I have to disagree with this as a general rule, though given that all of your classes sound like they were in experimental design rather than in theory, I see why you think so.
Probability, you absolutely need calculus for, unless you just mean understanding the bare minimum basics of “marbles and decks of cards.” Start going into different distributions and their properties, and the calculus starts getting pretty intense very quickly.
Statistics, you can get by with maybe one to two classes of non-calculus, where you learn about the basics of normal distributions, sample testing, and t-distributions. You can have statistical software do a lot for you, which will abstract away a lot of the calculus. But if you want to have any understanding of the field, beyond arbitrary rules and checklists of properties, you’re going to have to start learning mathematical statistics, which is also very calculus-heavy. There comes a point where heuristics start becoming horribly insufficient and it’s best to just learn the math.
@neodymium, I think anything directly related to a person’s ability to perform at a level acceptable for the job is a reasonable requirement. If it falls under “anyone smart enough to be in this profession should be able to do x” doesn’t work for me. My failure to master the material in Algebra 2 had no affect on my ability to do well in any graduate or undergraduate class, and as far as I can tell hasn’t affected my career path. Obviously this is a microscopic sample size, but I also think it’s reasonable to assume my case isn’t unique. I tend to away from “anyone who wants to do x needs to know y” statements unless it can be shown that mastering y impacts one’s ability to do x. If you can demonstrate causation, you can convince me.
The problem is that an education isn’t just about the next job, or even about any specific job, but about a qualification for a wide range of work. So it makes a lot of sense for the education to “paint with a broad brush” and to teach things that may or may not come up on the next job or in any one person’s career, but that have macro-relevance and are notable enough to be worth knowing for enabling a broad swath of paths for the future. I also remember feeling that my education went further in general mathematical knowledge than I would have needed for a career, until a few years later I realized how said general requirements helped unlock further study (both academic and self-directed) that would not have been possible had I not learned those basics. I’m sure many others would have chosen a different path that would require less math, and yet I don’t think they would have been better off with relaxed requirements either. The degree is only the start of your education and it should at the very least teach you some ways to educate yourself further, even if you ultimately choose not to take any certain one of them. In any field that even remotely deals with experiments, data, or physics, math is definitely one important, if supporting, direction.
As for “anyone smart enough to be in this profession should be able to do x” : that statement is true for certain basic skills. Let’s choose biology, for example. Anyone smart enough to be in that profession should be able to run experiments, know how to perform research (in the most basic sense, of gathering new data from sources), know how to analyze results from experiments (which can be quantitative), know how to communicate ideas, etc. It may just logically follow that if a certain profession does require quantitative skills, then a basic competence in math at an Algebra II level is a perfectly reasonable requirement to be part of that profession. And it’s not a particularly daunting or unreasonable requirement - all it requires is an above-average general academic competence, a reasonable expectation of college-bound students.
Imagine you’re an admissions rep back in 1982. You get an application from a student with mostly good grades, but with a D in Algebra 1 and a D- in Algebra 2. The student has a high C or low B in geometry, and A’s or B’s in all other academic classes. The overall scores in both the SAT and ACT are in the top 10%, with math scores lower than the verbal scores but not by as large a margin as the grades would indicate. The college is a middle of the road liberal arts college with a fairly strong reputation locally. Is this student rejected as not college material?
If math in the high school curriculum is declared non-essential, what other subjects can also be declared non-essential?
Science -- only prospective science or engineering majors in college will need high school science to prepare for college science.
History -- generally not a prerequisite for anything, including college history courses.
Foreign language -- most do not get to a functional level of proficiency on high school foreign language courses (as opposed to heritage learning or beginning in elementary school).
English *literature/i -- most will not analyze works of fictional literature after high school.
Art and/or music -- most do not have the talent to do artistic things that others will like.
I’m not sure passing Algebra should be a requirement for graduation. That said, I think the vast majority should at least attempt it. I’m less comfortable making it a graduation requirement. It wasn’t in my high school when I graduated.
I teach mathematics at several colleges. This is REALLY happening. Colleges are being accused of discriminating against students who cannot perform any type of abstract or logic-based mathematics. Might start seeing huge swell in dyscalculia diagnoses, leading to protections by the Individuals with Disabilities Acts.
Where two college level math courses were previously required, the second may now be replaced with a “how to use a computer” course.
Learning algebra is the fastest route to learning how to think logically and work methodically. That's a more important benefit than the mathematical aspect for a majority of students.
This conversation occurs ten times each semester…
Older Student: I’ve been working 25 years and have never needed algebra.
Me: How do you know you did not need it? You did not even know it existed?
Alright, let me rewrite your question into something that I hope we could agree is equivalent:
That definitely looks like a student I’d worry about. While the SAT and ACT scores show that the student does not lack the mental ability to succeed in learning English, the grades show that the student failed to get grades that indicate that such knowledge was obtained. The student likely has some notable deficiencies in skills that are important to understanding English that are not well-demonstrated by the rather superficial evaluation that can be given within a timed test, which means that the student likely has some noticeable gaps in their ability to read and understand longer pieces of writing, conduct basic research, and communicate ideas. Further, given that the SAT/ACT suggest no lack of ability, there is either a mental block or a lack of work ethic leading to the poor grades in English. Although this student is headed for a more quantitative field, where these skills will only be of secondary importance, the issue of lopsided performance and likely gaps of knowledge in a critical skill of general widespread importance is a cause for concern. University-level study, even of quantitative topics, does require a strong enough work ethic to learn difficult subjects one may not like, and will still need to make use of the skills that should have been learned in English class. I would therefore recommend one of two courses of action (based on admissions space and general criteria):
The student should take a detour through community college to validate that they can keep up with a college-level curriculum. Admission will be reevaluated if the student can successfully complete English to the level of competency required of him or her.
The student can be admitted to the program, but will require deficiency coursework to be completed to ensure that he or she will be at the proper level of general education necessary for university-level study.
Substitute a few words, and the exact same argument works for the original. The student in the second story got bad grades in English because he/she did not find any point in doing long essays in MLA format, reading literature, and writing documents like precis that only come up in English academia anyways, and those are pointless because he/she cares more about math anyways and won’t need any of that English garbage after graduation. All those important things that will actually matter for his/her career, like writing persuasive essays and looking up information by sources, he/she already learned in Freshman English.
And in fact, it’s not just a hypothetical - I know many engineering majors I studied with who were incapable of writing a well-composed essay, likely due to poor high school education and a highly lax college-level English series.
Our oldest son is actually similar to your hypothetical student. He made D’s in English sophomore and junior years. Here’s where it changes: his M+CR was 1460. He was a NMSF, but obviously didn’t advance to finalist. He also got a 4 on the AP English exam. He got significant merit aid everywhere he applied.
Of course, the story only barely begins with admission to college. And while I have seen it go both ways for others, I would have to say that those that were just generally successful in high school with no glaring deficiencies, were most successful in college because their work ethic was where it needed to be. Those who were remarkably lopsided, or who took AP exams to turn their D grades into A grades because they chose exams over homework, tended to find trouble adapting to college.
This is analogous to saying medical doctors need to understand subatomic physics because ultimately, everybody is made up of subatomic particles.
The only people who need to know statistics to this extent are statistics professors. I love statistics and will conservatively guess that I know more about it than 99% of the people out there. I’ve never felt I needed calculus to make use of statistics.
You’re leaving out the possibility the student concerned received low grades in a subject he/she isn’t as strong in because he/she attends an academically rigorous HS where teachers would give D/D- level grades for work which would have received an A or B in most other high schools or sometimes even respectable colleges*. At my public magnet, it wasn’t unheard of for students who received high 90s/100s on the statewide regents exams, 5s on AP exams, and excelling on the SATs to be receiving C, D, or even F grades in the HS classes covering the subjects in question.
There were plenty of students including yours truly who received D or even F level grades in HS classes and yet, excelled in college courses in those very subjects/fields.
To be fair, such a student is a risk…but if he/she is evaluated in full context…including an allowance for HS academic environment…such risks can be mitigated.
With the Prof's ok to my TA friend, I anonymously turned in the very same English paper I did in 9th grade which received a -D because it didn't meet my HS English teacher's high academic standards to an undergrad lit class at a top 50 research U. Didn't alter a word of the paper from the original I turned in to my HS English teacher. Prof did make some remarks about requiring greater clarity, but felt I wrote a reasonably good paper and awarded a B+.
I think a lot of the time people want to “learn about” science subjects rather than actually learn the science. And, sorry to break it to everyone who doesn’t like math, real science NEEDS math. Even biology, a subject once regarded as being relatively math-light, is undergoing a transformation. We’re seeing differential equations being used a lot to quantify relationships in biology. Linear algebra is employed in tons of labs to analyze biological data. Computational biology/bioinformatics are making great use of calculus, linear algebra, statistics, and computer science/programming to solve problems involving absolutely huge amounts of biological data.
The next step in STEM is not to steer away from math education – it’s to revitalize our math education. A lot of people like pop-science such as Neil de Grasse Tyson and Bill Nye because they’re just talking about science, rather than actually explaining what’s going on in any sort of rigorous way. That’s great for television and podcasts and motivational speeches, but at the end of the day if you don’t know what a sine wave is or can’t understand exponents and logarithms, you don’t understand science.
Too many people want to be armchair scientists, even at the university level. I don’t understand how someone could get through four years of chemistry classes and not understand how to take the derivative of a function. It boggles my mind that it’s seen as okay for people to want to learn science without having any rigor behind it. How can you even verify anything besides the most basic results for scientific experiments without math? I also don’t see the motivation for cutting trigonometry as an essential class. Maybe the trigonometric functions in and of themselves aren’t particularly useful, but then why single out math when all of the humanities essentially are useless from a practical standpoint…
It’s more like saying that medical doctors need to understand genetics (and by extension the math behind it), because while it is perfectly feasible to be able to do quite a large number of procedures and operations without ever having learned it, but you will be a worse doctor for it (and for the disdain of academic knowledge that comes with it). And given that doctors are at least in principle supposed to be academics (the more adept of them contribute to medical research), disdain for theory isn’t really good.
Same with statistics. Sure, you can design and run an experiment and get some useful results without ever touching probability theory and the calculus that comes with it. But then, you’re pretty much only going to be doing variations on a normal distribution because without any theory, that is the catch-all that you will ultimately revert to. I’ve read some rather impressive treatises on statistics that go into remarkable depth on experimental analysis without ever even touching the subject of probability or even linear algebra. And guess what? They’re so much the worse for it, as they treat linear regression as “magical elves inside the computer using their wizardry to figure it out” (the book actually used this term). Or they could have just learned that it is a simple optimization problem on normalized errors, which would be a lot simpler and more explanatory.
There comes a point where “intuition” and “heuristics” stop being enough, and you start getting contradictory logic from them (for statistics, that comes in the form of tests that sometimes don’t work when all assumptions are met, or do work when some of them are not). The math fills in those gaps and gives a full explanation, if you are willing to actually look at it. And it also gives you more that you can use than just variations on the normal distribution, which is a good enough assumption for a wide range of problems but horribly insufficient for enough of them to make a difference. Plus we have some [unfortunate failures from people who think they know statistics](Study delivers bleak verdict on validity of psychology experiment results | Psychology | The Guardian) stemming from overreliance on unreliable assumptions. Besides, straight probability coupled with statistics is very commonly used in STEM, which certainly requires calculus.
Certainly a possibility, though personally I’ve found that high-quality students usually manage to survive even if the rigor is significantly increased. And that’s not really the story that “bad in English, good in everything else” tells. It suggests more of a failure to learn or care.
Indeed. Some risky prospects do blossom into talented individuals. Many do not, and they repeat their low performance. That’s why they are a risk.
Was this just one isolated paper, or a consistent string of low grades? I know some teachers give lower grades to “motivate” students to rise to the occasion and get better. I’m not a fan, but I know that if it was the former, with all future grades being improved, that is a pretty common learning curve for high-quality students.
Voting with Neo again. I cringe every time I read a “study” in a newspaper on a treatment or ailment or whatnot that was based on a skewed sample with errors that even I- a relative math moron- understand makes the entire “study” suspect. Doctors are making life and death decisions without understanding the underpinnings of how to actually measure a biological or medical phenomenon.
People who eat breakfast are thinner than the general population- that got skewered a week ago even though we’ve all heard it a thousand times. Guess what- people who are interested enough in diet and exercise to participate in voluntary and self-reported nutritional diary regimens are thinner than the general population. Duh. People who cook in aluminum pots get Alzheimer’s; people who drink diet soda get MS.
Should I get a mammogram? Do I need a colonoscopy?
Bad enough the general population can’t understand a simple table or bar graph. But even MD’s admit to not being able to interpret data. Cringe.
A few years back, they stopped teaching kids to write in cursive in our state as they felt it was unnecessary. Luckily my son’s teacher did it anyway. Without getting into the pros/cons of it, what I could not understand is it is not that the elementary kids are that busy. There is still plenty of time watching movies and doing things that do not seem to be useful that it seemed like there was no reason to stop teaching writing in cursive.
I get that it does not make sense to keep doing what you have always done but what is the goal? As others have mentioned, arguments could be made to drop many subjects. I was at a meeting once where one mom asked why do schools still teach fractions as her snowflake struggled with them and since everyone had a smartphone these days, fractions were not necessary to learn.
Perhaps it would be better to have a very good “household finance” course instead of Alg II for some kids where the teachers would delve into credit card debt, mortgages, etc? My problem has been that my son has not been challenged with the current curriculum so we have supplemented his learning which is what many families do when their kids are not being challenged. If Alg II is removed, it seems it will only continue to widen the gap in academic abilities of kids today given that many parents will just supplement more.
As many on CC know, Asians dominate many, if not most, US academic competitions and it seems China is advancing beyond the US in various scientific areas (eg., fastest supercomputer). If it is viewed from a US perspective, it does not seem advisable to get too far behind?