Technically yes. But as mentioned here, the label of “liberal arts” is often used in a context that means “non-technical subjects within liberal arts.” I’ve seen the label “liberal arts and sciences” be used often enough as well.
So to make it a bit more specific: it should go both ways. If math/science/engineering majors should take some significant coursework in the humanities and social sciences (which I believe they should) then humanities and social science majors should have to take some significant math/science/engineering coursework.
I agree @50N40W. However, my anger is at the imbalance that currently exists. Can you imagine the outrage if more institutions tried to institute a core curriculum like Caltech’s, that requires all students to take a year of math, a year of physics, 2/3 a year of chemistry, etc.? (They’re on the quarter system). Yet they too have humanities requirements, and if you look at the # of units required, then there’s still more humanities units in their core than there are STEM units. So an English major at Caltech would, contrary to perception of a tech school, still get more humanities. But there the balance b/w required STEM and humanities + social sciences subjects is about 50/50. That’s actually quite fair, but based on the way ppl feel the need to defend liberal arts institutions despite those being the majority, this 50/50 balance would never sit right w/ ppl.
Speaking as a social scientist, are y’all lumping social science gen-ed requirements in with the humanities requirements in your counts? Because that isn’t quite right, really. (Nor is it if you’re calling the fine arts humanities, either.)
And that’s part of the problem with a lot of these discussions—you start to get into issues of definition in ways that may get a bit slippery.
This completely anecdotal on my part and maybe biased as an English major (plus a lack of old age as I’m only 20)
BUT I feel as though there should be some happy medium.
My entire life I’ve struggled with math, and had it not been for the fact my middle school offered Algebra I for high school credit, I would not have graduated on time. I failed regular old pre cal (not honors or anything) and yes I do mean a straight up F even with studying, tutoring, and help from the teacher. All my other classes were honors or AP and I’d consistently get A’s in all my other classes (my AP scores in history and English were 3-4’s). I excelled in my extracurriculars, but math just ruined my GPA and any chance I had of getting into a good college straight out of high school.
Thankfully I’ve since transferred to my dream school and this past semester taken my very last math course ever (after withdrawing from pre cal fall semester to save my GPA- and yes I went to the tutoring center and office hours) some people just can’t do math, no matter how hard they try.
Of course, I’m lucky in that I’ve always loved/been good at English, and doing mock trial and debate (both at the high school and collegiate level) has just confirmed my desire to be a Lawyer. Not everyone is so fortunate to know for certain what they’d like to do in the future, especially at 14.
It’s interesting to see how people misinterpret what others write. (Apparently, including me.)
I never said that what gets taught needs to be immediately applicable to anything. I do think that what gets taught in early math classes like algebra, which everybody has to take and that serve as a gateway to advanced math, ought to be clearly relevant to students’ future personal and professional lives. Otherwise students think the purpose of math is to torture them, and they end up hating it. The way math is taught, where the focus is on difficult-to-understand abstract concepts with no practical application, doesn’t demonstrate relevance. The result is that the majority of students are motivated to avoid math rather than learn it, and we end up losing all kinds of potential engineers and scientists.
The idea that if you teach people abstract concepts, then they’ll intuitively be able to apply them to all kinds of real-world situations, doesn’t work for most people. Things just don’t stick unless they see concrete, relevant examples, and that’s what’s lacking. I would like to see the emphasis on proofs and derivations pushed off until later in peoples’ mathematical education. You can give students a taste of those in algebra, but don’t use them as a primary means of teaching at that point. And why spend so much time on things like factoring in algebra class? I don’t think I’ve ever had to factor something in my life outside of math class.
Anyone who defends the current way of teaching math because “it teaches you to think” need to be aware that humans are born with an innate ability to think. They don’t need to be taught to think any more than they need to be taught to walk or breathe.
(Some people may recognize the above as the “old math” vs. “new math” argument from back in the day.)
There’s also no need for the great majority of scientists and engineers to understand math at a deep conceptual level. They only need to understand it enough to be able to use it. If I want to use linear regression to model something, I don’t need to know gradient descent to be able to do that. I just need enough practical knowledge to know what kind of information to feed into a computer program, and how to interpret the numbers that come out.
And the College Board agrees. They have AP Statistics, which is so non-mathy our high school uses it for the kids who aren’t recommended for Precalculus. Most kids don’t take calculus anyway, but we can say plainly that it’s better to learn something about it than not to.
Engineering technology is a more supposedly practical version of engineering, where one is more hands-on and doesn’t do such rigorous science and math. So this base is already covered. If a company wants that type of training, they can hire an engineering technologist, but they often prefer to pay more for an engineer. The market is speaking.
The article is a bit scattered. First it says not everyone needs geometry and calculus. But those are not high school graduation requirements in my state anyway. Most colleges don’t require calculus either for graduation in non-technical majors; often “college algebra” is enough, which I think is somewhere between Algebra 1 and Algebra 2.
But I would be against removing Algebra 1 from the high school curriculum, or from pressuring university departments from reducing their math requirements. These are elements in the meaning of the degree, a part of the professional standards expected in that field.
Though I do disagree with your conclusions on how to deal with these issues and your general apparent distaste for academic knowledge, I will agree on this quoted point. Personally I don’t really like the tendency of early math to be structured around higher level concepts that are quickly forgotten and never taught in enough depth to be appreciated. For example, I definitely remember not caring very much about the Fundamental Theorem of Calculus the first time I learned calculus, and only saw any meaning in it after real analysis. It was very important but I just wasn’t in a position to see it back then.
If every person who took calculus were a math major, I’d recommend a 2-3 year integrated discrete math / calculus/ real analysis sequence. Wouldn’t be good for engineers and scientists though. And that sort of alludes to the problem: we either have a curriculum that is a giant slop of compromise that neither the most or least academic students particularly like, or we start tracking students very early. The US education model does the former (and I don’t think I need to describe the results of that system), and the latter is done by many European countries, which have the issue of pigeonholing people based on early results. Would suck to be put on the wrong track and have to retake a lot of coursework to go into a different field, wouldn’t it?
I will also add that personally, I don’t like the fact that the mathematical academia has effectively shunned a lot of its most applied fields that spawned directly out of the results of mathematics, such as computability, probability and statistics, and the like. Sure, those fields have been picked up by other parties, such as computer science, engineering, and business. But they don’t influence mathematical pedagogy as much as mathematicians themselves. The result is that math self-selects to the fields that tend to be downright nasty for most people, such as graph theory, analysis, PDEs, and abstract algebra. Anyone except those “beauty of mathematics” people find those topics to be generally distasteful (one of my degrees is in math, even I have a sour taste in my mouth from abstract math).
So yes, you are not without a point that there are issues with math education and with math academia that need addressing. But your general response is de facto anti-education, anti-academic, and sounds a lot like trade school. That, I would say, is the major point of contention here.
In theory, a college could offer such a math sequence to math majors and others highly interested in math. But few do; most which do have a separate honors math sequence follow the standard courses with more theory and difficult problems.
But many colleges do have lower level math sequences, like calculus for business majors.
Yes, the conflict between optimizing the curriculum for a given type of student versus avoiding too-early specialization is one where the choices made in different countries and different schools differ.
(I don’t know how to quote but this is a reply to NeoDymium just above.) Stats is a separate department in a lot of universities. The attempt to integrate probability theory (where one has to use a number to measure probability) with mathematics, as you know, ran into the measurability problem, a fundamental issue with real numbers, hence the awful Kolmogorov stuff. (There’s a cute alternative by John Nelson that would probably be better than real numbers and it avoids all those problems. Did it bother you that all thru calculus you were told to use Real Numbers and they never told you what they are?) This is not a probability specific problem. You can’t really apply calculus to physical problems either, or anything else with real numbers.
These are issues in analysis. Analysis is fundamental to continuous math, and algebra is relevant in many ways. Discrete and especially finite groups are things you can see and touch, which makes them a good first course in proofs. (High school geometry sort of gives this flavor, but it isn’t rigorous because it doesn’t have nearly all the axioms it needs.) Discrete math is a bit of a backwater, usually better approximated continuously. PDE’s are intellectually demanding and easier learned in context e.g. Maxwell’s equations or fluid flow equations. Much of math is developed from questions asked in physics, but discrete math and statistics are not so important there.
I really don’t think math departments are elitist. Maybe they are elite. They emphasize a skill of rigorous mathematical thought. Engineers don’t need so much of it, but they do need enough to do their physics courses, and that’s significantly greater than zero.
It occurs to me: A good chunk (not all, probably not most) of the arguments being raised in this thread, but something that is certainly core for Hacker’s ideas, is based around the idea that pushing as many students as possible toward degree or diploma completion is an inherently good thing. I question that underlying assumption. A degree or diploma shows that expert gatekeepers have determined that the recipient has demonstrated competency across a delimited set of fields; changing the requirements for those fields and competencies so that it’s easier to achieve them may be useful in selected cases, but if we do that with everything people have trouble with we then water down the value of our degrees and diplomas (as many would argue has already happened with high school diplomas) to the point that they’re effectively meaningless achievements that signify nothing.
I like proofs! In my private school (in a galaxy far away), I learned proofs from 4th to 8th grade For 4 years. Proofs were one of the most beloved classes we had. It was a lot of fun to play with the concepts and to prove/disprove something.
Proofs are useful! Extremely useful! I am working with a number of legal documents. I don’t have any legal background, but I am considered very sharp by my colleges and very good in interpretation of contracts and legal agreements. My English is terrible. But I use math, the proofs, to analyze legal documents. And it works.
Again, some people know math and use it every day, and are very happy about it. Some people never “got” it, live happily, and believe that math is useless.
And regarding tracking done in many European and I’d add Asian and countries on other continents, once one was placed on a given track…especially below the academic track for college aspirants, it was practically impossible to change one’s track back to the academic track until recent decades. Also, one could be placed on a lower-track/be prevented from continuing one’s education for disciplinary reasons for infractions which would be considered minor or at most, some detention.
This was a reason why many European and Asian international students I knew through the late '90s had to come to the US to attend college. If that had not, they’d be stuck in the lower vocational tracks or even be expected to start working in the unskilled farming/labor force from the end of middle school onwards.
One example from my undergrad years was an older Japanese undergrad at a friend’s Boston area college who because he got into one schoolyard fistfight in 7th grade which wouldn’t have been considered noteworthy in most American schoolyards was effectively banned from continuing his education at most academic and even vocational track schools despite having been an academically topflight student up until that point. The level of disgrace in that period in his own immediate family was such they disowned him and as a result, he ended up spending several years cobbling together odd/unskilled labor jobs in factories to make ends meet.
It was only a chance meeting with a wealthy Japanese benefactor who felt he deserved a second chance that he was sent on the benefactor’s dime to the US to finish his middle/HS education and attend college here in the US. When I met the older Japanese undergrad, he was 26 years old and about to graduate from college with flying colors.
Or worse, that having them signifies very little, but not having them is a significant negative point. The high school diploma may be most of the way there. For a bachelor’s degree, there seem to be a significant number of jobs where it is listed as a qualification, even though the jobs do not require either the specific skills taught nor the higher level of general thinking skills practiced in earning a bachelor’s degree, so one can argue that some view a bachelor’s degree that way also.
