As <i>always</i>, this is written by someone who admits to never having learned to reason abstractly about algebraic objects, because it is hard.<p>Quoting from the OP:<p><i>> 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.</i><p>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."<p><a href="https://www.susanrigetti.com/math" rel="nofollow">https://www.susanrigetti.com/math</a><p><a href="https://www.susanrigetti.com/physics" rel="nofollow">https://www.susanrigetti.com/physics</a><p><a href="https://www.susanjfowler.com/blog/2016/8/26/from-the-fledgling-physicist-archives-if-susan-can-learn-physics-so-can-you" rel="nofollow">https://www.susanjfowler.com/blog/2016/8/26/from-the-fledgli...</a>
> 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.<p>Isn't the opposite true? I thought the 'learning styles' theory had been debunked by science?<p><a href="https://www.psychologicalscience.org/news/releases/learning-styles-debunked-there-is-no-evidence-supporting-auditory-and-visual-learning-psychologists-say.html" rel="nofollow">https://www.psychologicalscience.org/news/releases/learning-...</a>
There are a lot of difficulties in math education in the US, but ejecting algebra from the curriculum just strikes me as utterly bizarre.<p>A few other, major issues:<p>* 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.<p>* 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.<p>* 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?<p>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.
I think there's a logical contradiction in the conclusion:<p>> "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."<p>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:<p><a href="https://www.mathsisfun.com/associative-commutative-distributive.html" rel="nofollow">https://www.mathsisfun.com/associative-commutative-distribut...</a><p>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).<p>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?
With the anti-calculus post from last time, I'd love to see less of these types articles.<p>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.<p>I hate to make a meta-psycho-point but I must:<p>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.
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.
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.
Interesting note. The author is <a href="https://www.templegrandin.com/" rel="nofollow">https://www.templegrandin.com/</a>, who is one of the best known cases of a successful high-functioning autistic person.<p>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?
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.<p>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.<p>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.<p>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.<p>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?<p>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.<p>The author is essentially implying that animal sciences is stem and animal sciences dont need math, therefore STEM doesnt really need math.
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.
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.<p>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.<p>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.<p>See:<p><a href="https://www.frontiersin.org/articles/10.3389/fpsyg.2020.00164/full" rel="nofollow">https://www.frontiersin.org/articles/10.3389/fpsyg.2020.0016...</a><p><a href="http://doi.org/10.1016/j.compedu.2016.12.006" rel="nofollow">http://doi.org/10.1016/j.compedu.2016.12.006</a><p><a href="https://www.educationnext.org/stubborn-myth-learning-styles-state-teacher-license-prep-materials-debunked-theory/" rel="nofollow">https://www.educationnext.org/stubborn-myth-learning-styles-...</a><p><a href="https://www.psychologicalscience.org/news/releases/learning-styles-debunked-there-is-no-evidence-supporting-auditory-and-visual-learning-psychologists-say.html" rel="nofollow">https://www.psychologicalscience.org/news/releases/learning-...</a><p>etc
Author is Temple Grandin.<p>Everybody should read <i>"Thinking the Way Animals Do: Unique insights from a person with a singular understanding."</i> <a href="https://web.archive.org/web/20210417083222/https://www.grandin.com/references/thinking.animals.html" rel="nofollow">https://web.archive.org/web/20210417083222/https://www.grand...</a><p>I think she is right.<p>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.<p>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.
> Students need more exposure to the way everyday things work and are made.<p>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.
Meanwhile, the rest of the world will go on teaching it and their students' academic performance will continue to trounce the US's.<p>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.<p>So I see advice like this as worsening class divides and increasing the likelihood that you live the same life as your parents.
> pointing out that the math taught there was nothing like the math people use in their jobs<p>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.<p>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.<p>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.<p>Maybe we could get rid of "algebra" but what exactly would it be replaced with? Something that is algebra in all but the name?<p>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)
> ...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<p>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.
<<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?>><p>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.<p>Asking what are you good at is the most useless question.
For people who think in pictures, actually you can do a lot of algebra by diagrams [0]<p>[0] <a href="https://en.wikipedia.org/wiki/Commutative_diagram" rel="nofollow">https://en.wikipedia.org/wiki/Commutative_diagram</a>
Not a good article.<p>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.
For another point of view, I recommend this article from the New Yorker:<p><a href="https://www.newyorker.com/science/elements/california-students-are-struggling-in-math-will-reforms-make-the-problem-worse" rel="nofollow">https://www.newyorker.com/science/elements/california-studen...</a>
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.