15 ms·

Against Algebra

29 points by miobrien 4y ago

raydiatian 4y ago
The Atlantic: > Students need more exposure Also The Atlantic: > Paywall
- deleted 4y ago
  [deleted]
- IshKebab 4y ago
  Are you implying that those things are somehow in conflict? Because they very clearly aren't.
zozbot234 4y ago
> Students need more exposure to the way everyday things work and are made. Why does it have to be one or the other? Besides, algebra can also be taught in a more visual way and featuring more concrete reasoning, such as via complex word-problems that can be solved with a mix of arithmetic and algebraic approaches.
- WillPostForFood 4y ago
  Why does it have to be one or the other? The point of the article is that it should not be one or the other, different students need different things. It is the removal of tracking, the removal of vocational education, the denial of differences in students and the insistence in homogenized education that is wrecking schools. If only 37 percent of 12th graders can do the math needed to start college, maybe only 37 percent of 12 graders should be going into debt for a college education.
  - readthenotes1 4y ago
    The push for equity says that no students should be able to do the math needed to start college
  - zozbot234 4y ago
    Tracking is a terrible idea. To make it work effectively you need very efficient remedial teaching for the students who fall off of the "advanced/gifted" track, and that's antithetical to the whole "students should all be learning their math by themselves, not via rote instruction" schtick that's increasingly being pushed in elite "education" degree programs.
    - ndriscoll 4y ago
      What does effectively mean here? Do you mean to somehow catch the remedial kids up to the advanced kids, or just help everyone move at the pace they're capable of? Having everyone move at the pace of the most advanced is obviously not possible, but why do you need specifically efficient remedial teaching for them to move at an appropriate pace?
      - zozbot234 4y ago
        > but why do you need specifically efficient remedial teaching for them to move at an appropriate pace? Maybe you wouldn't if all teaching was appropriately structured. But remedial instruction is where the flaws of the nowadays-conventional approach of expecting students to "inquire" about math on their own and come up with their own ways of problem-solving are most evident.
        ndriscoll 4y ago
        I'm not sure I understand still; when I was a student I found my classes to move at a tediously slow pace, often going into detail about and even repeating obvious things. Even in university engineering classes (e.g. walking through "Fourier's trick" multiple times when it's just a dot product/projection). You seem to be saying we need more of that (and maybe that's true for most people!). Wouldn't that mean tracking is a better solution? Let the advanced kids who can quickly understand/infer the ideas and techniques move on, and walk through the details/give lots of practice to the other kids?
Rallen89 4y ago
like most things on this site, this is a critique of the American education system
- rawgabbit 4y ago
  American public school system is broken. It is feast or famine. Many teachers are bad at teaching. Many schools are no more than daycare centers. Many students are not interested in school. I don’t know what the answer is. The fact of the matter is many American universities also have fundamental problems. The university seeks prestige via research and publishing as many articles as it can. Educating students seem to be an after thought.
- cardamomo 4y ago
  That has certainly been a recent trend here! I wonder why that is. As an educator, I can offer my own hunches: - The COVID pandemic forced students' and teachers' experiences into the open; schools still haven't returned to "normal" since 2020 - Folks here are trying to grapple with the roles technology can play in learning and in our education system - Software engineering and related fields require a decent education; perhaps folks are worried about who may be prepared or under-prepared for the field in the future
- authpor 4y ago
  algebra is taught comparably badly in many other places...
nobody0 4y ago
For people who think in pictures, actually you can do a lot of algebra by diagrams [0] [0] https://en.wikipedia.org/wiki/Commutative_diagram https://en.wikipedia.org/wiki/Commutative_diagram
- mjhay 4y ago
  It's really the "more advanced" way to do it. There are a lot of people, myself included, that are actually much better at thinking in abstractions - I suspect the author might be the same, despite her thinking of over-abstraction as a barrier.
- contravariant 4y ago
  If that qualifies then surely symbolic notation itself is also a visualisation. It's not as if it's just a syntax tree, quite a few properties (associativity, distributivity, symmetry) are suggested purely by the way we denote sums and multiplication. If you wants things to be even more visual you could use Penrose diagrams [0], though I don't find them particularly intuitive. [0]:https://en.m.wikipedia.org/wiki/Penrose_graphical_notation https://en.m.wikipedia.org/wiki/Penrose_graphical_notation
  - Someone 4y ago
    > quite a few properties (associativity, distributivity, symmetry) are suggested purely by the way we denote sums and multiplication. I disagree. If “a + b + c” suggests “+” is associative, and “a × b × c” that “×” is associative, what about “a - b - c”, “a / b / c” and “a ^ b ^ c”? Or are you suggesting Σaᵢ and Πaᵢ suggest associativity? If so, how? (I also think you mean “commutativity”, not “symmetry” (https://en.wikipedia.org/wiki/Commutative_property https://en.wikipedia.org/wiki/Commutative_property) symmetry typically is about relations (https://en.wikipedia.org/wiki/Symmetric_relation https://en.wikipedia.org/wiki/Symmetric_relation)
- carapace 4y ago
  Also https://iconicmath.com https://iconicmath.com a collection of, uh, iconic math, math done with icons and diagrams and graphical patterns, etc.
melling 4y ago
“The fact that some people are visual thinkers while others are auditory” I thought the “visual learner” classification was a myth.
- hprotagonist 4y ago
  It is. https://www.theatlantic.com/science/archive/2018/04/the-myth-of-learning-styles/557687/ https://www.theatlantic.com/science/archive/2018/04/the-myth...
  - ff317 4y ago
    For me personally, I classify myself (whether it's valid or not!) as an experiential learner. I have a very hard time learning abstract things in purely abstract ways. I can read a book about a branch of mathematics and try intently to learn from it and totally fail. But give me one practical, real-world problem which demands some knowledge of that type of mathematics, and I might pick up the bulk of the same subject matter quickly, to the degree necessitated by the project. Whatever my conscious intentions may be, my brain throws a toddler tantrum about it and is like "Prove to me that I can use this for real or I'm not investing in it".
    - vaidhy 4y ago
      I will go back to the top comment as of now.. you do not learn math by reading. You learn it by solving the problems. Some subjects (maybe some of the softer humanities) are more theory than practice.. Math and programming are not one of those.
- caddemon 4y ago
  "visual learner" as it is used in education theory does appear to be mostly bunk. For a variety of reasons, one of which is that most people have both auditory and visual thoughts. However I would caution not throwing the baby out with the bathwater. There is a growing body of evidence that some people are better or worse at visualizing, have a stronger or weaker internal monologue, etc. than others. There are reported neurophysiological differences as well as task behavior differences if you look at people with Aphantasia for example. As the other article sent to you mentions, someone who is not very visual could potentially benefit even more from visual examples, so these results are not really in conflict with the failures of education theory. It's also not clear how common large disparities in the modalities of thinking are, so perhaps it is not something worthwhile to consider for mass education policy regardless. But I think in a neuroscience context it remains an interesting topic for future research. I'll also note that the author of the original piece is autistic, and she has clearly demonstrated savant-level abilities on certain visualization tasks. It's not surprising that she would feel this way about "learning styles", because her entire life experience has likely been extremely lopsided towards visual thinking.
geebee 4y ago
For another point of view, I recommend this article from the New Yorker: https://www.newyorker.com/science/elements/california-students-are-struggling-in-math-will-reforms-make-the-problem-worse https://www.newyorker.com/science/elements/california-studen...
cs702 4y ago
As always, this is written by someone who admits to never having learned to reason abstractly about algebraic objects, because it is hard. Quoting from the OP: > The traditional arithmetic I learned in the early grades made sense to me because I could relate it back to real-world things. Later, when I was learning how to design, finding the area of a circle proved essential to practical tasks such as sizing hydraulic and pneumatic cylinders. I could do trigonometry by visualizing, for example, the cables on a suspension bridge. But algebra: no. For a different perspective, I recommend reading instead Susan Rigetti (nee Fowler)'s posts about overcoming challenges to learn Math and Physics. She says she had to solve what felt like "millions of exercises" to become familiar with many abstract concepts, until they finally clicked for her and she was able to reason about them. In her words: "Solving problems is the only way to understand mathematics. There's no way around it." https://www.susanrigetti.com/math https://www.susanrigetti.com/math https://www.susanrigetti.com/physics https://www.susanrigetti.com/physics https://www.susanjfowler.com/blog/2016/8/26/from-the-fledgling-physicist-archives-if-susan-can-learn-physics-so-can-you https://www.susanjfowler.com/blog/2016/8/26/from-the-fledgli...
- PartiallyTyped 4y ago
  I’d argue that people need to be taught basic group theory and abstract algebra first, preferably in the form of puzzles to get familiar with more abstract thinking, and to see things in terms of composition of objects instead a of mixing numeracy in the mix. I think that numbers create all sorts of problems because people focus on them as they are familiar and miss the bigger picture.
  - qsort 4y ago
    I don't think it really works, at least not for most people. Abstract algebra (i.e. actual algebra, as opposed to doing useless stuff to poor polynomials) requires one to have developed the mathematical maturity to iron out informal thinking. Good luck explaining "prime" and "irreducible" are not the same. I think a path that would work better is through problem solving, like olympiad problems. But even that definitely isn't for everyone.
  - 4y ago
jjslocum3 4y ago
> ...studied the disconnect between the excitement with which kindergartners and first graders greet learning and the boredom and disaffection that seems to overtake many by high school It seems myopic to search for the answer to this discrepancy purely within teaching styles. In high school, coincident with the onset of puberty, many students simply become more interested in achieving social goals than academic learning.
jeffreyrogers 4y ago
You need algebra to make things. Lots of machining involves algebra and geometry. Maybe it isn't taught that well, and maybe kids would learn it better if they were motivated by practical examples, but it's far from useless. Besides reading and addition, algebra is probably the most useful thing kids learn in school.
ok123456 4y ago
The "Learning Styles" dogma has been shown to be unfounded. Within the confines of general education, there's no such thing as a "visual" or "kinetic" learner. There are just students who are less practiced at learning through textural means.
math_dandy 4y ago
The more off ramps from challenging mathematics we build into the education system, the more students will be excluded from studying science and engineering in university. Avoid the tyranny of low expectations.
c7b 4y ago
> The fact that some people are visual thinkers while others are auditory- or language-oriented is better understood than it was when I was growing up. Isn't the opposite true? I thought the 'learning styles' theory had been debunked by science? https://www.psychologicalscience.org/news/releases/learning-styles-debunked-there-is-no-evidence-supporting-auditory-and-visual-learning-psychologists-say.html https://www.psychologicalscience.org/news/releases/learning-...
- krastanov 4y ago
  A popsci video on how that is indeed a debunked theory: https://www.veritasium.com/videos/2021/7/9/the-biggest-myth-in-education https://www.veritasium.com/videos/2021/7/9/the-biggest-myth-...
  - LeifCarrotson 4y ago
    It's "better understood" to be completely false.
  - mindcrime 4y ago
    Be careful with this line of thinking. What has been debunked, as I recall, is a very specific formulation of what is meant by "learning styles". It is not necessarily the case that every colloquial use of that term represents the thing that has been debunked. And as I recall, the possibility that some people simply have a preference for certain learning modalities has not been debunked, and that may be what people who use that term in routine conversation mean. The question then would be whether or not that preference matters at all.
- ch4s3 4y ago
  Yes, it has no basis in evidence but is sadly still commonly referenced in education and in popular discussion.
uptownfunk 4y ago
I heard the Russians have an excellent culture of problem Solving based mathematics, how do we bring a similar culture in our schools ?
- walnutclosefarm 4y ago
  One reflection of which is the cute little book, The Chicken from Minsk: https://www.amazon.com/Chicken-Minsk-Infuriating-Challenging-Teasers/dp/0465071279 https://www.amazon.com/Chicken-Minsk-Infuriating-Challenging.... Love that book.
powera 4y ago
Not a good article. Chesterton's Fence applies to many of the complaints; the OP doesn't understand math, but implies it's a bad thing they would have been prevented from becoming an engineer because of that. Which is just wrong.
davesque 4y ago
Meanwhile, the rest of the world will go on teaching it and their students' academic performance will continue to trounce the US's. I am 100% confident that I would not have gone into engineering if algebra had not been part of my compulsory education. And I'm very happy with the career I discovered for myself. Neither one of my parents were engineers. And I wasn't a particularly good student in middle or high school. Therefore, I doubt anyone in my family would have thought to enroll me in extra curricular math. I discovered that I was good at those things late in high school. So I see advice like this as worsening class divides and increasing the likelihood that you live the same life as your parents.
btilly 4y ago
Interesting note. The author is https://www.templegrandin.com/ https://www.templegrandin.com/, who is one of the best known cases of a successful high-functioning autistic person. If a particular subject doesn't "click" for her, it will be a lot more of a barrier than it is for most. But, conversely, how many more like her have been accidentally excluded by cognitive barriers that most of us can't even see?
newaccount2021 4y ago
jelkand 4y ago
There are a lot of difficulties in math education in the US, but ejecting algebra from the curriculum just strikes me as utterly bizarre. A few other, major issues: * Math has a severe stigma. How many people do you know would readily confess "I'm just not good at reading," almost as a badge of pride? This is common with math. * Most teachers don't have a strong math foundation. They are not acquainted with some of the foundational ideas that can really enhance teaching and learning math. In some cases, teachers who don't like math will perpetuate the above issue. * There is little incentive for those strong in math to become teachers. Why go teach introductory math when you can become a software developer and make 4x the salary, with less stress to boot? I'd look to remedies like paying teachers better, improving their workload, and even revising math curriculums to focus on concepts over testing before jettisoning a whole field like this article advocates.
- unethical_ban 4y ago
  >Math has a severe stigma. How many people do you know would readily confess "I'm just not good at reading," almost as a badge of pride? This is common with math. Perhaps because it is genuinely less important on the pyramid of human skills. Reading, language comprehension, and critical thinking are more universally needed than, say, matrix multiplication or integrals.
  - 2devnull 4y ago
    “Reading, language comprehension, and critical thinking are more universally needed than, say, matrix multiplication or integrals.” Based on current wisdom. Current wisdom has a spotty track record though. It was once an obvious truth that reading was only for a select group. Universal literacy would have been as absurd back then as the notion of universal math literacy is now. Which is depressing, because one would hope that at least this historical analogy, and it’s implications, had occurred to more people.
  - jelkand 4y ago
    1. Numeracy is just as valuable as literacy. Sure, matrix multiplication and integrals may not be useful day to day, but the article is talking about algebra. 2. I may be biased, but I believe math is distilled critical thinking. The difficulty is teaching math critical-thinking-first as opposed to test-first.
noobermin 4y ago
With the anti-calculus post from last time, I'd love to see less of these types articles. Imagine an article saying we need less English and less composition in college and high school, except you wouldn't see such an article because writers do not hate writing (at least not beyond some ironic sense). But sure, if you ask any teenage with a 10 page report due next week, they definitely would like less writing in their curriculum. I feel like we will however never seen op-eds critique writing and generally humanities in education because those who write op-eds value it. They however, do not value mathematics in their own lives (probably having others do the mathematics they would otherwise need to do for themselves), and thus they incessantly attack it. I hate to make a meta-psycho-point but I must: Some part of me wonders if stuff like this is some people in the humanities having a reaction to the status quo today in academia where they are undervalued--I do feel that in status and funding in education today, the humanities generally does not receive the respect they deserve. Too much emphasis is given to STEM (and lately, STEAM which still leaves the humanities out). That said, I don't think attacking STEM is the way to ameliorate the issue, and it really leaves me with the same feeling I had when my peers cracked jokes about "the English department," that they simply did not understand what they study and are painting other fields and experts with broad generalizations.
- Turing_Machine 4y ago
  > Imagine an article saying we need less English and less composition in college and high school, except you wouldn't see such an article because writers do not hate writing On the contrary, I've seen many such articles. Education in general has been under attack for quite some time now.
photochemsyn 4y ago
I think there's a logical contradiction in the conclusion: > "We don’t need Americans to be better at algebra, per se. We need future generations that can build and repair infrastructure, overhaul energy and agriculture, develop robotics and AI." If the issue is how algebra is taught (dissociated from physical objects), well, perhaps there's a curriculum problem. The fundamental concepts of algebra - such as commutation, association, and distribution, do indeed have nice visual and physical representations: https://www.mathsisfun.com/associative-commutative-distributive.html https://www.mathsisfun.com/associative-commutative-distribut... Everything else in algebra, trigonometry, even into calculus and more abstract math relies on understanding how those rules can be used to manipulate equations, and then you can put the equation on a computer and build models of bridges, robots, power grids, etc. You can also grasp compound interest and so not be screwed over by shady mortgage brokers pushing adjustable rate loans... (although one wonders if such widespread financial literacy is really something the oligarchs who control both political parties really want to encourage). Perhaps the real problem is the failure of the America system to place the appropriate value on education and hence invest resources in educational programs, and that's the real reason for the poor performance of American children on math relative to all other industrialized countries?
nerdjon 4y ago
> pointing out that the math taught there was nothing like the math people use in their jobs This ignores that much of the fundamentals (like Math) are less about teaching you the basics but teaching you the skills you need to learn as an adult. At least this is how I have come to view my time in school as an adult. Now obviously there are exceptions of this (I mean you did have to be taught to learn and to read) but with this basic fundamentals when you are presented with a problem later in life you have those skills to pull from. Even of the algebra is not exactly what you did, The idea of "solving for x" should be so ingrained in your head that when you need to solve a simple problem that is basically exactly that, you do it without even realizing that is actually what you are doing. Even as a software engineer, most of what I learned in school I am not actually truly using on a day to day basis. Except when I am working on learning something new. Maybe we could get rid of "algebra" but what exactly would it be replaced with? Something that is algebra in all but the name? Also my system had different levels of classes, I know some kids were taking pre-cal in high school while some only finished algebra 1 (2?, I don't remember)
- nerdjon 4y ago
  Also I have to wonder how much of this "math" hate is societal. It isn't uncommon for parents to say how much they hate math so of course their kids are going to start to think that. Or to talk about how much they hate school. Leaning should feel rewarding and yet, it feels like it isn't in this country.
achenatx 4y ago
my daughter is in advanced algebra II as a freshman. She is not naturally good at algebra. What this means is that she simply needs to work harder. The school estimates 3-4 hours/work a week for advanced algebra. My daughter does 10-15 hours a week and still only has around an 85. What she has learned is that things that can seem impossible can sometimes be broken apart into small pieces and conquered with hard work. The author probably had certain subjects come easy to her. When it got hard she probably didnt know how to do the repetitions required to become good. Instead of becoming good, she is trying to tell us in STEM disciplines that the subject simply isnt necessary. Algebra is fundamental to all other math I dont see how you can do statistics (as the author mentions) without algebra. In fact probability is much harder than algebra and probability problems often times require algebra. Further the work habits you learn to master algebra are used for other abstract subjects. As you get into the sciences and advanced statistics, you might need calculus. As you get into engineering you surely need calculus. There are often times versions of the subjects that allow you to memorize the equations and the author probably doesnt realize the difference between memorizing the statistical equations to be able to execute them and deeply understanding how they were derived. It is the difference between an electrician and an electrical engineer. As a biology student you might not need much math, but as a scientist in general you do need physics and chemistry. Without algebra, how can you do even basic newtonian physics? I have an electrical engineering and a microbiology degree. The biological sciences require little to no abstract problem solving, they are essentially all memorization. It is easy to get by without having to do a certain kind of thinking that exists within algebra. That kind of thinking though exists in virtually every engineering class, physics, and even a little bit in chemistry. The author is essentially implying that animal sciences is stem and animal sciences dont need math, therefore STEM doesnt really need math.
DannyBee 4y ago
I somewhat agree with the thrust of the article (IE we are not letting people learn well), but unfortunately, the "different kinds of learning styles" thing that it relies heavily on has been debunked many times. There is simply no evidence for it, and study after study shows that trying to match method to perceived learning style does not improve performance. It is one of those things that seems like it should be true, and therefore people like it, but there is no evidence that it is in fact, true, and plenty against, for well over a decade at this point. See: https://www.frontiersin.org/articles/10.3389/fpsyg.2020.00164/full https://www.frontiersin.org/articles/10.3389/fpsyg.2020.0016... http://doi.org/10.1016/j.compedu.2016.12.006 http://doi.org/10.1016/j.compedu.2016.12.006 https://www.educationnext.org/stubborn-myth-learning-styles-state-teacher-license-prep-materials-debunked-theory/ https://www.educationnext.org/stubborn-myth-learning-styles-... https://www.psychologicalscience.org/news/releases/learning-styles-debunked-there-is-no-evidence-supporting-auditory-and-visual-learning-psychologists-say.html https://www.psychologicalscience.org/news/releases/learning-... etc
achenatx 4y ago
<<One of the most useless questions you can ask a kid is, What do you want to be when you grow up? The more useful question is: What are you good at?>> The author makes this ridiculous assertion. When people first do anything they are always bad. Over time, through an accumulation of small efforts they can become good at something. Asking what are you good at is the most useless question.
- Turing_Machine 4y ago
  Indeed. When I was a baby, what I was good at was drinking milk, crying, and making messes in my diapers.
- krferriter 4y ago
  > When people first do anything they are always bad Depending on what you mean by "bad", this is not necessarily true. Some people are better at certain things than others if you control for the amount of practice they've had. Take a group of children who have never played the piano. Give them a recording of a simple song, and tell them to listen to the song and play around with the piano for 1 hour and try to play something that sounds like that song at the end of that hour. Even with zero practice, some people will do better at this than others.
paulpauper 4y ago
Forget learning calculus, now you need to win math competitions, too. You need a GitHub repository and know Python well. It's like you got one half of society that cannot do arithmetic, and then the top 5% who are competitive and pulling way ahead. It shows how important possibly innate factors are. No matter how hard educators try to instill algebra, a certain, largely fixed percentage will never get it.
Nokinside 4y ago
Author is Temple Grandin. Everybody should read "Thinking the Way Animals Do: Unique insights from a person with a singular understanding." https://web.archive.org/web/20210417083222/https://www.grandin.com/references/thinking.animals.html https://web.archive.org/web/20210417083222/https://www.grand... I think she is right. Everybody should study as much math as possible in school, more than today. But nobody should study math abstractly just to pass exams. They should study more but only at the rate they understand, in a way that they understand. If everyone would study math 5h/week for 9 years with speed they understand and grok what they learn, some would learn to master only 50% of the math curriculum. Some would master 200%, some even more. But even those who would master only 50% would have better math skills than those who pass all exams but don't undestand.

Against Algebra

29 points by miobrien 4y ago

raydiatian 4y ago

The Atlantic: > Students need more exposure Also The Atlantic: > Paywall

deleted 4y ago
[deleted]
IshKebab 4y ago
Are you implying that those things are somehow in conflict? Because they very clearly aren't.

zozbot234 4y ago

> Students need more exposure to the way everyday things work and are made. Why does it have to be one or the other? Besides, algebra can also be taught in a more visual way and featuring more concrete reasoning, such as via complex word-problems that can be solved with a mix of arithmetic and algebraic approaches.

WillPostForFood 4y ago
Why does it have to be one or the other? The point of the article is that it should not be one or the other, different students need different things. It is the removal of tracking, the removal of vocational education, the denial of differences in students and the insistence in homogenized education that is wrecking schools. If only 37 percent of 12th graders can do the math needed to start college, maybe only 37 percent of 12 graders should be going into debt for a college education.
- readthenotes1 4y ago
  The push for equity says that no students should be able to do the math needed to start college
- zozbot234 4y ago
  Tracking is a terrible idea. To make it work effectively you need very efficient remedial teaching for the students who fall off of the "advanced/gifted" track, and that's antithetical to the whole "students should all be learning their math by themselves, not via rote instruction" schtick that's increasingly being pushed in elite "education" degree programs.
  - ndriscoll 4y ago
    What does effectively mean here? Do you mean to somehow catch the remedial kids up to the advanced kids, or just help everyone move at the pace they're capable of? Having everyone move at the pace of the most advanced is obviously not possible, but why do you need specifically efficient remedial teaching for them to move at an appropriate pace?
    - zozbot234 4y ago
      > but why do you need specifically efficient remedial teaching for them to move at an appropriate pace? Maybe you wouldn't if all teaching was appropriately structured. But remedial instruction is where the flaws of the nowadays-conventional approach of expecting students to "inquire" about math on their own and come up with their own ways of problem-solving are most evident.
      - ndriscoll 4y ago
        I'm not sure I understand still; when I was a student I found my classes to move at a tediously slow pace, often going into detail about and even repeating obvious things. Even in university engineering classes (e.g. walking through "Fourier's trick" multiple times when it's just a dot product/projection). You seem to be saying we need more of that (and maybe that's true for most people!). Wouldn't that mean tracking is a better solution? Let the advanced kids who can quickly understand/infer the ideas and techniques move on, and walk through the details/give lots of practice to the other kids?

Rallen89 4y ago

like most things on this site, this is a critique of the American education system

rawgabbit 4y ago
American public school system is broken. It is feast or famine. Many teachers are bad at teaching. Many schools are no more than daycare centers. Many students are not interested in school. I don’t know what the answer is. The fact of the matter is many American universities also have fundamental problems. The university seeks prestige via research and publishing as many articles as it can. Educating students seem to be an after thought.
cardamomo 4y ago
That has certainly been a recent trend here! I wonder why that is. As an educator, I can offer my own hunches: - The COVID pandemic forced students' and teachers' experiences into the open; schools still haven't returned to "normal" since 2020 - Folks here are trying to grapple with the roles technology can play in learning and in our education system - Software engineering and related fields require a decent education; perhaps folks are worried about who may be prepared or under-prepared for the field in the future
authpor 4y ago
algebra is taught comparably badly in many other places...

nobody0 4y ago

For people who think in pictures, actually you can do a lot of algebra by diagrams [0] [0] https://en.wikipedia.org/wiki/Commutative_diagram https://en.wikipedia.org/wiki/Commutative_diagram

mjhay 4y ago
It's really the "more advanced" way to do it. There are a lot of people, myself included, that are actually much better at thinking in abstractions - I suspect the author might be the same, despite her thinking of over-abstraction as a barrier.
contravariant 4y ago
If that qualifies then surely symbolic notation itself is also a visualisation. It's not as if it's just a syntax tree, quite a few properties (associativity, distributivity, symmetry) are suggested purely by the way we denote sums and multiplication. If you wants things to be even more visual you could use Penrose diagrams [0], though I don't find them particularly intuitive. [0]:https://en.m.wikipedia.org/wiki/Penrose_graphical_notation https://en.m.wikipedia.org/wiki/Penrose_graphical_notation
- Someone 4y ago
  > quite a few properties (associativity, distributivity, symmetry) are suggested purely by the way we denote sums and multiplication. I disagree. If “a + b + c” suggests “+” is associative, and “a × b × c” that “×” is associative, what about “a - b - c”, “a / b / c” and “a ^ b ^ c”? Or are you suggesting Σaᵢ and Πaᵢ suggest associativity? If so, how? (I also think you mean “commutativity”, not “symmetry” (https://en.wikipedia.org/wiki/Commutative_property https://en.wikipedia.org/wiki/Commutative_property) symmetry typically is about relations (https://en.wikipedia.org/wiki/Symmetric_relation https://en.wikipedia.org/wiki/Symmetric_relation)
carapace 4y ago
Also https://iconicmath.com https://iconicmath.com a collection of, uh, iconic math, math done with icons and diagrams and graphical patterns, etc.

melling 4y ago

“The fact that some people are visual thinkers while others are auditory” I thought the “visual learner” classification was a myth.

hprotagonist 4y ago
It is. https://www.theatlantic.com/science/archive/2018/04/the-myth-of-learning-styles/557687/ https://www.theatlantic.com/science/archive/2018/04/the-myth...
- ff317 4y ago
  For me personally, I classify myself (whether it's valid or not!) as an experiential learner. I have a very hard time learning abstract things in purely abstract ways. I can read a book about a branch of mathematics and try intently to learn from it and totally fail. But give me one practical, real-world problem which demands some knowledge of that type of mathematics, and I might pick up the bulk of the same subject matter quickly, to the degree necessitated by the project. Whatever my conscious intentions may be, my brain throws a toddler tantrum about it and is like "Prove to me that I can use this for real or I'm not investing in it".
  - vaidhy 4y ago
    I will go back to the top comment as of now.. you do not learn math by reading. You learn it by solving the problems. Some subjects (maybe some of the softer humanities) are more theory than practice.. Math and programming are not one of those.
caddemon 4y ago
"visual learner" as it is used in education theory does appear to be mostly bunk. For a variety of reasons, one of which is that most people have both auditory and visual thoughts. However I would caution not throwing the baby out with the bathwater. There is a growing body of evidence that some people are better or worse at visualizing, have a stronger or weaker internal monologue, etc. than others. There are reported neurophysiological differences as well as task behavior differences if you look at people with Aphantasia for example. As the other article sent to you mentions, someone who is not very visual could potentially benefit even more from visual examples, so these results are not really in conflict with the failures of education theory. It's also not clear how common large disparities in the modalities of thinking are, so perhaps it is not something worthwhile to consider for mass education policy regardless. But I think in a neuroscience context it remains an interesting topic for future research. I'll also note that the author of the original piece is autistic, and she has clearly demonstrated savant-level abilities on certain visualization tasks. It's not surprising that she would feel this way about "learning styles", because her entire life experience has likely been extremely lopsided towards visual thinking.

geebee 4y ago

For another point of view, I recommend this article from the New Yorker: https://www.newyorker.com/science/elements/california-students-are-struggling-in-math-will-reforms-make-the-problem-worse https://www.newyorker.com/science/elements/california-studen...

cs702 4y ago

As always, this is written by someone who admits to never having learned to reason abstractly about algebraic objects, because it is hard. Quoting from the OP: > The traditional arithmetic I learned in the early grades made sense to me because I could relate it back to real-world things. Later, when I was learning how to design, finding the area of a circle proved essential to practical tasks such as sizing hydraulic and pneumatic cylinders. I could do trigonometry by visualizing, for example, the cables on a suspension bridge. But algebra: no. For a different perspective, I recommend reading instead Susan Rigetti (nee Fowler)'s posts about overcoming challenges to learn Math and Physics. She says she had to solve what felt like "millions of exercises" to become familiar with many abstract concepts, until they finally clicked for her and she was able to reason about them. In her words: "Solving problems is the only way to understand mathematics. There's no way around it." https://www.susanrigetti.com/math https://www.susanrigetti.com/math https://www.susanrigetti.com/physics https://www.susanrigetti.com/physics https://www.susanjfowler.com/blog/2016/8/26/from-the-fledgling-physicist-archives-if-susan-can-learn-physics-so-can-you https://www.susanjfowler.com/blog/2016/8/26/from-the-fledgli...

PartiallyTyped 4y ago
I’d argue that people need to be taught basic group theory and abstract algebra first, preferably in the form of puzzles to get familiar with more abstract thinking, and to see things in terms of composition of objects instead a of mixing numeracy in the mix. I think that numbers create all sorts of problems because people focus on them as they are familiar and miss the bigger picture.
- qsort 4y ago
  I don't think it really works, at least not for most people. Abstract algebra (i.e. actual algebra, as opposed to doing useless stuff to poor polynomials) requires one to have developed the mathematical maturity to iron out informal thinking. Good luck explaining "prime" and "irreducible" are not the same. I think a path that would work better is through problem solving, like olympiad problems. But even that definitely isn't for everyone.
- 4y ago

jjslocum3 4y ago

> ...studied the disconnect between the excitement with which kindergartners and first graders greet learning and the boredom and disaffection that seems to overtake many by high school It seems myopic to search for the answer to this discrepancy purely within teaching styles. In high school, coincident with the onset of puberty, many students simply become more interested in achieving social goals than academic learning.

jeffreyrogers 4y ago

You need algebra to make things. Lots of machining involves algebra and geometry. Maybe it isn't taught that well, and maybe kids would learn it better if they were motivated by practical examples, but it's far from useless. Besides reading and addition, algebra is probably the most useful thing kids learn in school.

ok123456 4y ago

The "Learning Styles" dogma has been shown to be unfounded. Within the confines of general education, there's no such thing as a "visual" or "kinetic" learner. There are just students who are less practiced at learning through textural means.

math_dandy 4y ago

The more off ramps from challenging mathematics we build into the education system, the more students will be excluded from studying science and engineering in university. Avoid the tyranny of low expectations.

c7b 4y ago

> The fact that some people are visual thinkers while others are auditory- or language-oriented is better understood than it was when I was growing up. Isn't the opposite true? I thought the 'learning styles' theory had been debunked by science? https://www.psychologicalscience.org/news/releases/learning-styles-debunked-there-is-no-evidence-supporting-auditory-and-visual-learning-psychologists-say.html https://www.psychologicalscience.org/news/releases/learning-...

krastanov 4y ago
A popsci video on how that is indeed a debunked theory: https://www.veritasium.com/videos/2021/7/9/the-biggest-myth-in-education https://www.veritasium.com/videos/2021/7/9/the-biggest-myth-...
- LeifCarrotson 4y ago
  It's "better understood" to be completely false.
- mindcrime 4y ago
  Be careful with this line of thinking. What has been debunked, as I recall, is a very specific formulation of what is meant by "learning styles". It is not necessarily the case that every colloquial use of that term represents the thing that has been debunked. And as I recall, the possibility that some people simply have a preference for certain learning modalities has not been debunked, and that may be what people who use that term in routine conversation mean. The question then would be whether or not that preference matters at all.
ch4s3 4y ago
Yes, it has no basis in evidence but is sadly still commonly referenced in education and in popular discussion.

uptownfunk 4y ago

I heard the Russians have an excellent culture of problem Solving based mathematics, how do we bring a similar culture in our schools ?

walnutclosefarm 4y ago
One reflection of which is the cute little book, The Chicken from Minsk: https://www.amazon.com/Chicken-Minsk-Infuriating-Challenging-Teasers/dp/0465071279 https://www.amazon.com/Chicken-Minsk-Infuriating-Challenging.... Love that book.

powera 4y ago

Not a good article. Chesterton's Fence applies to many of the complaints; the OP doesn't understand math, but implies it's a bad thing they would have been prevented from becoming an engineer because of that. Which is just wrong.

davesque 4y ago

Meanwhile, the rest of the world will go on teaching it and their students' academic performance will continue to trounce the US's. I am 100% confident that I would not have gone into engineering if algebra had not been part of my compulsory education. And I'm very happy with the career I discovered for myself. Neither one of my parents were engineers. And I wasn't a particularly good student in middle or high school. Therefore, I doubt anyone in my family would have thought to enroll me in extra curricular math. I discovered that I was good at those things late in high school. So I see advice like this as worsening class divides and increasing the likelihood that you live the same life as your parents.

btilly 4y ago

Interesting note. The author is https://www.templegrandin.com/ https://www.templegrandin.com/, who is one of the best known cases of a successful high-functioning autistic person. If a particular subject doesn't "click" for her, it will be a lot more of a barrier than it is for most. But, conversely, how many more like her have been accidentally excluded by cognitive barriers that most of us can't even see?

newaccount2021 4y ago

jelkand 4y ago

There are a lot of difficulties in math education in the US, but ejecting algebra from the curriculum just strikes me as utterly bizarre. A few other, major issues: * Math has a severe stigma. How many people do you know would readily confess "I'm just not good at reading," almost as a badge of pride? This is common with math. * Most teachers don't have a strong math foundation. They are not acquainted with some of the foundational ideas that can really enhance teaching and learning math. In some cases, teachers who don't like math will perpetuate the above issue. * There is little incentive for those strong in math to become teachers. Why go teach introductory math when you can become a software developer and make 4x the salary, with less stress to boot? I'd look to remedies like paying teachers better, improving their workload, and even revising math curriculums to focus on concepts over testing before jettisoning a whole field like this article advocates.

unethical_ban 4y ago
>Math has a severe stigma. How many people do you know would readily confess "I'm just not good at reading," almost as a badge of pride? This is common with math. Perhaps because it is genuinely less important on the pyramid of human skills. Reading, language comprehension, and critical thinking are more universally needed than, say, matrix multiplication or integrals.
- 2devnull 4y ago
  “Reading, language comprehension, and critical thinking are more universally needed than, say, matrix multiplication or integrals.” Based on current wisdom. Current wisdom has a spotty track record though. It was once an obvious truth that reading was only for a select group. Universal literacy would have been as absurd back then as the notion of universal math literacy is now. Which is depressing, because one would hope that at least this historical analogy, and it’s implications, had occurred to more people.
- jelkand 4y ago
  1. Numeracy is just as valuable as literacy. Sure, matrix multiplication and integrals may not be useful day to day, but the article is talking about algebra. 2. I may be biased, but I believe math is distilled critical thinking. The difficulty is teaching math critical-thinking-first as opposed to test-first.

noobermin 4y ago

With the anti-calculus post from last time, I'd love to see less of these types articles. Imagine an article saying we need less English and less composition in college and high school, except you wouldn't see such an article because writers do not hate writing (at least not beyond some ironic sense). But sure, if you ask any teenage with a 10 page report due next week, they definitely would like less writing in their curriculum. I feel like we will however never seen op-eds critique writing and generally humanities in education because those who write op-eds value it. They however, do not value mathematics in their own lives (probably having others do the mathematics they would otherwise need to do for themselves), and thus they incessantly attack it. I hate to make a meta-psycho-point but I must: Some part of me wonders if stuff like this is some people in the humanities having a reaction to the status quo today in academia where they are undervalued--I do feel that in status and funding in education today, the humanities generally does not receive the respect they deserve. Too much emphasis is given to STEM (and lately, STEAM which still leaves the humanities out). That said, I don't think attacking STEM is the way to ameliorate the issue, and it really leaves me with the same feeling I had when my peers cracked jokes about "the English department," that they simply did not understand what they study and are painting other fields and experts with broad generalizations.

Turing_Machine 4y ago
> Imagine an article saying we need less English and less composition in college and high school, except you wouldn't see such an article because writers do not hate writing On the contrary, I've seen many such articles. Education in general has been under attack for quite some time now.

photochemsyn 4y ago

I think there's a logical contradiction in the conclusion: > "We don’t need Americans to be better at algebra, per se. We need future generations that can build and repair infrastructure, overhaul energy and agriculture, develop robotics and AI." If the issue is how algebra is taught (dissociated from physical objects), well, perhaps there's a curriculum problem. The fundamental concepts of algebra - such as commutation, association, and distribution, do indeed have nice visual and physical representations: https://www.mathsisfun.com/associative-commutative-distributive.html https://www.mathsisfun.com/associative-commutative-distribut... Everything else in algebra, trigonometry, even into calculus and more abstract math relies on understanding how those rules can be used to manipulate equations, and then you can put the equation on a computer and build models of bridges, robots, power grids, etc. You can also grasp compound interest and so not be screwed over by shady mortgage brokers pushing adjustable rate loans... (although one wonders if such widespread financial literacy is really something the oligarchs who control both political parties really want to encourage). Perhaps the real problem is the failure of the America system to place the appropriate value on education and hence invest resources in educational programs, and that's the real reason for the poor performance of American children on math relative to all other industrialized countries?

nerdjon 4y ago

> pointing out that the math taught there was nothing like the math people use in their jobs This ignores that much of the fundamentals (like Math) are less about teaching you the basics but teaching you the skills you need to learn as an adult. At least this is how I have come to view my time in school as an adult. Now obviously there are exceptions of this (I mean you did have to be taught to learn and to read) but with this basic fundamentals when you are presented with a problem later in life you have those skills to pull from. Even of the algebra is not exactly what you did, The idea of "solving for x" should be so ingrained in your head that when you need to solve a simple problem that is basically exactly that, you do it without even realizing that is actually what you are doing. Even as a software engineer, most of what I learned in school I am not actually truly using on a day to day basis. Except when I am working on learning something new. Maybe we could get rid of "algebra" but what exactly would it be replaced with? Something that is algebra in all but the name? Also my system had different levels of classes, I know some kids were taking pre-cal in high school while some only finished algebra 1 (2?, I don't remember)

nerdjon 4y ago
Also I have to wonder how much of this "math" hate is societal. It isn't uncommon for parents to say how much they hate math so of course their kids are going to start to think that. Or to talk about how much they hate school. Leaning should feel rewarding and yet, it feels like it isn't in this country.

achenatx 4y ago

my daughter is in advanced algebra II as a freshman. She is not naturally good at algebra. What this means is that she simply needs to work harder. The school estimates 3-4 hours/work a week for advanced algebra. My daughter does 10-15 hours a week and still only has around an 85. What she has learned is that things that can seem impossible can sometimes be broken apart into small pieces and conquered with hard work. The author probably had certain subjects come easy to her. When it got hard she probably didnt know how to do the repetitions required to become good. Instead of becoming good, she is trying to tell us in STEM disciplines that the subject simply isnt necessary. Algebra is fundamental to all other math I dont see how you can do statistics (as the author mentions) without algebra. In fact probability is much harder than algebra and probability problems often times require algebra. Further the work habits you learn to master algebra are used for other abstract subjects. As you get into the sciences and advanced statistics, you might need calculus. As you get into engineering you surely need calculus. There are often times versions of the subjects that allow you to memorize the equations and the author probably doesnt realize the difference between memorizing the statistical equations to be able to execute them and deeply understanding how they were derived. It is the difference between an electrician and an electrical engineer. As a biology student you might not need much math, but as a scientist in general you do need physics and chemistry. Without algebra, how can you do even basic newtonian physics? I have an electrical engineering and a microbiology degree. The biological sciences require little to no abstract problem solving, they are essentially all memorization. It is easy to get by without having to do a certain kind of thinking that exists within algebra. That kind of thinking though exists in virtually every engineering class, physics, and even a little bit in chemistry. The author is essentially implying that animal sciences is stem and animal sciences dont need math, therefore STEM doesnt really need math.

DannyBee 4y ago

I somewhat agree with the thrust of the article (IE we are not letting people learn well), but unfortunately, the "different kinds of learning styles" thing that it relies heavily on has been debunked many times. There is simply no evidence for it, and study after study shows that trying to match method to perceived learning style does not improve performance. It is one of those things that seems like it should be true, and therefore people like it, but there is no evidence that it is in fact, true, and plenty against, for well over a decade at this point. See: https://www.frontiersin.org/articles/10.3389/fpsyg.2020.00164/full https://www.frontiersin.org/articles/10.3389/fpsyg.2020.0016... http://doi.org/10.1016/j.compedu.2016.12.006 http://doi.org/10.1016/j.compedu.2016.12.006 https://www.educationnext.org/stubborn-myth-learning-styles-state-teacher-license-prep-materials-debunked-theory/ https://www.educationnext.org/stubborn-myth-learning-styles-... https://www.psychologicalscience.org/news/releases/learning-styles-debunked-there-is-no-evidence-supporting-auditory-and-visual-learning-psychologists-say.html https://www.psychologicalscience.org/news/releases/learning-... etc

achenatx 4y ago

<<One of the most useless questions you can ask a kid is, What do you want to be when you grow up? The more useful question is: What are you good at?>> The author makes this ridiculous assertion. When people first do anything they are always bad. Over time, through an accumulation of small efforts they can become good at something. Asking what are you good at is the most useless question.

Turing_Machine 4y ago
Indeed. When I was a baby, what I was good at was drinking milk, crying, and making messes in my diapers.
krferriter 4y ago
> When people first do anything they are always bad Depending on what you mean by "bad", this is not necessarily true. Some people are better at certain things than others if you control for the amount of practice they've had. Take a group of children who have never played the piano. Give them a recording of a simple song, and tell them to listen to the song and play around with the piano for 1 hour and try to play something that sounds like that song at the end of that hour. Even with zero practice, some people will do better at this than others.

paulpauper 4y ago

Forget learning calculus, now you need to win math competitions, too. You need a GitHub repository and know Python well. It's like you got one half of society that cannot do arithmetic, and then the top 5% who are competitive and pulling way ahead. It shows how important possibly innate factors are. No matter how hard educators try to instill algebra, a certain, largely fixed percentage will never get it.

Nokinside 4y ago

Author is Temple Grandin. Everybody should read "Thinking the Way Animals Do: Unique insights from a person with a singular understanding." https://web.archive.org/web/20210417083222/https://www.grandin.com/references/thinking.animals.html https://web.archive.org/web/20210417083222/https://www.grand... I think she is right. Everybody should study as much math as possible in school, more than today. But nobody should study math abstractly just to pass exams. They should study more but only at the rate they understand, in a way that they understand. If everyone would study math 5h/week for 9 years with speed they understand and grok what they learn, some would learn to master only 50% of the math curriculum. Some would master 200%, some even more. But even those who would master only 50% would have better math skills than those who pass all exams but don't undestand.