@boneh3ad we’re going around in circles - I pointed out that not knowing algebra as a music teacher would be a trivial inconvenience to your job. Being short would probably hurt you more. The part that I’m trying to emphasize is that yes, we should make all of these teachers try algebra, but some of them just can’t do it no matter how hard they try, and then they could still make great mentors that change students’ lives, and you’re denying the students and the teachers that because maybe the math teacher has to spend 20 seconds a day checking her arithmetic? What?
You are an engineer, yes? Do you speak Chinese? No? Because maybe someday your company will need to do business with a Chinese company, and so they should chuck you because you’ll need a translator. This is probably just as likely to happen as it is for a music teacher to need to do analytical algebra.
I used to be very elitist when it comes to STEM-master-race mentalities, but I’ve mellowed in that regards significantly. It doesn’t seem very logical anymore to place barriers like that for really trivial reasons like “what if the child is inspired to also suck at math”.
It’s algebra. Everyone without a learning disability should have the ability to do it. Some people don’t because they weren’t properly inspired as a student for one reason or another and gave up, and once people give up, they are difficult to get back on track.
You are missing my point. Algebra is not some fringe skill with no bearing on a music teacher’s life (in contrast to some of the other examples used here). It’s a relatively basic life skill.
Some people *do* have a learning disability though (see: discalculia). That's the point.
I keep making specific justifications as to why it isn't very crucial to a music teacher's life, and you keep responding by just restating your assertion that it is and ignoring what I'm saying - that this really isn't all that important for a music teacher.
Don’t get me wrong - everybody should have to try to learn algebra, but if they have a disability, it’s useless and pretty cruel to punish them for it if it serves no societal purpose.
Do you feel the same way about being illiterate? Because in 99% of cases where I’ve seen someone insist that they cannot do algebra, it wasn’t true. I’ve tried teaching a wide assortment of people to do it - just about everyone had the capability to learn, but many of the worst students simply insist otherwise and don’t put in the effort. It’s a mindset problem.
It’s a small percentage of the population that have such a disability. Referring to the original question here, said people probably just can’t be engineers. This is in line with what I said earlier about how I think certain learning disabilities are one reason why certain people maybe can’t really be engineers.
Further, I have provided at least one example of why I believe algebra is important even for a music teacher and, more importantly, life in general. I realize many teachers just plug random numbers into Excel, but I truly believe this is the wrong way to do things and is just kind of sad. Algebra really is not a difficult subject and it really saddens me when I come across people who just gave up for whatever reason. It’s kind of like when you have a waiter that just cannot correctly figure out how you are paying them or a clerk who can’t give you the correct change. It’s just sad when people are so poor at basic math skills. I fee like the system has failed them somehow.
anyone can learn elementary algebra outside of having a learning disability. It almost always the fault of the schooling system, at some point they fail the student miserably and at which point the student works themselves into the “my brain just cant do math” mindset and will forever forgo it.
I have a 28 year old sister who doesn’t know the difference between area or volume, and who if asked to solve some simple equation like 5x=20, couldn’t do it. BUT if you asked her in the form “What number when multiplied by 5 yields 20?” she’ll spit out 4.
The system failed her miserably, she sees something with symbols, her eyes go wide and exclaims her mind doesn’t work mathematically.
My sister has a BA in communications.
Algebra, like mathematics in general, is about more than just it use as a computational tool. Its about thinking in abstract mindsets with logic and order, something EVERYONE can benefit from.
Because my edit timer ran out before saving (15 minute timer is ridiculous)
A lot of people, at least in my experience, seem to be of the impression that mathematicians are some kind of weird type of people who get some sort of masturbatory effect out of discovering new mathematics or performing mathematics. When in reality a large part of mathematics is closely related to solving real life problems were a quantitative measure is needed. There are a few fields, like number theory, which was considered useless but then Alan Turing built the first modern day computer, and from this the modern field of cryptography was born and found a use for number theory.
Okay, I went off in a bit of tangent with the number theory, but my point is mathematics is essential in teaching good problem solving skills. Sure you probably wont use 95% of what you learn in everyday life but its not about that, its about the skills you gain while learning algebra that’s important. Much like the skills you gain from your college education, which like mathematics, you wont use the majority of except for a very tiny portion, but that’s okay, because you learn lots of other skills from the process of learning the materials like:time management, communication ability, problem solving, etc.
@NeoDymium That’s actually a good example to illustrate my point, because some people actually are dyslexic, and that has nothing to do with “laziness” or even intelligence. Sure it would be great if everybody could read fluently - that doesn’t mean everyone can, nor does it mean that you should arbitrarily bar people from pursuing careers that have nothing to do with reading, or in this case, mathematics. Make them try, but if they fail, there’s no point in trying to “punish” them for it.
@ImUrHuckleBerry Yeah, I’ve noticed that too when I was teaching my younger sister math - some people who can’t understand it suddenly do when you phrase it like a casual word problem. I think there’re even studies showing that you can dramatically increase kids’ performance on math tests by just replacing x’s with hearts.
I think everybody agrees that these skills can be trained to some extent, but the question is how much, and at what cost - it would be cool if there were some function quantifying the relationship between certain types of training and improvements in these fields.
My writing abilities, for example, have significantly improved since I started high school. When I was cleaning out my papers after graduation, I stumbled upon some of the essays I had written when I was younger and couldn’t finish them without cringing at their awfulness. But even in this case, I had access to plenty of evidence that I was naturally talented in the liberal arts (at least by general standards - I make no claims to be special in the CC community), from my performance on standardized tests, early cognitive development, etc. Likewise, when I first started doing olympiad-style math competitions in middle school, I was horrible at it and consistently embarrassed to be the only person on the math team who couldn’t get any of the problems right - by high school I was far more competitively successful. But again, I was always talented at math, with my early struggles largely stemming from anxiety and a lack of exposure, so my improvement was somewhat predictable. This doesn’t mean that someone who is bad at math can become an engineer, or that I could ever win an IMO medal.
We should absolutely encourage people to try their best to understand math and science, but they can’t give it any more than 100%. If someone is just bad at math, you may be able to help them improve, but it’s pointless to “shame” them for not being born with that cognitive ability by claiming that they are just lazy or unmotivated. So long as they don’t try to pass themselves off as experts in fields they don’t understand (a real pet peeve of mind), it’s fine to acknowledge that you’re going to be weak in some areas.
People, with the exception of those with a true learning disability, are not innately bad at math. Intelligence in a particular subject is not fixed and can improve with time and training in a properly motivated individual. I’m sure that takes additional effort in some people compared to others, of course, but most of those who are “bad at math” are people who were demotivated earlier in life and hold the view you espouse: that mathematical aptitude is innate, unchanging, and in changeable. On the contrary, modern psychology shows that to be false, and shows that teachers who believe that are less effective, and students who believe it are less successful at learning those skills.
Math skills are probably malleable to a certain degree, nobody is disagreeing with that. Someone who got a C in algebra can probably get an A with a better tutor and some motivation. But as engineer(-ing majors)s, we shouldn’t make vague qualitative judgments like this - this just begs the question of how much we can reasonably improve. I cannot win an IMO gold medal nor can I ace the Putnam, and an average student probably cannot get a P.hD in mathematics. This view is not mutually exclusive from believing that math skills can be improved to some extent and that we should encourage kids to try their best.
And with all due respect, I don’t know why you’re claiming that I think math aptitude is “innate” when I have explicitly stated that I do not think that this is the case, and gave an anecdote of my own abilities improving.
There is a large body of research that suggests that mathematical aptitude is not fixed and therefore, your position, as stated numerous times in this thread, that some people just can’t do math is just wrong. Basically, those without a learning disability who “just can’t do math” are generally just those who gave up early and just never learned how. They are mentally capable. They are also typically those who clearly believe that intelligence is fixed and cannot be improved.
I would isn’t want any teacher teaching any particular subject to pass that view onto my kids. I don’t care if it is math or English or music. I don’t know what kind of subject a given kid will grow up to enjoy, but if they are discouraged in it early, they may never get the chance. So like I’ve said, I don’t care if a music teacher can’t do calculus since it’s generally not a high school graduation requirement and isn’t all that useful for most people in their lives or jobs. On the other hand, algebra is something everyone ought to be able to do, is useful purely in a mathematical sense to most people (whether they realize it or not), and is useful just in terms of logical thinking. I do care if the people teaching children gave up on something that early.
Of course in reality, music teachers are not disqualified based on their mathematical abilities and there are definitely teachers out there who are ready to dismiss a kid as just being bad at math or any other subject. Luckily, a parent can probably teach their kids otherwise and keep them willing to work at things that are difficult but worthwhile.
Um, my position was that some people have a disability when it comes to math - which you agree with. My other position was that not everyone can do engineering math. This is not mutually exclusive from the idea that you can get better at math. None of your studies report turning people with significant math problems into CalTech engineering graduates.
I don’t think we really disagree on much here - we both agree that people should have to try to learn math if they can, and that math skills are malleable to some extent. I do not think that someone who tries to learn algebra and fails should be barred from being a music teacher due to very vague speculation about how this will inspire kids to suck at math, and I do think that there is some genetic component to math ability - I don’t think either of these propositions is very contestable.
The population of people with a genuine math disability is miniscule compared to the population of people who think it to be so.
Though I know motivated, intelligent students who simply could never properly learn calculus. Maybe they needed a better teacher, maybe it’s beyond them. Not that at that level, anyone really puts in the effort to find out which it is.
I’m in the “No” camp. When I was an undergrad at a not particularly selective state flagship University, I worked in the remedial math tutoring room. I doubt that many of the students who struggled to grasp pre-algebra would not have been able to graduate with an engineering degree from the same University.
I vote no.
Getting a degree is very different from being an engineer. I’ve known a couple solid but non-degreed engineers. I’ve also known some advanced degreed engineers who really, really needed to be in a different field and generally they get that opportunity fairly quickly. Unsurprisingly most engineers are somewhere in the middle.
On that last point, it sometimes comes down to common sense and sometimes it’s the ability to design a functional, practical thing at a manufacturable price within the allotted time. Not everyone can do this and it isn’t a question of training or intelligence, IMO. It’s something different. So is teaching it, and not many engineers ought to be anywhere near a lectern.
So maybe nearly everyone could get an engineering degree. But actually being an engineer? I’m gonna be quiet but slowly shake my head.
I think that being an engineer (lots of different job options) is easier than surviving rigorous/rigid engineering academics. I really enjoyed my first 20 years as an engineer. (After a re-org, I had to retrain in a different field… … more of an analyst).
One of my kids stuck with engineering. The other switched to econ, with much more course flexibility. Both would probably be decent engineers, but only one has the required degree. Both are happy at their jovs, so all is well.
If they’re only in for the money, then they’re going to get run over very quickly unless if they’re a very determined person that wants to go into management/business with an engineering degree.
If they have a strong interest in an area that relates to engineering, and they’re willing to take on the challenges and accept setbacks (many engineering student had that one test or project, or a course where they struggled), then they’ll do fine in engineering.
I had Bs and Cs in high school math courses, and AP Calc crushed me. Yet I went into engineering anyways, and I’m currently working at an internship that I enjoy.
I skipped a lot of parties and other sorts of distractions in order to focus on studying, engineering student organizations and career networking.
EDIT: There was also an Uni of Penn research that proved there was a direct correlation between mathematical skills and ability to concentrate.