 | | Move -2x to the other side (flipping sign) | | 12x = 24 | | Recover 12*2 = 24 via memorization, quick division | (though not long division), or whatever method | | Therefore, x = 2. Then I drew a square and was done. | snvzz wrote: | >Then I drew a square and was done. | | I don't get this part. | | You mean to highlight the end result? In that case, it | would, most of the time, be a rectangle (or try to be). | texaslonghorn5 wrote: | I was joking, I meant the QED box. | snvzz wrote: | I know about QED, but I am not familiar with the concept | of "QED box". | | A cursory web search yielded nothing. | ludwigschubert wrote: | It's a symbol that goes by many names: the tombstone, | end-of-proof, or Q.E.D. | | "[?]" | jeffbee wrote: | But strong arithmetic fundamentals are absolutely | necessary for strong algebra. I've watched kids struggle | with basic algebra because when they don't instantly | recognize that 7x8=56, they also don't recognize that | 7zx8z=56z(edit: squared). | | Edit: thanks to the reply; HN ate my superscript 2. | Apparently it doesn't like the unicode multiplication x, | either: x 2 ? | RangerScience wrote: | Hmm. Alright, I can see solid arithmetic being good for | introducing the concept of a variable... | | ...but the only time I ever saw significant numbers when | actually doing math was in toy problems that deliberately | chose weird, big coefficients, where the arithmetic part | was by far the least significant. | texaslonghorn5 wrote: | Good point ... however, 7z*8z=56z^2. | roody15 wrote: | I have worked in education for 16 years and just wanted to add my | perspective. Here in Illinois over the last few years the state | has shifted its goals to "equitable outcomes". This in and of | itself is responsible for much of the lowering of academic | standards since it is a flawed (but perhaps well intention-ed) | goal. | | In a excellent school district in a suburb of Chicago a district | goal was adopted to reach equitable outcomes in higher Math. In a | nutshell since black students scored statistically lower on AP | Calculus this was seen as a failure in the school district. | Despite increasing the number of black students able to pass AP | Calculus the school district looked to cancel offering the course | since Asian and affluent white students still scored | statistically higher. | | The idea that all races, genders, or whatever categorization you | can come up with must have the same equitable outcome is a flawed | goal. Education used to be about taking a student where they are | and showing improved learning outcomes. | | Equality used to be about striving for equal opportunity. The | shift to conflating equality with equalized outcomes simply | doesn't work. | [deleted] | thaumasiotes wrote: | > Equality used to be about striving for equal opportunity. The | shift to conflating equality with equalized outcomes simply | doesn't work. | | Note that to the extent there was a shift, it took place in the | 70s. | | https://en.wikipedia.org/wiki/Disparate_impact#The_80%_rule | roody15 wrote: | "Note that to the extent there was a shift, it took place in | the 70s." | | This really has ramped up in the last 2-3 years. | [deleted] | slowmovintarget wrote: | The worst thing about the CMF effort is that it would only deepen | the disparities between rich and poor. Public education is often | the only shot poor kids have to gain knowledge and skills that | might propel them into STEM fields. | | Do we need to mail copies of _Stand and Deliver_ to the entire | California school board? Or am I the only one that recalls that | movie... based on something that actually happened... in | California. | | https://en.wikipedia.org/wiki/Jaime_Escalante | [deleted] | john_moscow wrote: | Well, why do you think the elites are unanimously supporting | the recent equity initiatives? Because in reality they penalize | the potential contenders from the rank-and-file class, while | the top ladder plays by their own playback. | iamleppert wrote: | I'll save you from reading and get to the point: | | It's a lot easier to just move the goal post than to actually | achieve the goal. | idoh wrote: | SF CA resident, parent of two school age children chiming in. The | direction with math seems pretty dismal, in that as of right now, | everyone is singly tracked together for math through freshman | year of high school. This results in children who have higher | aptitudes[1] to not be well served by schools. The majority of | people I know who have the means opt out of the public school | system, which probably makes the problem worse generally but | solves a pain point for them. | | [1] - I take it as a fact that different people have different | talent levels for different things, but not everyone agrees with | that, and disagreement on this point is a big driver (but not the | only driver) in the "everyone gets exactly the same" approach | that is trending now. | 300bps wrote: | https://en.wikipedia.org/wiki/Harrison_Bergeron | | _In the year 2081, the 211th, 212th, and 213th amendments to | the Constitution dictate that all Americans are fully equal and | not allowed to be smarter, better-looking, or more physically | able than anyone else_ | micromacrofoot wrote: | I'm not sure that would be worse than the current system | where the richer American is smarter, better looking, and | more physically able | 300bps wrote: | There are quite literally billions of people that are | richer, smarter, better looking and/or more physically able | than I am. | | I'm glad for it. I would never want to bring anyone else | down to meet me at my level on any metric. | micromacrofoot wrote: | It doesn't bother you sometimes that some people starve | while others hoard wealth that rivals the gdp of entire | countries? | | I don't want everyone to be the same, but unbridled | disparity seems equally as bad to me... especially | considering how arbitrary it can be. | bendbro wrote: | Nobody should care about disparity, people should care | about maximizing benefit for every American. I'm not | saying it is easy to evaluate this, but it is obviously | all we should care about. The existence of gazillionares | is fine so long as individual wellbeing in this system is | higher relative to other potential systems. | bpoyner wrote: | That would drive my wife up the wall. Our school district in | the Pittsburgh suburbs has 5 math tracks from grades 4-12. They | just added linear algebra because so many kids were maxing out | the available math curriculum. | selimthegrim wrote: | And the course is what, elementary row operations? | dan-robertson wrote: | My understanding is that in the US 'linear algebra' is used | for both the thing that involves manipulating grids of | numbers in various ways (so the basis is implicit), the | thing that is a bi like algebra but for matrices and | vectors, the thing you have in physics where linear maps | have specific geometric meanings (so you care about being | mostly basis-agnostic, and you care about how the objects | change when you change basis), and the thing which is | abstract algebra for vector spaces and so on. | | When I was in school in the U.K. we did the first and | second things, including eg multiplying matrices, | eigenstuff, diagonalising them, inverting small matrices, | some determinant/cross product stuff, and we maybe did the | thing where you solve a first order linear ODE system by | converting to matrix exponentiation, though I don't quite | remember. I think we just called it vectors and matrices. | | There was some useful stuff there. The problem is that it | was at a course so close to the leaves of the 'x allowed to | depend on material from y' tree that we didn't get to apply | that much (related example: we had to waste a bunch of time | on silly equations in physics because they couldn't depend | on us knowing about the y' = kx ODE) | | At university we did some courses in vectors and matrices / | vector calculus that went down the practical route towards | physics things and useful tools, and we had a course called | 'linear algebra' that covered the abstract algebra side of | things, where everything was lemmas/theorems/proofs | beginning with e.g. suppose e1, e2, ..., en is a basis for | a vector space V over F, .... However it is certainly | possible that the US terminology (linear algebra for | everything) was more common outside of the courses I took. | verall wrote: | Sounds the Linear Algebra for Engineers course I took in | undergrad... | luca3v wrote: | I don't know if it's still there in the revision, but in | chapter one of the earlier draft of the California framework it | said, in a prominent place "we reject ideas of natural gifts | and talents" | | Edit: in the new version it has been changed to "high-level | mathematics achievement is not dependent on rare natural gifts, | but rather can be cultivated" | NaturalPhallacy wrote: | Sounds like the author didn't have any. | [deleted] | quirino wrote: | As a student who participated in Math Olympiads throughout | middle and high school, having to be on the same track as | everyone was downright painful. This type of thing really | shouldn't exist. | kodah wrote: | I think I can respond to your footnote. I went to a Catholic | school that split us up into separate tracks for maths | specifically in grades 4-8. I was in the upper level math class | for a year before they moved me. I had a teacher who celebrated | and encouraged bullies, slapped children with a ruler, and | threw a chalkboard eraser at me from the front of the classroom | because I appeared to be falling asleep. When my grades fell | the knee jerk reaction was that I was wrongly assigned to this | class and it was expected to have below some magical threshold | of attrition. The ramifications for me were that my old friend | group would no longer interact with me the way they used to, I | was immediately bored in our lower maths class, and I was now a | "dumb" kid. | | It wasn't until I'd dropped out of college and taught myself | math, because of the interviews in this industry, that I | learned to enjoy math again. My point is that you're really | fucking with the social firmware of kids when you do that. | Also, reading between the lines of my life, _not being in that | upper level math class_ clearly had no impact on the latter | parts of my life. | TimPC wrote: | This curriculum has been brought to you by the campaign to import | all technology workers from foreign countries. | Drblessing wrote: | Recipe for societal collapse | russellbeattie wrote: | Here's my experience as a parent of a 20yo who went through the | MVLA school district in Mountain View. | | It's a warning to any parents of younger children: Unless | something has changed radically in the past 8 years, your child | will be put into a math track in 6th grade: Separated into | standard, accelerated and advanced classes. Which track you're in | is determined by grades, standardized tests and teacher input | after _5th grade_. | | This track determines which classes you can take in 7th and 8th. | If you were in the advanced class, you will have finished Algebra | 1 by the end of 8th grade. This allows the student to begin 9th | grade taking Algebra 2, and then extending from there so that by | their senior year they can take AP Calculus. | | If you want little Suzy to be in more advanced classes, you | better be prepared to be the most vocal Tiger Mom Karen you can | imagine, because you'll have plenty of competition. As a result, | almost no child moves between tracks. And in fact, in my opinion, | the difference between normal and accelerated is so little, I'm | pretty sure it's there just to give those children somewhere to | go. | | In other words, if your child doesn't demonstrate math skills as | an 11yo, they will unlikely be able to take AP calculus 7 years | later without doing something extra like taking summer classes, | redoing an entire school year (an option a fellow parent I know | took), or extraordinary effort like that. | | Even if the MVLA education system isn't exactly the same now, or | you live in a district that does something totally different, or | even if you're in another state, I suspect this sort of thing is | happening everywhere. | | I personally was happy my son was in accelerated classes, right | up until 9th grade when I realized how this circumscribed his | future options for classes. In the end he would never have wanted | to take AP Calculus, so it was fine. But I personally felt like I | had fucked up as a parent because I simply wasn't paying | attention. Planning out your kid's future math classes in detail | in the 5th grade never crossed my mind, or if it had, I would | have dismissed it as ludicrous overparenting! Had I known, I | might have sent him to a math camp or something if I had realized | how important the difference between a B+ and an A in math was at | that moment. And he my have really gotten into mathematics as a | subject. I really don't know. | | So anyways, that's my experience. California is such a massive | change from where I grew up in rural NH, I honestly can't imagine | where to begin to fix a system with so many millions of children | from such a varied socioeconomic and cultural backgrounds. I | barely got my one kid through the system unscathed, and I live in | one of the wealthiest districts in the country. | [deleted] | bigbillheck wrote: | My high school didn't offer calculus, and now thirty years later | I'm posting on the hacker news forums. ___________________________________________________________________ (page generated 2022-04-26 23:00 UTC)